![Page 1: Round Colliding Beams at VEPP-2000jaiweb/slides/2016_Shwartz.pdf · 44 244 mA. Flip-flop (simple linear example) 11 = 0.1 1 0 2 0 1 1 0 0 cos cos 2 sin sin sin ** 22 0 0 0 0 2022](https://reader035.vdocuments.site/reader035/viewer/2022081408/6058a930784de14b83185a35/html5/thumbnails/1.jpg)
Implementation of Round Colliding
Beams Concept at VEPP-2000
Dmitry Shwartz
BINP, Novosibirsk
Oct 28, 2016
JAI, Oxford
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Introduction
2
Beam-Beam
Effects
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Circular colliders
3
Interaction Points (IP)
e e
Low-beta insertion
(Interaction Region − IR)
Different schemes:
Single ring / two rings
Multibunch beams
Number of IPs
Head-on / crossing angle
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Colliders
4
LHC pp, PbPb 7 TeV, 2.8 TeV/n 1×1034 cm-2s-1, 1×1027 cm-2s-1
RHIC pp, AuAu 250 GeV,100 GeV/n 1×1032 cm-2s-1, 1.5×1027 cm-2s-1
DAFNE e+,e 0.5 GeV 4×1032 cm-2s-1
BEPC-II e+,e 1.89 GeV 7×1032 cm-2s-1
VEPP-4M e+,e 5.5 GeV 2×1031 cm-2s-1
VEPP-2000 e+,e 1 GeV 1×1032 cm-2s-1
SuperKEKB e+,e 4×7 TeV 8×1035 cm-2s-1
NICA AuAu 4.5 GeV/n 1×1027 cm-2s-1
AdA (1961) – first collider (e+,e)
ISR (1971) – first hadron collider (pp)
SLC (1988) – first (and only) linear collider
LEP (1988) – highest energy e+,e collider (104.6 GeV)
HERA (1992) – first (and only) electron-ion collider
KEKB (1999) – highest luminosity collider (2.1×1034 cm-2s-1)
+ 19 others
in operation:
under construction:
stopped:
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Luminosity
5
processN L Number of events per second:
1 2 0
2 2 2 2
1 2 1 22
b
x x z z
N N n fL
0 1 2
, , ,
2 ( , , ) ( , , )b
x z s t
L n f c x z s ct x z s ct dxdzdsdt
For Gaussian distributions,
non-equal beam profiles:
2
221( )
2
y
y
y
y e
, ,y x z s
How many interacts?
32 2 1 24 2
6
0
10 10~ ~ 10
12 10
processL cm s cm
f Hz
Compare to 11~ 10bunchN
Other particles do not interact with each other but with opposite bunch field
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Linear beam-beam effects
6
Linear focusing
Beam-beam force for Gaussian
bunches
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
cos sin sin 1 0
sin cos sin 1
cos sin sin sin
sin cos sin cos sin
Mp
p
p p
Perturbation: thin
axisymmetric linear
lens.
The sign depends
on particles type.
Focusing for
particle-antiparticle
beams.
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Linear beam-beam effects (2)
7
0 0
1 1Tr( ) cos cos sin
2 2M p 0 1
0 0cos cos sin
0 / 2p
*
4
p
Beam-beam parameter
0 0cos cos 2 sin 0 0 0
1arccos(cos 2 sin )
2
=0.025
=0.075 =0.15 =0.25
= 0.3
= 0.2 = 0.1 = 0.05
,
*
2
,
,2 ( )
x ze
x z
x z x z
N r
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Dynamic beta
8
0 0cos cos 2 sin 0 0sin sin
0 0 0 0
2 2 2 2
0 0 0 0 0 0
0
2
0
sin sin
1 (cos 2 sin ) sin 4 cos sin (2 ) sin
1 4 cot (2 )
= 0.3
= 0.2 = 0.1 = 0.05
(1960s)
One of the reasons to choose
working point close to half-
integer resonance: additional
(dynamic) bonus final
focusing
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Dynamic emittance
9
0 10 20 30 40 501
2
3
4
5 BetaX
BetaY WS
BetaX
BetaY RING
Beta
- function,
cm
Current, mA
0 10 20 30 40 500,0
2,0x10-6
4,0x10-6
6,0x10-6
8,0x10-6
1,0x10-5
1,2x10-5
Em
itta
nce
e1
e2 WS
e1
e2 RING
Current, mA
0 10 20 30 40 500,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09 as
bs WS
a
b RING
Siz
e, m
m
Current, mA
3
0 2
2
0
/55
1/32 3
e
x
X
H r
J r
In electron synchrotron radiative
beam emittance:
2 2( ) ( ) ( ) 2 ( ) ( ) '( ) ( ) '( )x x xH s s D s s D s D s s D s
Perturbed -function (dynamic beta)
propagates to arcs and modifies H(s).
(1990s)
VEPP-2000
examples
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Dynamic beta & emittance
10
Beam profile monitors
at VEPP-2000 2 2 mA2
44 44 mA2
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Flip-flop (simple linear example)
11
= 0.1
1 0 2 0
1 1 0 0
cos cos 2 sin
sin sin
2 2* *
0 0 0 0
2 02 2
2 22 04 4
e eNr Nr
Assume round beams, unperturbed emittance
2 2
20 0 0
0 0 0
1 2 2
1 4 cot 2
21
12
22 2
0 0 2 0
22 2
0 0 1 0
1 4 cot 2
1 4 cot 2
b b b
b b b
0
1,2
1,2
b
Self-consistent solutions:
equal sizes below threshold ,
non-equal above th.
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Coherent beam-beam
12
-mode, unperturbed tune, = 0
-mode, shifted tune,
= 0 + 0 = 0 +
Without going into details, ~1 K.Hirata, 1988
IP
IP
Two beams modes coupling via beam-beam interaction: new eigenmodes.
-modes -modes VEPP-2000
example
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Coherent beam-beam
13
-modes -modes
Example: coherent beam-beam modes monitoring at VEPP-2000.
Shifted tune drift with beam current decay.
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Beam-beam tune spread
14
Linear beam-beam:
tune shift
Nonlinear beam-beam:
tune spread (footprint)
LHC example:
pp − defocusing
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Beam-beam limit
15 J.Seeman (1983)
Beam-beam parameter saturation ,
emittance (and beam size) growth
,
*
2
,
,2 ( )
x ze
x z
x z x z
r N
Final limit:
1) emittance blowup,
2) lifetime reduction,
3) flip-flop effect
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Nonlinear beam-beam limit
16
Typical dependence of specific
luminosity on beam current
* *
2 2
2 ( ) 2
z ze e
z
z x z x z
N r r N
1 0 2
4
b
x z
N n f NL
0 2
1 2 1
1
4
b
spec
x z
n f NLL
N N N
(VEPP-2M example)
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Distribution deformation
17
LIFETRAC simulations example
DAFNE example: beam profile
measurements.
Vertical profile significantly differs
from Gaussian distribution.
“Long” tails – lifetime reduction
(+ hard background in detectors).
z = 398 m
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Nonlinear beam-beam
18 VEPP-4 simulations example (flat e+,e beams)
6th order betatron resonances &
synchro-betatron satellites
Resonances in
normalized
amplitudes plain
FMA: footprint
BB-interaction produces:
1) High-order resonance grid
2) Footprint, overlapping resonances
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Integrable beam-beam?
19
What can be done to increase significantly beam-beam parameter threshold?
Integrability should be implemented!
Half-integrability:
1) Round beams (+1 integral of motion >> 1D nonlinearity remains)
2) Crab-waist approach for large Piwinsky angle
3) Vicinity to half-integer resonance.
Even closer to full-integrable beam-beam?
1) Round beams + special longitudinal profile?
2) …?
Reduction of nonlinear motion dimensions number is
very important: diffusion along stochastic layer
through additional dimension is suppressed
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Round beams at e+e- collider
Luminosity increase scenario:
Number of bunches (i.e. collision frequency)
Bunch-by-bunch luminosity
2
*2
2
1
x
y
ye
xyx
r
fL
Round Beams:
Geometric factor:
Beam-beam limit enhancement:
IBS for low energy? Better life time!
2
1 / 4y x
0.1
2 2
2
4
e
fL
r
02/19
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The concept of Round Colliding Beams
• Head-on collisions!
• Small and equal β-functions at IP:
• Equal beam emittances:
• Equal fractional parts of betatron tunes:
x y
x y
x y
Axial symmetry of counter beam force together with x-y symmetry
of transfer matrix should provide additional integral of motion
(angular momentum Mz = xy - xy). Particle dynamics remains
nonlinear, but becomes 1D.
V.V.Danilov et al., EPAC’96, Barcelona, p.1149, (1996)
Round beam
Mx = My
Lattice requirements:
03/19
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Historic beam-beam simulations
I.Nesterenko, D.Shatilov, E.Simonov, in
Proc. of Mini-Workshop on “Round
beams and related concepts in beam
dynamics”, Fermilab, December 5-6,
1996.
Beam size and luminosity vs. the
nominal beam-beam parameter
(A. Valishev, E. Perevedentsev,
K. Ohmi, PAC’2003 )
“Weak-Strong” “Strong-Strong”
04/19
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VEPP-2000 main design parameters @ 1 GeV
Circumference 24.388 m Energy range 150 1000 MeV
Number of bunches 1 Number of particles 11011
Betatron tunes 4.1/2.1 Beta-functions @ IP 8.5 cm
Beam-beam parameter 0.1 Luminosity 11032 cm-2s-1
13 T final focusing
solenoids
VEPP-2000 layout (2010-2013)
max. production rate:
2×107 e+/s
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VEPP-2000
06/19
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Beam size measurement by CCD cameras
07/19
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Flat to Round or Mobius change
needs polarity switch in solenoids
and new orbit correction.
Round beam due to coupling resonance?
The simplest practical solution!
Round Beams Options for VEPP-2000
Both simulations and experimental tests
showed insufficient dynamic aperture for
regular work in circular modes options.
08/19
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Machine tuning
1) Orbit correction & minimization of steerers currents using ORM techniques
(x,y < 0.5mm)
2) Lattice correction with help of ORM analysis ( < 5%)
3) Betatron coupling in arcs (min ~ 0.001)
4) Working point small shift below diagonal
Lifetrac by D.Shatilov, 2008
After correction
Before correction
Specific luminosity & linear lattice correction
09/19
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Simulations for E = 500 MeV.
50 mA corresponds to ~ 0.1.
Invariance of beam sizes @ IP is
the essential VEPP-2000 lattice
feature.
Dynamic beta, emittance and size
10/19
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nom ~ 0.12
Dynamic sizes at the beam-size monitors
11/19
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Obtained by CMD-3 detector
luminosity, averaged over
10% of best runs
Luminosity vs. beam energy 2010-2013
Fixed lattice energy
scaling law: L 4
Peak luminosity overestimate
for “optimal” lattice variation
* , L 2
e+ deficit Beam-beam effects
DA, IBS lifetime
Energy ramping
12/19
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E = 240 MeV,
Ibeam ~ 55 mA
0.17 0.2 0.25
0.17 0.2
0.17 0.2
Pickup spectrum of the coherent oscillations
Coherent beam-beam -mode
interaction with machine
nonlinear resonances?
“Flip-flop” effect
13/19
TV
e+
e
regula
r blo
wn-u
p e
blo
wn-u
p e
+
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Е = 392.5 MeV
Urf = 35 kV (purple)
Urf = 17 kV (blue)
0
0 0
arccos(cos( )
2 sin( )) /
= 0.175 = 0.125/IP
Beam-beam parameter
Coherent oscillations spectrum
14/19
BB-threshold improvement
with beam lengthening:
Beam-beam parameter extracted
from luminosity monitor data
*
*24
e nomnom
nom
N r
*
*24
e nomlumi
lumi
N r
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33
Bunch lengthening: microwave inst.
Bunch length measurement with phi-
dissector as a function of single beam
current for different RF voltage @ 478 MeV.
Energy spread dependence, restored from
beam transverse profile measurements.
15/19
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Proper profile of longitudinal distribution together
with = n betatron phase advance between IPs
makes the Hamiltonian time-independent, i.e.
integral of motion.
1( )
( )s
s
2*
*( )
ss
(Danilov, Perevedentsev, 1997)
Integrable round beam?
16/19
* = 5cm
s = 5cm
= 0.15
as = 0.0 as = 1.0
D.Shatilov, A.Valishev, NaPAC’13
Synchrotron motion should
prevent full integrability(?)
Beam-beam resonances suppression
due to hour-glass effect(?) S. Krishnagopal, R. Seeman., Phys.Rev.D, 1990
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Beam sizes data analysis @ 392.5 MeV
URF= 35 kV
URF= 17 kV Note: bunch lengthening is
current-dependent…
17/19
I = 15 mA corresponds to ~ 0.1
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VEPP-2000 upgrade: 2013 >> 2016
BINP Injection complex
VEPP-2000
complex
1. e+, e beams from new BINP Injection Complex (IC):
high intensity
higher energy (400 MeV);
high quality (!);
2. Booster BEP upgrade to 1 GeV.
3. Transfer channels BEP VEPP to 1 GeV.
4. VEPP-2000 ring modifications.
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Summary
Round beams give a serious luminosity enhancement.
The achieved beam-beam parameter value at middle energies amounts to
~ 0.1–0.12 during regular operation.
“Long” bunch (l ~ *) mitigates the beam-beam interaction restrictions,
probably affecting on flip-flop effect.
VEPP-2000 is taking data with two detectors across the wide energy range
of 160–1000 MeV with a luminosity value two to five times higher than that
achieved by its predecessor, VEPP-2M. Total luminosity integral collected
by both detectors is about 110 pb-1.
Injection chain of VEPP-2000 complex was upgraded and commissioned.
Achieved e+ stacking rate is 10 times higher than formerly.
During upcoming new run we intend to achieve the target luminosity and
start it’s delivery to detectors with an ultimate goal to deliver at least 1 fb1
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Backup slides
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Beam-beam parameter evolution
392.5 MeV,
June-2013
537.5 MeV,
June-2011
511.5 MeV,
May-2013
0.07
0.08
0.09 (purple points)
13/19
*
*24
e nomnom
nom
N r
*
*24
e nomlumi
lumi
N r
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LIFETRAC predictions
1. Very high threshold values for ideal linear machine lattice, th ~ 0.25.
2. Chromatic sextupoles affect significantly on bb-effects decreasing threshold down
to th ~ 0.15. (Break of the angular momentum conservation by nonlinear fields
asymmetric to x-y motion)
3. Working point shift from coupling resonance under diagonal (x > z) preferable
than vise versa. (Emittances parity breaking.)
4. Uncompensated solenoids acceptable in wide range (x,z ~ 0.02) while coupling
in arcs provided by skew-quadrupole fields should be avoided. (Angular
momentum conservation break by skew-quads, breaking x-y symmetry of
transport matrix.)
5. Inequality of x-y beta-functions in IP within 10 % tolerance does not affect on bb-
effects.
6. Bb-effects do not cause emittance blow-up but reduce beam lifetime via non-
Gaussian “tails” growth in transverse particles distribution.
7. Beam lifetime improves with working point approach to the integer resonance.
Qualitative agreement of all predictions with experimental experience.
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2 2 2 2
0 NN
4 x x z z
fL
*
02
NN
4
fL
SND and CMD-3 luminosity monitors:
1) Slow (1 measurement ~ 1/2 minute)
2) Large statistical jitter at low beams intensities
Needed:
1) Beams current measurement e+, e (ФЭУ)
2) 4 beam sizes * (with current dependent dynamic * and emittance)
reconstruction from 16 beam profile monitors.
Assumptions:
1) Lattice model well known (transport matrices)
2) Focusing distortion concentrated within IP vicinity.
3) Beam profile preserve Gaussian distribution.
2 4 = 8 parameters /
8 2 2 = 32 measured values. * * * *, , , , , , ,x z x z x z x z
Luminosity measurement via beam sizes @
CCD cameras
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800 MeV
180 MeV
Luminosity monitor
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537.5 MeV
Extracted from luminosity
beam size @ IP
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Weak-strong tune
scan of threshold
counter beam current
value.
Ib, mA
{}
Single positron beam lifetime
as a function of betatron tune.
20mA @ 500MeV
High order resonances
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Intrabeam scattering and DA
Single beam emittance
growth with beam current,
E=220 MeV
Calculated in simple model
DA dependence with *
variation. {}=0.128, E=1 GeV