Beam-Beam Simulation for PEP-II

Yunhai Cai

January 18, 2006

Machine Advisory Committee Meeting at SLAC

Acknowledgment

Beam-beam task force: John Seeman (co-chair, PEP-II, SLAC) Uli Wienands (PEP-II, SLAC) Kiran Sonnad (PEP-II, SLAC) Franz-Josef Decker (PEP-II, SLAC) Witold Kozanecki (PEP-II, BaBar)

MIA model and nonlinear map: Yiton Yan (ARDA, SLAC)

Benchmark codes: Kazuhito Ohmi (KEKB) Masafumi Tawada (KEKB) Joe Rogers (CESR, Cornell)

Outline

• Introduction• Crossing angle

experiments• Low specific luminosity• Peak luminosity: 1034 cm-2s-1, last

October• Effects of linear optical

errors• Projected luminosity• Future plan

Simulation Tools

• Self-consistent and strong-strong code running on a parallel PC cluster at SLAC

• Include crossing angle and parasitic collisions• Benchmarked to many beam-beam experiments

at PEP-II• Benchmarked against KEKB code at both the

current operating condition and super-B parameters

• Being used to optimize the PEP-II operation

Crossing Experiments at PEP-II• Simulation was carried out prior to

the experiments to make sure there was enough sensitivity.

• ‘By-4’ bunch pattern to avoid parasitic collision (30 x

- separation).• The orbit bump used to change the

angle. The knob was carefully calibrated against a pair of BPMs next to the IP.

• Luminosity feedbacks were on to align beams transversely after each change.

• Tune changes were necessary to compensate the optical errors introduced from the nonlinearity of the fringe field and magnets inside the bumps.

0.75

0.80

0.85

0.90

0.95

1.00

1.05

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Half crossing-angle q c (mrad)

Lsp

/ L

sp (

q c=0)

Sim: 0.16/0.09 mA/b

Sim: 1.35/0.85 mA/b

by-4, 1.43/0.89 mA/b

by-4, fit

geometric

Experiment of Crossing Angle and Parasitic Collisions

• ‘By-2’ bunch pattern was used to include parasitic collisions (3.2 mm or 11x

- nominal separation)

• Crossing angle and the separation of parasitic collisions are related: x = x0 -2qsc. The corresponding range of separation is 3.6 to 2.7 mm.

• Both simulation and experiment showed small nonzero crossing angle are preferred to move away from the parasitic collisions.

• It is not clear why the optimum luminosity is actually better when both parasitic collisions and crossing angle are present than the head-on collision without the parasitic collision.

0.75

0.80

0.85

0.90

0.95

1.00

1.05

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Half-crossing angle q c (mrad)

Lsp /

Lsp

(q c

=0

)

No parasitic

withparasitic

0.75

0.80

0.85

0.90

0.95

1.00

1.05

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Half crossing-angle q c (mrad)

Lsp

/ L

sp (q c=0)

Sim. with PCSim. w/o PCby-2, 1.4/0.9 mA/bby-2, fit

measurement

Specific Luminosity for PEP-II

Developed a Link between MIA and LEGO

• Load the fitted K1 values to LEGO to reconstruct the optics models

• Steer x and y orbits to the design orbits with a residual difference at 100 microns level

• Move all sextupoles to compensate the optical effects due to the residual orbit

• Achieved a good agreement between MIA and LEGO

• Use LEGO to compute equilibrium beam distribution and emittances

MIA/LEGO Models

May 25, 2004 August 9, 2005 August 24, 2005

x*[cm] 50.10 17.50 23.38

y*[cm] 1.34 1.28 1.21

x*[mm] -33 -25 -23

y*[mm] 0.56 1.73 2.65

q*[mrad] -21 -30 -37

a*[m] 125 94 101

b*[m] 5.45 5.00 6.55

x[nm-rad] 30 45 39

y[nm-rad] 1.4 1.5 1.4

MIA/LEGO ModelsMay 25, 2004 August 9, 2005 August 24, 2005

x* -0.20 -0.16 -0.32

y* 0.015 0.018 -0.02

x*[m] 125 94 101

y*[m] 6.08 5.80 7.55

x 0.5157 0.5272 0.5221

y 0.6129 0.6199 0.5979

s 0.029 0.029 0.029

w11* 0.020 0.028 0.0197

w12* 0.012 0.0044 0.0122

w21* 0.245 -2.147 -0.428

w22* 0.494 0.285 -0.100

Lb Lsp x+

[m]x

- [m]

y+

[m]y

- [m]

x

[m]

y

[m]

August 24, 2005

4.96 3.50 77 100 7.58 4.65 126 8.75

x+=30nm 5.19 3.66 66 101 6.86 4.94 121 8.45

x+=50cm 3.89 2.75 111 102 8.39 3.89 151 9.25

x+=0.5157 4.90 3.46 76 100 7.69 4.41 126 8.86

x+=40cm

x+=23nm

5.21 3.68 75 100 6.96 4.57 125 8.32

x+=0.5157 5.18 3.65 73 100 7.00 4.61 124 8.38

+) y+=0.5639 5.79 4.08 71 101 5.76 4.99 123 7.62

Horizontal Dispersion Knob

• Dispersion is not fitted in MIA. Good agreement between the measurement and model was a pleasant surprise

• A dispersion knob based on 24 asymmetric horizontal orbit bumps was built to adjust horizontal emittance in the LER

• The knob was used during a normal delivery shift. We gained a few percent of luminosity at a half value of the knob. The setting was left in the machine.

• Later, individual asymmetric horizontal orbit bumps played very important role in achieving the peak luminosity by our operation colleagues as the beam current increased

A Strategy to Improve the Luminosity

PEP-II collider

MIA(YY)

LEGO(YC)

BBI(YC)

FJD,YC

MS,JT

Model based and adiabatic correction scheme for luminosity improvement.Tuning was done during the delivery and guided by the luminosity reading.

Parameters Description(10/4/05) LER(e+) HER(e-)

E(Gev) beam energy 3.1 9.0

Nb bunch population 7.783x1010

(1.70 mA)

4.585x1010

(1.00 mA)

x*(cm) beta x at the IP 40 35.0

y*(cm) beta y at the IP 1.08 1.08

x(nm-rad) emittance x 33.0 55.0

y(nm-rad) emittance y 1.50 1.30

x x tune 0.5250 0.5160

y y tune 0.5790 0.6223

s synchrotron tune 0.032 0.049

z(cm) bunch length 1.25 1.15

p energy spread 6.5x10-4 6.1x10-4

t(turn) transverse damping time 9800 5030

l(turn) longitudinal damping time 4800 2573

Peak Luminosity October 10, 2005(I+=2940mA, I-=1733mA, nb=1732)

Data taken in the history buffer for a 24 hours period. The simulation used an approximately fixed current ratio.

037.0

086.0

070.0

098.0

y

x

y

x

beam-beam parameters:

Specific Luminosity October 10, 2005(I+=2940mA, I-=1733mA, nb=1732)

Data taken in the history buffer for a 24 hours period. The simulation used an approximately fixed current ratio.

Definition of Coupling Parameters

,cossin

sincos

0

0

cossin

sincos

2

1

Iw

wI

u

u

Iw

wIM

Given one-turn matrix M, we can decouple it with a symplectic transformation:

where u1 and u2 can be parameterized as if no coupling case and w is asymplectic matrix:

.

,sincossin

sinsincos

,sincossin

sinsincos

2221

1211

22222

222222

11111

111111

ww

www

u

u

We have det(w)=1. There are ten independent parameters. Bar notessymplectic conjugate.

Luminosity Degradation due to Coupling at the IP (s=sin)

sW11=0.012

sW21=1.0 (m-1)

sW12=0.003 (m)

sW22=0.15

Beam Size at the Interaction Point

,cossin)2(

,sin)2(cos2

222

12

121121112

111332

22

212212222

2222

21111

2

wwww

wwww

y

x

In general coupled lattice, we have

where are Courant-Snyder parameters in the eigen modes, w11,w12,w22,are four coupling parameters, and is eigen emittance.

1. In an electron storage ring, usually 1>>2

2. 1 and 2 are invariant in a ring.

3. w21 does not appear in the beam size directly.

4. Most time, 1=0, 1<1.0, the most sensitive parameter to luminosity is w12.

MIA/LEGO Models on October 4, 2005 (s=sin)

• High energy ring: sw11 = 1.27x10-2, sw12 = 8.48x10-3

sw21 = -0.924, sw22 = 0.262• Low energy ring:

sw11 = 6.13x10-3, sw12 = 1.50x10-2

sw21 = -2.07, sw22 = -0.82• Luminosity was reduced by a factor of two if we

used these coupling values in the simulation• Final empirical tuning based on the luminosity

monitor by our operation colleagues are very important to reach the high luminosity

Underline Assumptions for the Projected Luminosity: 2E34 cm-2s-1

• HER 900 lattices to lower momentum compaction factor and beam emittance

• Low-beta optics near y* = 8 mm

• Use wiggler in the LER as a damping wiggler• More RF stations in the HER, LER?• More currents 4000/2200 mA in the machine• Shorten the bunch length to 9 mm• Adequate dynamic aperture to ensure a good

beam-beam lifetime

Parameters Description(2007) LER(e+) HER(e-)

E(Gev) beam energy 3.1 9.0

Nb bunch population 1.066x1011

(2.325 mA)

5.865x1010

(1.279 mA)

x*(cm) beta x at the IP 30 30

y*(cm) beta y at the IP 0.85 0.80

x(nm-rad) emittance x 30.0 40.0

y(nm-rad) emittance y 1.20 1.80

x x tune 0.5162 0.5203

y y tune 0.5509 0.6103

s synchrotron tune 0.0381 0.049

z(cm) bunch length 0.95 0.90

p energy spread 6.5x10-4 6.1x10-4

t(turn) transverse damping time 8424 5030

l(turn) longitudinal damping time 4128 2573

Projected Luminosity in 2007

Simulated by Kiran Sonnad

Projected Luminosity: 2E34 cm-2s-1

Simulated by Kiran Sonnad

Future Plan

• Build coupling knobs at the interaction point and calibrate them with experiments

• Study a scheme of using a magnetic wire to compensate parasitic collisions

• Implement nonlinear errors into the beam-beam code including chromatic effects

• Reliably calculate both beam-beam lifetime and luminosity

Conclusion• A link from MIA to LEGO has been developed to make a complete

machine model, including beam parameters and nonlinear effects• Along with the optics models, beam-beam simulation have been

judicially applied to improve the PEP-II luminosity with some successes

• The peak luminosity 1E34 cm-2s-1 is reproduced with a good accuracy by the simulation using the input parameters generated by the optics models

• Linear optics errors are implemented in BBI code. The simulation showed at the coupling errors at the interaction point could significantly reduce the luminosity. The simulation indicates that the coupling at the IP in our models could not achieve the accuracy required for high luminosity

• A set of consistent machine and beam parameters were optimized with simulation to achieve luminosity of 2E34 cm-2s-1 in 2007