Post on 13-Jan-2016
description
Beam-beam studies for Super KEKB
K. Ohmi & M Tawada (KEK)
Super B factories workshop in Hawaii
20-23 Apr. 2005
Luminosity limit• Fundamental limit due to the beam-beam
interaction.• Super B factories target the fundamental limit.• How high is the beam-beam limit?
• The beam-beam limit is discussed in two papers,K. Ohmi et al, PRL 92, 214801 (2004). Beam-beam limit in Super KEKBK. Ohmi et al, PRST 7, 104401 (2004). Crossing angle effect in KEKB
• The beam-beam limit can be understood by using strong-strong simulation (based on the Particle in cell method).
• Design of super KEKB is discussed from the view of the beam-beam limit using the simulation.
Parameter table of super KEKBHER LER HER LER
I 4.4A 10A 1.27A 1.7A
Nb 5000 5000 1293 1293
Ne 5.5x1010 1.26x1011 6.1x1010 8.2x1010
x 24nm 24nm 24nm 18nm
y 0.18nm 0.18nm 0.18nm 0.18nm
z 3mm 3mm 6mm 6mm
x 20-30cm 20-30cm 60cm 60cm
y 3mm 3mm 6mm 6mm
yR 0.16 0.16 0.05 0.085
Lb 0.8x1032 0.12x1032
L 4x1035 R=0.7 1.5x1034
KEKB
Tune scan• Bunch luminosity v.s. tune• Total luminosity = 5000x bunch luminosity• Green line sketches progr
ess of KEKB.
Ltot = 4x1035 cm-2 s-1
By M. Tawada
Luminosity evolution• Equilibrium state is realized for equal damping times.• Design damping time is 4000 and 6000 turns for HER an
d LER, respectively.• Slow luminosity decrease is observed for unequal dampi
ng times.
x=30 cm 20cm
Difference of the damping time• Beam size asymmetry
and luminosity decrease arise.
• Emittance equalization is required.
Equal damping time (6000 turn) 4000 (HER) & 6000 (LER) turn
What disturb to achieve the fundamental beam-beam limit?
• Nonlinear diffusion1. Linear coupling of arc2. Nonlinearity of arc lattice
• External diffusion 1. Phase jitter of crab and accelerating cavities
2. Feedback noise • Parasitic interaction• Other issues1. Heating, bunch lengthening, electron cloud …
Optics error at the collision point• One turn map is multiplication of beam-beam int
eraction and map of arc section.• Total luminosity performance is determined by th
e map of arc section, which is controllable by us.
• X-y coupling, dispersion (xy- coupling) and crossing angle (x-z coupling)
• A symplectic diffusion is induced by the couplings. Mixing of degree of freedom seems to enhance Arnold diffusion.
Vertical dispersion• Diffusion behavior due
to dispersion in a system without synchrotron radiation.
• Luminosity and beam size are degraded.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1 1.2
hy (mm)
L/L0
0
1
2
3
4
5
6
0 0.2 0.4 0.6 0.8 1 1.2
hy (mm)
y/
y0e-e+
Gaussian approx.
PIC simulation
X-y coupling
• Diffusion due to x-y coupling.
• Luminosity and beam size degradation.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.05 0.1 0.15 0.2 0.25
r4
L/L0
0
1
2
3
4
0 0.05 0.1 0.15 0.2 0.25
r4
y/
y0e-e+
Gaussian approx.
PIC simulation
Crossing angle• Crossing angle is equivalent to x-z coupling.• Diffusion and luminosity degradation due to cros
sing angle
Gaussian approx. PIC simulation
Nonlinear terms• Effect of chromaticity, d/d, d/d, d/d,
has been studied.
• The effect was very weak for d/d ~7.
• Life time degradation may be issue.
• Higher nonlinearity using a Taylor map will be included in the beam-beam simulation.
• Detailed studies will be done.
External diffusion: Vertical offset noise
• Since the beam-beam system is chaotic, such noise enhances the diffusion of the system.
• Luminosity degradation for the noise without correlation between turns.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.02 0.04 0.06 0.08 0.1Dy/ y
L/L0
Tcor=1
0
1
2
3
4
5
6
0 0.02 0.04 0.06 0.08 0.1
Dy/ y
y/
y0e-e+
2( ) ( ') ( ')y t y t y t tD D D
Orbit offset (static)
• Static vertical offset. Tolerance is easier than the fast noise.
• For slower variation than radiation damping time, emittance can be an adiabatic invariant.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.2 0.4 0.6 0.8 1Dy/ y
L/L0
Offset
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Dy/ y
y/
y0e-e+
2( ) ( ') exp( )y t y t y t D D D
Phase jitters of RF systems: horizontal offset noise
• Noise of RF system. Deviation of RF phase, .
• Phase error between two crab cavities.
• The transverse offset affects the beam-beam performance.
tanRF
RF
cx
cos( ( *, ))tan tan
2sinx c
c cRF x RF
s sc cx
D
5(m) 2.5 10 (deg)x
Effect on the beam-beam performance of the phase jitter of RF’s
0
0.5
1
1.5
2
2.5
0 0.02 0.04 0.06 0.08 0.1 0.12
Dx/ x
x/
x 0e-e+e-e+
• Luminosity and beam size as functions of x.
• Correlation time of the jitter, 1 or 10 turns, is important for the degradation.
• Since Q=200,000 and H=5120, the correlation time will be larger than 10 turns.
• Tolerance is 0.05 degree.
0
0.2
0.4
0.6
0.8
1
1.2
0 0.02 0.04 0.06 0.08 0.1 0.12Dx/ x
L/L0
Tcor=10Tcor=1
Parasitic collision• Nonlinear force (~1/r) with very large amplitude• Separation at the parasitic collision
• Dynamic beta and emittance (simulation)
,min 9 mm : half crossing anglesp crs crsx L D
,min,min 2
( 2) (0) 1 0.069 2.2 0.15 mm x=604sp
x sp x xx
LL
D
(0) 0.067 mm 0.028 (0.017 : analytic) m ( / 2) 0.93 mmx x x L
0.503, 0.5505x y
( 2)10 /xx LD
Luminosity with or without parasitic interaction• In fixed parasitic beam model, no effect is observed. • When parasitic beam is treated as soft Gaussian, a
stable solution was not obtained by beam loss at the early stage (unmatched).
• It may be critical situation, especially for the beam life time or injection.
Toward Higher luminosityHigher bunch current
with keeping total current
• Luminosity saturates for increasing bunch current. Beam-beam limit.
• Only HOM loss increases.
Toward higher luminosity, 1036 cm-2 s-1
• Two beam collision is limited by strong nonlinear diffusion coupled to synchrotron radiation around 4x1035 cm-2 s-1 .
• Compensation scheme is one of limited choices.
• Our first study (Ohnishi & Ohmi) did not give better results than that of the two beam collision.
4 eigenmodes of four-beam collision
No tune shift
=0
Focusing
=0
+
Defocusing
=0-
x,yz
Unstable modes
Rich unstable mode and no Landau damping
Summary
• Design and tolerance for Ltot = 4x1035 cm-2 s-1 were studied.
• Reduce optics error at the collision point. Maybe acceptable.
• Reduce external diffusions especially those with fast frequency component.
• Arc nonlinearity and life time issues will be studied soon by collaboration with BINP (D. Shatilov).
• Efforts on higher luminosity are continued.