Beam-beam Simulation at eRHIC

Yue HaoCollider-Accelerator DepartmentBrookhaven National Laboratory

July 29, 2010 EIC Meeting at The Catholic University of America

Outline• Overview of special features in beam-beam

simulation for ERL based EIC– Brief introduction of the code EPIC

• The electron beam effects– Disruption effects– Mismatch and pinch effects

• The ion/proton beam effects– Head-tail type instability (Kink Instability)

• Asymmetric collision– Electron distribution is distorted in one collision.

Single pass simulation is required.– Proton/ion beam is slightly affected, accumulated

effect needs investigation.• Dedicated code EPIC is developed– One pass electron beam tracking– The electron tracking result is used to evaluate

effects for proton/ion beam.– Parallel computation

Special Feature in Beam-Beam Simulation of ERL based EIC

Special Feature - Continued• The Electron beam experiences the focusing

nonlinear field– ‘Real’ emittance growth due to the nonlinearity– ‘Effective’ emittance growth due to the additional phase

advance relative to the design lattice– Is ‘pinched’ to form a much smaller beam size in IR

• The electron beam becomes a wake field for the proton beam and arise a possibility of coherent instability.

Parameter Table for eRHICeRHIC

(previous nominal)

eRHIC(new nominal)

eRHIC(new Low e

energywith same disruption)

P e P e P e

Energy, GeV 250 10 325 20 325 5

Number of bunches 166 166 166Bunch intensity, 1011 2.0 1.23 2.0 0.22 2.0 0.22

Beam current, mA 415 277 415 50 415 50Rms normalized

emittance, 1e-6 m, 1. 95.5 0.18 20 0.18 20

Emittance, 1e-9 m 3.8 4.9 0.52 0.52 0.52 2.1β*, cm 26 20 5 5 20 5

Beam-beam parameter for p; Disruption for e 0.015 5.9 0.015 27.1 0.015 27.1

rms bunch length, cm 20 1 4.9 0.2 4.9 0.2Luminosity x 1033 cm-2s-1

(with hourglass reduction)

2.2 15 3.9

Disruption Effect (Low e Energy)with the nominal parameters

Items Values

Luminosity including the pinch effectx 1033 cm-2s-1

5.7

Average Electron beam size [microns]

9.5

Minimum Electron beam size [microns]

4.5

Designed Electron beam size at IP

[microns]10.1

Disruption Effect (Low e Energy)Suggested optics

Items Values

Emittance [10-9m-rad]

4.2(2x)

β* 0.025(0.5x)

β waist position s*

[m] -0.03

Luminosity including the pinch effect[1033cm-2s-1]

5.1

Average Electron beam size [microns]

11.3

Minimum Electron beam size [microns]

7.5

Designed Electron beam size at IP

[microns]10.1

Different Initial Distribution of e-beam before Interaction

Up: BeerCan Distribution – The Initial distribution out of the gun.

Left: Gaussian Distribution – The equilibrium distribution due to the damping and excitation.

Upper left: Ellipse Distribution – Is assumed to be a distribution during transition.

Power (Beam) loss requirements on APERTURE

Aperture of 1KW loss @

Ini.BeerCan

Ini.Gaussian

5GeV 2.5mm 5mm

2.55GeV 3.5mm 7mm

0.1GeV 17mm 33mm

Mismatch compensationIf aperture is an issue, the mismatch between the beam distribution and design optics can be compensated, since it is mainly an linear effect.

Possible schemes: fast quadrupole, electron lens

Since mismatch is more severe in this case, up to 55% percent reduction in aperture can be achieved.

eRHIC(new nominal)

eRHIC(new Low e

energywith same disruption)

eRHIC(new Low e

energywith same luminosity)

P e P e P e

Energy, GeV 325 20 325 5 325 5Number of bunches 166 166 166Bunch intensity, 1011 2.0 0.22 2.0 0.22 2.0 0.22

Beam current, mA 415 50 415 50 415 50Rms normalized

emittance, 1e-6 m, 0.18 20 0.18 20 0.18 20

Emittance, 1e-9 m 0.52 0.52 0.52 2.1 0.52 0.52β*, cm 5 5 20 5 5 5

Beam-beam parameter for p; Disruption for e 0.015 27.1 0.015 27.1 0.015 108

rms bunch length, cm 4.9 0.2 4.9 0.2 4.9 0.2Luminosity x 1033 cm-2s-1

(with hourglass reduction)

15 3.9 15

Boost luminosity of Low e-energy set-up

Not a problem for electron effectsItems Values

Emittance [10-9m-rad]

1.05(2x)

β* 0.1(2x)

β waist position s* [m] -0.08Luminosity including

the pinch effect[1033cm-2s-1]

16

Average Electron beam size [microns] 7.3

Minimum Electron beam size [microns] 4.5

Designed Electron beam size at IP

[microns]5.1

Kink Instability

,

0 ,

, p p s

b p p s

xW s s

N r x

One turn map for two particle with kick between two particles leads to the matrix over one synchrotron oscillation is:

2

cos sincos sin

cos sincos sin

14 4

4sin

sin

coscos 2

s ss s

ss s

aN aNM N X N

TaN

X N M N

M

X M

aN s4

< 2 ⇒ <8νs

The stability condition is just to keep the Eigen value of T as imaginary number, which requires

The proton beam sees the opposing electron beam as wake field. The wake field can be calculated by simulation. It depends on the position of both leading and trailing particles.

Kink Instability is curableExample: eRHIC – Previous Parameters

For the parameters beyond threshold, use Landau damping to suppress the beam emittance growth. For eRHIC (old parameters), larger chromaticity is needed (5-7 unit) with 5e-4 rms energy spread. The study is undergoing for new parameters.

Feedback stabilization is possible

RHIC

ERL

IP

BPM

Feedback kicker

Kink instability can be stabilized by landau damping by introduce certain amount of chromaticity. However, large chromaticity is unpleasant in real machine operation.

Under this motivation, a feedback scheme is being carried out to stabilize the instability by measuring the electron bunch info after beam-beam interaction.

The info from the previous electron bunch is amplified by certain factor A and feed through the next opposing electron bunch for the same specific proton bunch.

The factor A is determined by proton transverse tune, the position of BPM and kicker. It can also related to the noise level and how frequently the feedback is added.

A preliminary state-of-art illustration

Use eRHIC parameters, to replace required 5-7 chromaticity, feedback loop is introduced.

We measure the transverse offset of the electron bunch after beam-beam collision, multiply a factor ‘Amp’ and apply this offset to next electron bunch with respect to same proton bunch.

Noise effect in the proton/ion beam

•The noise contains in the fresh electron beam is transported into proton/ion beam via each collision.

•The transverse offset presents a dipole-like error for the proton beam; while any error effect beam-beam parameter for proton presents an quad-like kick.

Assuming a white noise spectrum,

Dipole Errors:

Quad Errors:

A Lorentz spectrum is also evaluated (1/(α2ω0

2+ω2) and there will be a reduction factor:

Dipole:

Quadrupole:

To give the reasonable limitation on the electron accelerator stability, We need to evaluate the real frequency spectrum of the

Laser Magnet error

Earth movement.

Summary• We need to fight with electron disruption and

mismatch effects to minimize the beam loss after the interaction.– For both previous and current eRHIC layout, the effects

are studied and no showstoppers are found• The kink instability can be suppressed by

chromaticity. – A possible feedback scheme can also bring the system

stable without unpleasant large chromaticity.• The electron beam noise issue need the

measurements of the real spectrum.

The distribution of different disruption (0-108.4)