1. Beam-beam Simulation at eRHIC Yue Hao Collider-Accelerator Department Brookhaven National Laboratory July 29, 2010 EIC Meeting at The Catholic University of America

2. 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)

3. 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

4. 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.

5. Parameter Table for eRHIC eRHIC (previous nominal) eRHIC (new nominal) eRHIC (new Low e energy with same disruption) PePePe Energy, GeV25010325203255 Number of bunches166 Bunch intensity, 10 11 2.01.232.00.222.00.22 Beam current, mA415 277 415 50 415 50 Rms normalized emittance, 1e-6 m, 1.95.50.18200.1820 Emittance, 1e-9 m3.84.90.52 2.1 β *, cm262055 5 Beam-beam parameter for p; Disruption for e 0.0155.90.01527.10.01527.1 rms bunch length, cm2014.90.24.90.2 Luminosity x 10 33 cm -2 s -1 (with hourglass reduction) 2.2153.9

6. Disruption Effect (Low e Energy) with the nominal parameters ItemsValues Luminosity including the pinch effect x 10 33 cm -2 s -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

7. Disruption Effect (Low e Energy) Suggested optics ItemsValues Emittance [10 -9 m-rad] 4.2 (2x) β*β* 0.025 (0.5x) β waist position s * [m] -0.03 Luminosity including the pinch effect [10 33 cm -2 s -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

8. 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.

9. Power (Beam) loss requirements on APERTURE Aperture of 1KW loss @ Ini. BeerCan Ini. Gaussian 5GeV2.5mm5mm 2.55GeV3.5mm7mm 0.1GeV17mm33mm

10. Mismatch compensation If 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.

11. eRHIC (new nominal) eRHIC (new Low e energy with same disruption) eRHIC (new Low e energy with same luminosity) PePePe Energy, GeV325203255 5 Number of bunches166 Bunch intensity, 10 11 2.00.222.00.222.00.22 Beam current, mA415 50 415 50 415 50 Rms normalized emittance, 1e-6 m, 0.18200.18200.1820 Emittance, 1e-9 m0.52 2.10.52 β *, cm5520555 Beam-beam parameter for p; Disruption for e 0.01527.10.01527.10.015108 rms bunch length, cm4.90.24.90.24.90.2 Luminosity x 10 33 cm -2 s -1 (with hourglass reduction) 153.915 Boost luminosity of Low e-energy set-up

12. Not a problem for electron effects ItemsValues Emittance [10 -9 m-rad] 1.05 (2x) β*β* 0.1 (2x) β waist position s * [m]-0.08 Luminosity including the pinch effect [10 33 cm -2 s -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

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

14. Kink Instability is curable Example: 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.

15. 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.

16. 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.

17. 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/(α 2 ω 0 2 +ω 2 ) 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.

18. 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.

19. The distribution of different disruption (0-108.4)