optics design for nica collider · 2010. 10. 1. · x, ε y & σ p (σ s -fixed) until collider...
TRANSCRIPT
0
Optics design for NICA collider
SKostromin OKozlov IMeshkov VMikhailov ASidorin JINR Dubna VLebedev SNagaitsev
FNAL Batavia Illinois USA YuSenichev IKP Juelich Germany
RuPAC 2010 2709-0110 г Протвино
Россия
1
Main requirements
from physics experiment
RuPAC 2010 2709-0110 г Протвино
Россия
2
bull changeable experiment energy
for heavy ions collisions
Au + Au (45 35 15) GeVu
γ = 58 47 26
with luminosity ~1027 (at 45
GeVu)
bull operation with proton beams
(125 GeV - γ =143)
Possibility of variation of
gamma-tr ~3 divide 15
Main requirements
from physics experiment
Objectives for optics design
RuPAC 2010 2709-0110 г Протвино
Россия
3
Luminosity
232
2
1
22pyxyxyxyx
syy
xx
yxs
ip
YSC
SCD
C
A
NZrX
s
ip
SC
C
A
NZr
24 32
2
2
0
4
s
yx
ib HNnf
L
0
221
22
yx
dyexH
y
SCss
b
i
p
HnC
Nf
Zr
AL
0
2
32
2
For bunched beam with Gaussian distribution in all planes
For round beam smooth focusing and sufficiently small dispersion
For x = y
and head-on collisions the luminosity is
assuming x = y one obtains a luminosity limitation
limitation due to Beam Space Charge
- limits beam longitudinal density Ni s
RuPAC 2010 2709-0110 г Протвино
Россия
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
4
For the case of fixed ring acceptance and circumference one should also exclude Ni That
results in
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
Small circumference C
Luminosity limitation due to Beam Space Charge
Short separation length Cnb Large value of σsβ
Large emittance =gt large acceptance
Large luminosity requires
Objectives for optics design
Possibility of variation of
gamma-tr ~3 divide 15
Large acceptance
Small perimeter
Small beta-function at IP
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
5
Racetrack with 2 IPs
Optics optimized for Au+Au collisions at 45 GeVn
γtr asymp76
bull plusmn 45 m for particle detector
bull Phase advance 90deg per FODO-cell
bull Dispersion zeroing in straight sections
bull Vertical beam separation
bullTunes ~x44 (same as in FNAL Recycler)
(γ asymp58)
Slip factor
η=1γtr2-1γ2
asymp0013
Cross-section view of the NICA Collider dipole magnet
RuPAC 2010 2709-0110 г Протвино
Россия
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
1
Main requirements
from physics experiment
RuPAC 2010 2709-0110 г Протвино
Россия
2
bull changeable experiment energy
for heavy ions collisions
Au + Au (45 35 15) GeVu
γ = 58 47 26
with luminosity ~1027 (at 45
GeVu)
bull operation with proton beams
(125 GeV - γ =143)
Possibility of variation of
gamma-tr ~3 divide 15
Main requirements
from physics experiment
Objectives for optics design
RuPAC 2010 2709-0110 г Протвино
Россия
3
Luminosity
232
2
1
22pyxyxyxyx
syy
xx
yxs
ip
YSC
SCD
C
A
NZrX
s
ip
SC
C
A
NZr
24 32
2
2
0
4
s
yx
ib HNnf
L
0
221
22
yx
dyexH
y
SCss
b
i
p
HnC
Nf
Zr
AL
0
2
32
2
For bunched beam with Gaussian distribution in all planes
For round beam smooth focusing and sufficiently small dispersion
For x = y
and head-on collisions the luminosity is
assuming x = y one obtains a luminosity limitation
limitation due to Beam Space Charge
- limits beam longitudinal density Ni s
RuPAC 2010 2709-0110 г Протвино
Россия
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
4
For the case of fixed ring acceptance and circumference one should also exclude Ni That
results in
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
Small circumference C
Luminosity limitation due to Beam Space Charge
Short separation length Cnb Large value of σsβ
Large emittance =gt large acceptance
Large luminosity requires
Objectives for optics design
Possibility of variation of
gamma-tr ~3 divide 15
Large acceptance
Small perimeter
Small beta-function at IP
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
5
Racetrack with 2 IPs
Optics optimized for Au+Au collisions at 45 GeVn
γtr asymp76
bull plusmn 45 m for particle detector
bull Phase advance 90deg per FODO-cell
bull Dispersion zeroing in straight sections
bull Vertical beam separation
bullTunes ~x44 (same as in FNAL Recycler)
(γ asymp58)
Slip factor
η=1γtr2-1γ2
asymp0013
Cross-section view of the NICA Collider dipole magnet
RuPAC 2010 2709-0110 г Протвино
Россия
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
2
bull changeable experiment energy
for heavy ions collisions
Au + Au (45 35 15) GeVu
γ = 58 47 26
with luminosity ~1027 (at 45
GeVu)
bull operation with proton beams
(125 GeV - γ =143)
Possibility of variation of
gamma-tr ~3 divide 15
Main requirements
from physics experiment
Objectives for optics design
RuPAC 2010 2709-0110 г Протвино
Россия
3
Luminosity
232
2
1
22pyxyxyxyx
syy
xx
yxs
ip
YSC
SCD
C
A
NZrX
s
ip
SC
C
A
NZr
24 32
2
2
0
4
s
yx
ib HNnf
L
0
221
22
yx
dyexH
y
SCss
b
i
p
HnC
Nf
Zr
AL
0
2
32
2
For bunched beam with Gaussian distribution in all planes
For round beam smooth focusing and sufficiently small dispersion
For x = y
and head-on collisions the luminosity is
assuming x = y one obtains a luminosity limitation
limitation due to Beam Space Charge
- limits beam longitudinal density Ni s
RuPAC 2010 2709-0110 г Протвино
Россия
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
4
For the case of fixed ring acceptance and circumference one should also exclude Ni That
results in
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
Small circumference C
Luminosity limitation due to Beam Space Charge
Short separation length Cnb Large value of σsβ
Large emittance =gt large acceptance
Large luminosity requires
Objectives for optics design
Possibility of variation of
gamma-tr ~3 divide 15
Large acceptance
Small perimeter
Small beta-function at IP
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
5
Racetrack with 2 IPs
Optics optimized for Au+Au collisions at 45 GeVn
γtr asymp76
bull plusmn 45 m for particle detector
bull Phase advance 90deg per FODO-cell
bull Dispersion zeroing in straight sections
bull Vertical beam separation
bullTunes ~x44 (same as in FNAL Recycler)
(γ asymp58)
Slip factor
η=1γtr2-1γ2
asymp0013
Cross-section view of the NICA Collider dipole magnet
RuPAC 2010 2709-0110 г Протвино
Россия
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
3
Luminosity
232
2
1
22pyxyxyxyx
syy
xx
yxs
ip
YSC
SCD
C
A
NZrX
s
ip
SC
C
A
NZr
24 32
2
2
0
4
s
yx
ib HNnf
L
0
221
22
yx
dyexH
y
SCss
b
i
p
HnC
Nf
Zr
AL
0
2
32
2
For bunched beam with Gaussian distribution in all planes
For round beam smooth focusing and sufficiently small dispersion
For x = y
and head-on collisions the luminosity is
assuming x = y one obtains a luminosity limitation
limitation due to Beam Space Charge
- limits beam longitudinal density Ni s
RuPAC 2010 2709-0110 г Протвино
Россия
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
4
For the case of fixed ring acceptance and circumference one should also exclude Ni That
results in
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
Small circumference C
Luminosity limitation due to Beam Space Charge
Short separation length Cnb Large value of σsβ
Large emittance =gt large acceptance
Large luminosity requires
Objectives for optics design
Possibility of variation of
gamma-tr ~3 divide 15
Large acceptance
Small perimeter
Small beta-function at IP
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
5
Racetrack with 2 IPs
Optics optimized for Au+Au collisions at 45 GeVn
γtr asymp76
bull plusmn 45 m for particle detector
bull Phase advance 90deg per FODO-cell
bull Dispersion zeroing in straight sections
bull Vertical beam separation
bullTunes ~x44 (same as in FNAL Recycler)
(γ asymp58)
Slip factor
η=1γtr2-1γ2
asymp0013
Cross-section view of the NICA Collider dipole magnet
RuPAC 2010 2709-0110 г Протвино
Россия
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
4
For the case of fixed ring acceptance and circumference one should also exclude Ni That
results in
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
Small circumference C
Luminosity limitation due to Beam Space Charge
Short separation length Cnb Large value of σsβ
Large emittance =gt large acceptance
Large luminosity requires
Objectives for optics design
Possibility of variation of
gamma-tr ~3 divide 15
Large acceptance
Small perimeter
Small beta-function at IP
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
5
Racetrack with 2 IPs
Optics optimized for Au+Au collisions at 45 GeVn
γtr asymp76
bull plusmn 45 m for particle detector
bull Phase advance 90deg per FODO-cell
bull Dispersion zeroing in straight sections
bull Vertical beam separation
bullTunes ~x44 (same as in FNAL Recycler)
(γ asymp58)
Slip factor
η=1γtr2-1γ2
asymp0013
Cross-section view of the NICA Collider dipole magnet
RuPAC 2010 2709-0110 г Протвино
Россия
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
5
Racetrack with 2 IPs
Optics optimized for Au+Au collisions at 45 GeVn
γtr asymp76
bull plusmn 45 m for particle detector
bull Phase advance 90deg per FODO-cell
bull Dispersion zeroing in straight sections
bull Vertical beam separation
bullTunes ~x44 (same as in FNAL Recycler)
(γ asymp58)
Slip factor
η=1γtr2-1γ2
asymp0013
Cross-section view of the NICA Collider dipole magnet
RuPAC 2010 2709-0110 г Протвино
Россия
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
6
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
1
cos11
)(
1
n
n nrR
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
7
bull The solution of equation
bull with modulation of gradient and curvature
bull gives the expression for OCF
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
1
cos11
)(
1
n
n nrR
0
cos)(k
k kgk ε
])1(1[)1(4
11
12
2
2
2
k
ks r
kS
gR
kS
variation of gamma-tr
RuPAC 2010 2709-0110 г Протвино
Россия
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
8
Regular structure
Modulated dispersion Modulated radius of curvature
RuPAC 2010 2709-0110 г Протвино
Россия
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
9
Regular structure
Modulated dispersion
12 Cell 90deg =gt Qxarc=3
4 Superperiods 3 Cell
Dy=0
RuPAC 2010 2709-0110 г Протвино
Россия
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
10
Cell dimensions
90deg phase advance for Au 45 GeVn
RuPAC 2010 2709-0110 г Протвино
Россия
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
11
Arc
12 cell x 90deg phase advance
RuPAC 2010 2709-0110 г Протвино
Россия
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
12
Dispersion suppression
-using special quads
gradients in edges cells
(possible to adjust for the
different γtr ie different
phase advance in arc)
bullD=0 due to 2πn ndash phase advance
per Arc
RuPAC 2010 2709-0110 г Протвино
Россия
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
13
Straight sections
bullβ at IP ~35 cm
bullvertical beam separation
bull enough space for non
structural equipment RF-
resonators PU for SC injection
spin rotatorshellip
bull keep total tune of the ring x44
RuPAC 2010 2709-0110 г Протвино
Россия
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
14
Straight sections
RuPAC 2010 2709-0110 г Протвино
Россия
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
15
Straight insertions in arcs
2π phase advance
bull additional space for non
structural equipment e-cooler
injection spin rotatorshellip
RuPAC 2010 2709-0110 г Протвино
Россия
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
16
Full optics
5342m
perimeter
ξx= -38
ξy= -37
ξx= -29
ξy= -32
RuPAC 2010 2709-0110 г Протвино
Россия
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
17
ξx= -29
ξy= -28
ξx= -37
ξy= -34
Full optics
5342m
perimeter
RuPAC 2010 2709-0110 г Протвино
Россия
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
18
Ring tune
x44
Tune diagram (fractional part) with sum resonances up to 12th order
bbsc 2 lt005
RuPAC 2010 2709-0110 г Протвино
Россия
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
19
Chromaticity correction
1 Au 45 Gevn
Two families of
sextupoles
(16 total)
Sf1=0154 kGcm2
Sd1=-0264 kGcm2
2 3 Au 35 Gevn Au 15 Gevn
All sextupoles in the arc (near each quad) are used for chromaticity
correction (24 total)
Sf1=0054 kGcm2
Sd1=-0085 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
20
Chromaticity correction
4 Protons 1245 GeV
Only sextupoles near central lenses (four families) in each superperiod
(where dispersion function are positive) are used
(16 total)
Sf1=0072 kGcm2 Sf2=0110 kGcm2
Sd1=-0207 kGcm2 Sd2=-0284 kGcm2
RuPAC 2010 2709-0110 г Протвино
Россия
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
21
Dependence of the ring tune on dpp
RuPAC 2010 2709-0110 г Протвино
Россия
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
22
Dynamic aperture
helliptracking in MAD OptiM
Au 45 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
23
Dynamic aperture
Au 35 GevnPhase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
24
Dynamic aperture
Protons 1245 Gevn
Phase space at IP
RuPAC 2010 2709-0110 г Протвино
Россия
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
25
IBS
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
hellipTriplet focusing
looks preferable It
results in
essential increasing
IBS growth timehellip
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
26
IBS rates were tested for full ring FODO- amp ODFDO- structures
VAL4 optics
V Lebedev
Lring=4542м
45 53
nb=20
60 112
060
179 75
551120 580
622
-0026
-0039
-0007
-0010
6046
ODFDO Au
full optics
Lring=39246м
Fit to VAL4
45 53
nb=20
60 086
086
189 38
761320 580
864
-0026
-0031
-0008
-0008
6628
ODFDO Au
full optics
Lring=4022м
45 53
nb=20
60 090
079
158 45
80770 580
835
-0028
-0034
-0008
-0009
6624
FODO Au full
optics
Lring=36326м
Fit to VAL4
45 53
nb=20
60 114
076
162 45
54890 580
695
-0021
-0029
-0007
-0008
6629
FODO Au full
optics
Lring=37430м
45 53
nb=20
60 093
089
146 45
90560 580
713
-0024
-0030
-0008
-0008
6628
FODO Au full
optics
Lring=34350м
45 53
nb=20
60 126
077
169 101
63760 580
683
-0019
-0026
-0006
-0008
6610
IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics
Difference is due to
different straight
section structure
Acceptable IBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
27
bbsc 2 lt005
Adjust εx εy amp σp (σs -fixed) until
Collider Luminosity
Increase εx εy amp σp proportionally staying in the ring acceptance
Increase Ni ions in the bunch keeping bbsc 2 lt005
LuminosityIBS rates
RuPAC 2010 2709-0110 г Протвино
Россия
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
28
RuPAC 2010 2709-0110 г Протвино
Россия
Collider Luminosity
Energy of the
experiment
Ion-ion and collisions Polarize
d
protons
512
GeV
15
GeVn
35
GeV
u
45
GeVu
Ring acceptance
mmmrad300300 200200 4040 4070
Ring long
acceptance ppplusmn0005 plusmn0005
Maximum
acceptable RMS
emittance εxεy
mmmrad
1105 1106 1206 1106
RMS momentum
spread06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch
corresponding to
tune shift
Q = 005
04middot109 25middot109 49middot109 25middot1011
IBS growth time s 110 600 710 8700
Maximum
achievable
luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
scaling
2
324
65228 SC
sssb
p
HC
n
rZ
cAL
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
29
Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized
protons512 GeV
15 GeVn 35 GeVu 45 GeVu
Ring circumference m 5342
Transition energy γtr 32 58 76 68
Phase advance per cell deg 30 60 90 varied
Slippage factor 0051 0015 0013 0004
Betatron tune QxQy 844744 10441044 12441244 12441244
Number of bunches nbunch 26
bullTotal chromaticity of the ring(before correction) ξxξy
-288-275
-296-324
-383-366
-372-335
Ring acceptance mmmrad 200300 200200 4040 4070
Ring long acceptance pp plusmn0005 plusmn0005
Maximum acceptable RMS emittance xy mmmrad
1105 1106 1206 1106
RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3
Particle per bunch corresponding to tune shift Q = 005
04middot109 25middot109 49middot109 25middot1011
cm 35 35
Bunch length cm 60 60 60 60
IBS growth time s 110 600 710 8700
Maximum achievable luminosity cm-2 s-1
18middot1025 20middot1027 42middot1027 42middot1031
RuPAC 2010 2709-0110 г Протвино
Россия
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
30
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
31
Thank you
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
32
RD 2
RD
2
1
)3(
])1(1[2
1
])1(1)[1(2
1
14
1
])1(1)[1(4
11
1
2
2
2
2
2
22
24
2
jirgO
kS
grR
kSkS
grR
kS
r
kSkS
gR
j
k
i
k
k
kk
k
kk
k
k
k
ks
Classic optic structure
ldquoResonancerdquo optic structure for super-period
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
minkS-ν =gt maximum influence to orbit compaction factor
kS
10060
2
cellNS
3divide5 Cells per super-period
strs
ss
LLS
LS
Orbit compaction factorfor structure with str sec
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
33
bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc
Qxarc - integer
Sarc a- number of super-periods in Arc 1min arcarc kS
Sextupoles compensationSarc ndash even
Qxarc - odd arcarc
arc
arc S
S
2
2
Phase advance between Cells through Sarc2 super-periods
45 GeVn γ=58 =gt Qxarc γtr gt 6
Narc=2 =gt Qxarc=3 (γtr asympQx)
Min[Qxarc-1Sarc]=-1 =gt Sarc=4
32π ndash ph ad per super-per
3Cell 90deg - superperiod
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
34
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
35
Calc of Dynamic Aperture amp compensation of nonlinearities
NICA Conceptual Proposal for Collider Valeri
Lebedev Fermilab January 11 2010
NicaVAL4- ref point
Tracking in MAD
(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP
Agreement between tracking in MAD and OptiM
(MAD used for further investigationshellip)
bull Large acceptance
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
36
y
x
yx
ip
YBB
BB
A
NZrX
1
11
4
2
2
2
2
1
4
2
2
2
A
NZr ip
BB
22 12
C
sSCBB
Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution
For round beam =gt
Combining the above equation with the equation for space charge tune shift one obtains
For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s
results in phase averaging for high order resonances and significantly mitigates the beam-beam effects
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
37
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
38
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
39
NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection
2
210
p
p
p
pbbsc
lt005 (depends on working
point location)
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
40
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
41
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring
42
ρ(s)
D=k(s)K(s)+ds
Dd
1
2
2
p
eG(s)K(s)
p
G(s)ek(s)
C
dss
sD
C )(
)(1
0
cos)(k
k kgk ε
dkGp
egk cos
1 sLs 2
1
cos11
)(
1
n
n nrR
dnR
rn
)(
cos
)(~
)( DDD
))(~1(1
)(
1
r
R R
rD
R
D )(~)(~
- orbit compaction factor
(OCF)
where
Correlated change of
dispersion through the orbit
moves alfha close to zero
or to negative values
with
where
Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией
ЮВ Сеничевa и АН Чеченинb
variation of gamma-trdecrease phase advance per cell
90deg-gt 60deg -gt 30deg
ldquoresonancerdquo optic structure with
variation of D through the ring