Recent Beam-Beam Simulation for PEP-II

Yunhai Cai

December 13, 2004

PEP-II Machine Advisory Committee Meeting at SLAC

Acknowledgment

Beam-beam study group: John Seeman (PEP-II, SLAC) Witold Kozanecki (PEP-II, BaBar) Ilya Narsky (BaBar, Caltech) Frank Porter (BaBar, Caltech)

Nonlinear map: Yiton Yan (ARDA, SLAC)

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

Outline

• New PC cluster• Nonlinear maps• Closed orbit and tune

shift due to parasitic collision

• Crossing angle and parasitic collision

• Intensity• Year of 2007• Conclusion

SLAC PC FARM

• Linux cluster interconnected with 64-bit PCI-X (PCIXD, Lanai X) Myrinet 2000.

• All nodes are 2.6GHz dual-Xeon Pentium IV Rackable systems running RHEL 3.0.

• These are 128 of our 384 node Linux cluster.

• 20% faster than seaborg at NERSC for beam-beam simulation using 32 processors.

• We own 25% of the cluster.

Scaling on Parallel Supercomputers

Recently, SLAC has installed a Linux clusters with 128 processors. We have high priority on the cluster because of our contribution $50,000 to the purchase.

SP(IBM), T3E(CRAY), ALVAREZ(LINUX PC) are the super computers at NERSC. We gain a factor of 24In speed with 32 processors on theSP.

Main Features in the Code: Beam-Beam Interaction (BBI)

• Arbitrary beam distributions• Precision Poisson solver for the core • Equal-spacing or equal-area longitudinal slices• Linear interpolation between the slices• Numerical convergence in all three dimensions• Radiation damping and quantum excitation • Linear or nonlinear map for the lattices• Gaussian beam-beam kicks • Parallel supercomputing with 32 processors• Crossing angle and parasitic collisions• Object-oriented in C++ with MPI library

PEP-II with a Crossing AngleOctober 9, 2003

For a half angle of 3.0 mrad, we see a degradation of luminosityby 43%. Similar results have been obtained by Ohmi and Tawada using their code.

Luminosity Reduction due to Parasitic Collisions

April 15, 2004

The smaller y makes

more degradationto the luminosity In terms of the absolute values but not in relative ones. The reduction is about7% in both cases.

With 1412 bunches,we can achieve 1x1034 cm-2s-1 when*y = 7mm withoutIncreasing beam currents.

7.125x1030cm-2s-1

Comparison of map and element-by-element tracking (5y/step)

6th order

8th order

Taylor map (Zlib) Mix-variable generating function (Zlib)

element-by-element tracking (LEGO)

Parameters Description(5/21/2004) LER(e+) HER(e-)

E(Gev) beam energy 3.1 9.0

N bunch population 6.97x1010

(1.52mA)

4.40x1010

(0.96mA)

x*(cm) beta x at the IP 32 32.0

y*(cm) beta y at the IP 1.05 1.05

x(nm-rad) emittance x 22.0 59.0

y(nm-rad) emittance y 1.40 1.30

x x tune 0.5162 0.5203

y y tune 0.5639 0.6223

s synchrotron tune 0.029 0.049

z(cm) bunch length 1.30 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

PEP-II Parasitic CollisionsMay 21, 2004

crossing[m] x[mm] # of (e+) # of (e-)

0.32 0.1 0.84 0.51

0.63 3.22 17.38 10.61

0.95 9.69 36.87 22.51

1.26 17.78 52.16 31.85

1.58 28.86 68.28 41.69

1.89 43.6 86.75 52.97

2.21 60.53 103.38 63.13

2.52 77.61 116.52 71.15

2.84 94.73 126.41 77.19

3.15 112.31 135.28 82.61

Head-on Collision and Parasitic Collisions

• Head-on collision is calculated with particle-in-cell method

• Gaussian approximation is used for parasitic crossing and beam size is updated every 1000 turns

• Only the nearest parasitic crossings are included

• Drift is used between the parasitic collisions and head-on collision 2

2

2

2

x

Nr

x

Nr

yey

xex

Tune shift from parasitic collision

x

Tune Shift Due to Parasitic Crossings

LER(e+) HER(e-)

Horizontal -0.000958 -0.000523

Vertical 0.0233(0.026) 0.0123(0.014)

Two nearest parasitic collisions are included in the calculation. Single parasitic collision contributes half of the value.

Closed Orbit at the Interaction point due to Parasitic Collisions

• Horizontal kick:

• Nominal bunch:

x

rN ex

2

0))2cos((sin2

)cos(sin2

0*

0*

IP

2

Packman bunchor

e+: 3.81 m, 1.40 rade-: 2.07 m, 0.78 rad

Closed Orbits due to Parasitic Collisions in Beam-Beam Simulation

The angles of the orbits are so small that they do change theluminosity in the simulation.

x0+=x0

-=0

Luminosity Effects of Parasitic Collisions and Its Compensation

mmy 5.10*

Luminosity degradation due to parasitic collisions is about 5%.

The luminosity degradation can be completely recovered by the tune shifts in vertical plane for the machine parameters, May 21, 2004.

mmy 5.10*

Tune shift can be corrected byresetting the tune when the separation is larger enough compared to the beam size.

mmy 5.10*

Tune shift seen in the spectrumis consistent with the analyticcalculation.

Parasitic Collisions and Crossing Angle at PEP-II

Compared with the measured luminosity: 5.61 1030 cm-2s-1, the simulation result with -0.2mrad is closer.

Trade off between Parasitic Collisions and Crossing Angle

Best luminosity achieved when the vertical beam sizes are small and matched.

Dependency of Beam Currentswith Parasitic Collisions and Crossing angle

(-0.2mrad)

Luminosity

SpecificLuminosity

8x1030

5x1030

Beam Blowup as Currents Increasewith Parasitic Collisions and Crossing Angle

(-0.2mrad)

m

m

y

x

40.5

154

mx 59

Beam-beam scan at low current:

%56%,2

%43%,14

yx

yx

Luminous region from BaBar:

Blowup of beams:

Beam-Beam Parameters with Parasitic Collisions

)(2

)(2

2

0

yxx

xex

yxy

yey

yey

Nr

Nr

fN

Lr

May 21, 2004:

0465.0,1223.0

0413.0,0535.0

yx

yx

0.08

0.06

0.20

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

E(Gev) beam energy 3.1 9.0

N bunch population 12.03x1010

(2.62mA)

5.88x1010

(1.28mA)

x*(cm) beta x at the IP 28 28.0

y*(cm) beta y at the IP 0.8 0.8

x(nm-rad) emittance x 60.0 60.0

y(nm-rad) emittance y 1.0 1.0

x x tune 0.5162 0.5203

y y tune 0.5639 0.6223

s synchrotron tune 0.032 0.055

z(cm) bunch length 0.9 0.9

p energy spread 6.5x10-4 6.1x10-4

t(turn) transverse damping time 9800 5030

l(turn) longitudinal damping time 4800 2573

PEP-II Parasitic CollisionsYear of 2007

crossing[m] x[mm] # of (e+) # of (e-)

0.32 0.1 0.51 0.51

0.63 3.22 10.09 10.09

0.95 9.69 21.14 21.14

1.26 17.78 29.76 29.76

1.58 28.86 38.85 38.85

1.89 43.6 49.30 49.30

2.21 60.53 58.70 58.70

2.52 77.61 66.12 66.12

2.84 94.73 71.71 71.71

3.15 112.31 76.72 76.72

Tune Shift Due to Parasitic CrossingsYear of 2007

LER(e+) HER(e-)

Horizontal -0.00139 -0.00098

Vertical 0.0406 0.0286

Two nearest parasitic collisions are included in the calculation. Single parasitic collision contributes half of the value. Values are nearly doubledcompared to ones in 2004.

Luminosity Degradation due to Parasitic Collisions (Year of 2007)

-76%

Without parasitic collisions, the total luminosity = 1715x1.51x1031

cm-2s-1 = 2.59x1034cm-2s-1 compared to Seeman’s expected value: 2.4x1034cm-2s-1.

mmy 8*

mmy 8*

mmy 8*

mmy 8*

Tune and Crossing Angle Compensation for Parasitic Collisions

x = 3.85 mm at = -0.5mrad (3.22mm at =0) which isabout 12 x separation.

Expected luminositycan be achieved withtune compensationand small crossingangle (-2x0.5mrad).

1.55x1031

Crossing Angle and More Separation

Really Need Crossing Angle?

Yes. It helps litter but main gain is from the separation!

Future Work

• Detailed tune scan near half integer tune• All possible machine errors, including

coupling and dispersions • Symplectic tracking of non-linear map• Calculate beam-beam lifetime with

nonlinear maps & parasitic collisions• More study of upgrades scenarios• Combined effects of electron cloud and

beam-beam

Conclusion• Progress has been made to symplectify Taylor map. The

improvement of computational speed allows us to include machine nonlinearity in the beam-beam simulation. This is critical for beam-beam lifetime calculation.

• For current parameters, the luminosity degradation due to the parasitic collisions is about 5% which can be simply recovered with a change of the vertical tunes.

• Our simulation confirms the experimental observation that there is a possible trade off between a larger separation of parasitic collisions and small crossing angle.

• For 2007 machine parameters, the degradation of luminosity is much large, about 75%. However, the simulation shows that the degradation can be partially recovered by resetting the vertical tunes and full recovery requires further separation of beams at parasitic crossing point to 3.85 mm (12 x). Under these conditions, the simulation confirms that John’s expected value of luminosity can be achieved.

Expectations and Suggestions

• “lowering of x*(50cm->32cm)” in the LER should be backed out because it increases x and beam size at the parasitic collision points and makes beams more mismatched in the head-on collision.

• We should see stronger effects of parasitic collisions once wigglers is turned on. That implies that we may need to separate beams sooner rather than later.

• Parasitic collision may prevent us from moving closer to the half integer because the dynamic beta and emittance increase the beam size at parasitic crossings.

• We suggest to have more experiments to measure these effects and compare them to our simulation.