beam-beam simulations with crossing anlge + crab-waist
DESCRIPTION
Beam-beam simulations with crossing anlge + crab-waist. M. Biagini, M. Zobov, LNF-INFN P. Raimondi, SLAC/INFN I. Koop, D. Shatilov, BINP E. Paoloni, Pisa University/INFN SuperB III Workshop, SLAC, 14-16 June 2006. BB simulations. - PowerPoint PPT PresentationTRANSCRIPT
Beam-beam simulations with crossing anlge + crab-
waist
M. Biagini, M. Zobov, LNF-INFNP. Raimondi, SLAC/INFNI. Koop, D. Shatilov, BINP
E. Paoloni, Pisa University/INFN
SuperB III Workshop, SLAC, 14-16 June 2006
BB simulations
• New “crossing angle + crab waist” idea has solved disruption problems related to collisions with high current, small sizes beams back to two “conventional” rings
• With very small emittances and relatively low currents (comparable to present B-Factories values) a Luminosity of 1036 cm-2 s-1 is reachable without large emittance blow-up
Vertical waist has to be a function of x:
Z=0 for particles at –x (- x/2 at low current)
Z= x/ for particles at + x (x/2 at low current) Crabbed waist realized with a sextupole in phase with
the IP in X and at /2 in Y
2Sz
2Sx
z
x
2Sx/
2Sz*
e-e+Y
Crabbed waist removes bb betratron couplingintroduced by the crossing angle
Luminosity considerationsIneffectiveness of collisions with large crossing angle is illusive!!!Loss due to short collision zone (say l=σz/40) is fully compensated by denser target beam (due to much smaller vertical beam size!) cross
2 2 cross xz
lN N l 2 /
Number of particles in collision zone:
1 2 0
x y
N N fL
4
e 2 y
1yy x y
r N
2 ( )
1y 1 0 y 1y34 36 2 1
e y x y
N f E(GeV) I(A)L 1 2.167 10 1.2 10 cm s
2r (cm)
No dependence on crossing angle! Universal expression: valid for both, head-on and crossing angle collisions!
I. Koop et al, BINP
Tune shiftsRaimondi, Shatilov, Zobov:(Beam Dynamics Newsletter, 37, August 2005)
2 2 2x z xtan ( / 2)
e xx
2 2 2 2 2 2z x z x y
yey
2 2 2y z x y
r N
2 tan ( / 2) tan ( / 2)
r N
2 tan ( / 2)
SuperB:
e xx 2 2
z
yey
y z
2r N0.002
r N0.072
2 2 2z x xtan ( / 2) 100 m 2.67 m
2 2 2z x
y
tan ( / 2)8000!!!
One dimensional case for βy >>σx/θbut with crabbed waist for βy <σx/θ also!
I. Koop et al, BINP
“Crabbed” waist optics
1x x
x x x x1 1 11x x x xx x
y y y1 1 1y y y y
y y y y y
u 0 1 0u 0T T T T
F u 2u F 1F u
u F 0 F 1 0T T T T
F 0 F u 2u F 1
Appropriate transformations from first sextupole to IP and from IP to anti-sextupole:
IP
Δμx=πΔμy=π/2
Δμx=πΔμy=π/2
x,yT x,yT+ks -ks
Sextupole lens Anti-sextupole lens
Synchrotron modulation of ξy (Qualitative picture)
ξy(z-z0)
Relative displacementfrom a bunch center
z-z0
Head-on collision.Flat beams. Tune shiftincreases for halo particles
Head-on collisionRound beams ξy=const
Crossing angle collision.Tune shiftdecreases for halo particles
Conclusion: one can expect improvements of lifetime of halo-particles!
I. Koop et al, BINP
ξy increase caused by hourglass effect
For Super-B parameters set: Increase of ξy only by 26%
Dependence of ξy on βy for constant beam sizes at IP
2
y yy
1 zg(x(z)) dz
4
I. Koop et al, BINP
Collisions with uncompressed beamsCrossing angle = 2*25mradRelative Emittance growth per collision about 1.5*10-3
yout/y
in=1.0015
Horizontal Plane Vertical Plane
SuperB parameters
GuineaPig modifications
• With the large crossing angle scheme and long bunches the actual collision region is very short
• The code solves Poisson equation for all the volume occupied by the particles very long computing time, not needed !
• Modification of the code to perform fields calculation in the collision region only
• Computing time was reduced by a factor 10!!
GuineaPig modifiedE. Paoloni, Pisa
Luminosity vs Number of particles /bunch
Crab-waist simulations
• The new idea is being checked by several beam-beam codes:– Guinea-Pig: strong-strong , ILC centered– BBC (Hirata): weak-strong – Lifetrack (Shatilov): weak-strong with
tails growths calculation– Ohmi: weak-strong (strong-strong to be
modified for long bunches and large angles)
Sto
rag
e
rings
Ohmi’s weak-strong code
K2 is the strength of the sextupolar nonlinearity introduced to have crab waist
Luminosity Vertical blow-up
DANE (M.Zobov, LNF)• Hirata’s BBC code simulation
(weak-strong, strong beam stays gaussian, weak beam has double crossing angle)
• Np = 2.65x1010, 110 bunches
• Ib = 13 mA (present working current)
• x = 300 m, y = 3 m
• x = 0.3 m, by = 6.5 mm
• z = 25 mm (present electron bunch length)
• = 2x25 mrad• YIP = y+0.4/(* x * y’) crabbed waist shift• Lo=2.33x1024 (geometrical)• L(110 bunches,1.43A) = 7.7x1032
• Lequil=6x1032
(Geometric) Luminosity
Takes into account both bb interactions and geometric factor due to crab waist
0,5
0,6
0,7
0,8
0,9
1
1,1
1,2
0 0,2 0,4 0,6 0,8 1
L/Lo
n x [1/angle]
n/
Peak around 0.3/
M.Zobov, LNF
Scan vs crab waist n/
Vertical Tails(max amplitude
after 10 damping times)
Vertical Size Blow-up
2
4
6
8
10
12
14
16
0 0,2 0,4 0,6 0,8 1
Ay/y0
n x [1/angle]
n/
0,5
1
1,5
2
2,5
3
0 0,2 0,4 0,6 0,8 1
y/y0
n x [1/angle]
n/
M.Zobov, LNF
Present WP:x = 0.11y = 0.19
Possible WP:x = 0.057 y = 0.097
0
0,5
1
1,5
2
2,5
0 5 10 15 20 25
(0.11,0.19)(0.057,0.097)Theory
I [mA]
L [10^33]
Luminosity vs bunch currentfor 2 different working points
M.Zobov, LNF
0
2
4
6
8
10
12
14
0 10 20 30 40 50
200um,20mm200um,15mm100um,15mm
I [mA]
L [10^33]
110 bunches
M.Zobov, LNF
Luminosity with shorter bunch, smaller x
With the present achieved beam parameters (currents, emittances, bunchlenghts etc) a luminosity inexcess of 1033 is predicted.With 2A+2A L> 2*1033 is possibleBeam-Beam limit is way above the reachable currents
Luminosity scan
Without Crab Focus
Vertical Size blow-up scan
M. Zobov
With Crab Focus
Beam-Beam Tails Without Crab
WaistWith Crab Waist
Bunch core blowup
also reduced
Ay = 90
Ay = 45
Vertical tails growth Greatly reduced
(A is the amplitude in number of beamsize )
D.Shatilov, BINP
Beam size and tails vs Crab-waistSimulations with beam-beam code
LIFETRAC Beam parameters for DANE2
An effective “crabbed” waist map at IP:0 0
0
Vy y xy
y y
Optimum is shifted from the “theoretical” value V=1 to V=0.8,since it scales like z/sqrt((z2+x
2)D.N. Shatilov, BINP
0,5
0,6
0,7
0,8
0,9
1
1,1
1,2
0,06 0,08 0,1 0,12 0,14 0,16
Qx
L/L0 at Qy = 0.09
Some resonances
0
0,2
0,4
0,6
0,8
1
1,2
0,06 0,08 0,1 0,12 0,14 0,16
no crab focus0.25/teta0.40/teta
Qx
L/L0 at Qy = 0.05
M.Zobov, LNF
2Qx = 2Qy1Qx = 2Qy
(present with crossing angle only)
No crab waist
Crab waist
Very weak luminosity dependence from damping time given the very small beam-beam blow-up
0
0,2
0,4
0,6
0,8
1
0 5 104 1 105 1,5 105 2 105 2,5 105
x^(-0.37)
x^(-0.48)
x^(-0.56)
x^(-0.50)
y0/y
turns
(0.057,0.097,-0.01)(0.057,0.097,+0.01)
(0.11,0.19,-0.01)(0.11,0.19,+0.01)
Wigglers off
DANE Wigglers
SC Wigglers
M. Zobov,LNF
0,5
1
1,5
2
2,5
3
3,5
5 104 1 105 1,5 105 2 105
(0.057,0.097,-0.01)(0.057,0.097,+0.01)(0.11,0.19,-0.01)(0.11,0.19,+0.01)
turns
L, 10^33
Wigglers offSC Wigglers
DANE Wigglers
Vertical blow-up Luminosity
Preliminary results on Super PEPIIx = 20 nmy = 0.2 nmx = 14.4 my = 0.4 mz = 10 mmE = 7x10-4
x = 10 mmy = 0.8 mms = 0.03C = 2.2 kmfcol = 238 MHz = 2 x 14 mradx = 35 msN1 = 1.3x1011
N2 = 4.4x1010
I1 = 5 AI2 = 1.7 A
First approach with new parameters,weak-strong code
M. Zobov, D. Shatilov
L = 1.65x1035 cm-2s-1
Tune scan for Super-PEPII
M.Zobov, D.ShatilovSynchrobetatron resonances
Coupling resonance
crab focus on
crab focus off
Coupling resonance disappears
No dependence on tunes !!
Tails growth
M.Zobov, D.Shatilovn/= 0 n/= 0.6 n/= 1
x = 0.5325, y = 0.5775
x = 0.54, y = 0.5825
Crab OnCrab Off
30 y
10 y15 y
40 y
15 y
20 y
L=1.5x1035 L=1.65x1035L=1.64x1035
Conclusions
• The “crossing angle with crab waist” scheme has shown big potentiality and exciting results LNF, Pisa, BINP and KEKB physicists are working on the bb simulation with different codes to explore its properties and find the best set of parameters
• This scheme is promising also for increasing luminosity at existing factories, as DANE, KEKB and possibly PEPII