Beam-beam effects in SuperKEKB
Phase II commissioning
K. Ohmi, K. Hirosawa, D. Zhou (KEK)SuperKEKB MAC 2018
14-15 March, 2018
Thanks to E. Forest, Y. Funakoshi, N. Iida, H. Koiso, N. Kuroo, A. Morita,
Y. Ohnishi, N. Ohuchi, K. Oide, D. Sagan, H. Sugimoto, Y. Zhang

SuperKEKB• Luminosity upgrade strategy changes the crab cavity to the large crossing angle
scheme.
• Extremely low b IP optics, bx*=3cm by*=0.3mm.
• Large Piwinski angle,• Commissioning with collision starts with detuned beta*.
• IP beta is squeezed step by step,(8xbx*,8xby*), (4xbx*,8xby*), (4xbx*,4xby*),…, (bx*,by*)Two subjects are discussed,
1. IR nonlinearity, chromatic Twiss (b and coupling)
2. Coherent beam-beam instability

Y. Ohnishi,Dec. 2017

IR magnets and their nonlinearity• There are many nonlinear field components in IR magnets.
• Chromatic coupling
D. Zhou, SKEKB
MAC 2015

BBWS : arc expressed by simple transfer
matrix
SAD: complex lattice structure

Y. Zhang’s (IHEP) work at KEK• Vertical orbit is induced by a large horizontal betatron oscillation.
• Skew sextupole term at IP, x2y, is suspected for the luminosity
degradation.

QCS superconducting magnet system N. Ohuchi et al.

N. Ohuchi et al.

Evaluation of nonlinear term
• Focus on skew sextupole component.
• Reference axes in solenoid is chosen as a straight line with half crossing angle.
• Magnet components are defined on the reference orbit.
• Beam orbit deviate from the reference orbit.
• Skew sextupole component is induced by Skew sextupole and octupole with avertical orbit.
Skew sextupole component
upstream of IPdownstream

C10 from SK2 and K3+yCOD• Contribution to SK2 is coming from explicit Skew Sext SK20 andoctupole, K3+COD
There are 10 skew components.
• No contribution from higher order than K3.
𝑦 3 , 𝑦 2 𝑝 , 𝑦𝑝2 , 𝑝3𝑦𝑦𝑦𝑥 2 𝑦, 𝑥 2 𝑝𝑦 , 𝑥𝑝𝑥 𝑦, 𝑥𝑝𝑥 𝑝𝑦 , 𝑝𝑥2 𝑦, 𝑝𝑥2 𝑝𝑦
𝐻 = 𝑐10 𝑝𝑥2 𝑝𝑦• Skew sextupole coming from higher order nonlinearity is small.

Comparison with PTC• “SAD” means to do integration of thenonlinearity using SAD script.

D. ZhouLuminosity for H=c10px2py and chromatic Twiss

Skew sext
ChromaticSumSAD• The luminosity degradation due to Skew sext
component and chromatic Twiss almost explainsthat of beam-beam simulation with SAD.
• Study of Space charge force is next.

Detuning b*• c10=0.072 m is kept for b*change, because IR magnets are fixed in SuperKEKB.
• For normalized coordinates, 𝑃𝑖 = 𝛽𝑖 𝑝𝑖 , 𝑋𝑖 = 𝑥𝑖 / 𝛽𝑖𝑐10𝐶10 = ∗ ∗𝐻𝑁 = 𝐶10 𝑃𝑥2 𝑃𝑦
𝐻 = 𝑐10 𝑝𝑥2 𝑝𝑦
𝛽𝑥 𝛽𝑦• C10=136.9 m-1/2 for bx*=3.2cm, by*=0.27mm• Normalized C10 directly affects the beam dynamics. ∆𝑌 = 𝐶10 𝑃𝑥2∆𝑌 = 𝐶10 𝑃𝑥2 ≈ 136.9𝜀𝑥 ≈ 0.15 𝜀𝑦for bx*=3.2cm, by*=0.27mm• The effect is reduced by Detune of b*.
• C10 is 4.4% for 8x8, 8.8% for 4x8.
• C10 can be canceled by Octupole coils, but are not compatible with dynamic
aperture.

Measurement of the Coherent beam-beam
instability
Y. Ohnishi,• Beam-beam instability should beobserved at detuned lattice (8x8x) in
commissioning of Phase-II (this year).
• Design parameters of SuperKEKB wasstable.

Dec. 2017

Beam-beam effects in nano-beam collisionKEK-CERN-BINP-SLAC-BNL-Fermilab
Accelerator physics activity• Coherent beam-beam instability in collisions with a large crossing
angle is caused by cross wake force, which gives correlation
between two beams• Mode coupling instability can occur incollision witha large crossing
angle.

Analysis of the instability• Beam-beam eigenmode analysis. Solve eigenvalues of 1000x1000 matrix.
• Eigen tune is n=nx+-Lns. Mode coupling or synchro-beta resonance is casued.
• Synchrotron tune, ns(LER)=0.0247, ns(HER)=0.0280.
• Number of Sidebands increases. More unstable.

• strong-strong beam-beamsimulation.

Eigen mode analysis for nx=0.53• 8x8x4x8x

nx+ns(+)

nx-3ns(-)

skb8x8xb

Eigen mode analysis for nx=0.54• 8x8x4x8x

skb8x8xc

Eigen mode analysis for nx=0.55• 8x8x4x8x

skb8x8xd

Strong-strong beam-beam simulation
8x8x, 1.44mAx1.04mA, nx=0.53

skb2a4x8x, 1mAx0.8mA , nx=0.53

skb21bSummary of the strong-strong simulation
I=1.44mA x 1.04mA
nx

L/L0,

0.53 a0.58-0.66

0.535 g0.70-0.95

0.54

d0.545 f
0.55 e8x8xsx/sx0 (L & H)

3.0-7.5 2.2-6.2

2.5-6.2 1.4-4.0

1.04

1.2

1.0

0.75-0.95 2.5-6.0 1.4-4.0

1.05

2.1

1.1

0.94

5.2

1.7

0.75-0.77

8.6

3.5

7.2

4.5

L/L0,
0.75-1.0

0.83

6.5

osc.

4x8x
sx/sx0 (L & H)

1.2

no osc.

Horizontal emittance growth does not contribute luminosity drop incollision with a large crossing angle, when by is large.
Crab waist on in the simulation. CW-off may be serious for the horizontal
emittance growth.

osc.

Summary• SuperKEKB collision starts now, Mar 2018 (Phase II).
• Beta function is squeezed step-by-step.
• From the beam dynamics, these two issues are focused now.
1. IR nonlinearity. This becomes serious for squeezing beta*. Tuning using IR
multipole knob. Measurement of IR (chromatic) optics.
2. Coherent beam-beam in head-tail mode. Instability is seen in detuned beta,
but disappears squeezing beta*. The experiment is important for future collider
designs, and is good exercise for the commissioning.

Also studies to be continued
3. Electron cloud/ion
4. Impedance issues

Impedance estimation- transverse• Tune shift as function of bunch current
1 𝑁𝑟𝑒 𝐿 𝑖𝑍𝑒𝑓𝑓∆𝜈𝑥 = 3/2
𝛾 𝜈𝑥 𝜎𝑧 𝑍04𝜋𝑖𝑍𝑒𝑓𝑓 = 31 𝑥

LER x

53 𝑦 𝑘Ω/𝑚

HER y

∆𝜈𝑥
HER𝐼(𝑚𝐴)∆𝜈𝑥
LER𝐼(𝑚𝐴)= 58.2𝑖𝑍𝑒𝑓𝑓 = 43 𝑥

145 𝑦 𝑘Ω/𝑚𝑖𝑍𝑒𝑓𝑓 (𝑘Ω) = 33.3

Collimatordependence

KEKB-LER: -0.0034mA-1, 81kW/mcoll. open 33-46 kW/m T. Ieiri, EPAC00

Longitudinal impedance issueBunch length measurement•LMeasured by a Streak camera
The behaviors are similar as KEKB for both of LER and HER.
Bunch lengthening is stronger than that of simulation.

KEKB impedance model, Y.
Cai