1. Beam Dynamics in MeRHIC Mike Blaskiewicz On behalf of MeRHIC/eRHIC working group

2. Outline Linac Design and BBU Study Energy losses and compensation Electron Errors Coherent Synchrotron Radiation 2

3. Linac 1 Linac 2 Main ERLs; 6 cryomodules x 6 cavities x 18 Mev/cav = 0.65 GeV per linac 0.75, 2.05, 3.35 GeV 4 GeV 0.1, 1.4, 2.7 GeV Pre-accelerator 90 MeV ERL Electron gun 0.1 GeV Bunch: Q b =5 nC, σ z =2mm E inj /E max = 100MeV / 4GeV 3 acc./decel. passes N cavities = 72 (total) L module/period = 9.6 / 11.1m E f = 18.0 MeV/cav dE/ds ~ 10 MeV/m Linac Constant Gradient Quads (E. Pozdeyev) 3 Arcs not shown

4. Linac Scaled Gradient Quads Linac 1 Linac 2 Main ERLs; 6 cryomodules x 6 cavities x 18 Mev/cav = 0.65 GeV per linac 0.75, 2.05, 3.35 GeV 4 GeV 0.1, 1.4, 2.7 GeV Electron gun 0.1 GeV G max ~ 500 G/cm Quad strength G min ~ 100 G/cm Scaling gradient with energy produces more focusing and increases BBU threshold (E. Pozdeyev) 4

5. Beam Breakup Modes calculated with CST Simulations using GBBU 20 ms simulation time Single mode at a time with varying spreads in resonant frequency. One degree (+360n) of betatron phase advance in arcs is optimal. Constant gradient quads. (J. Kewisch)

6. Energy loss and compensation for dog bone design

7. Racetrack design improves things Increase in normalized emittance and energy spread are significantly reduced in the new racetrack lattice. Any corrections should be easier. Y. Hao

8. Beam losses Touschek – Total loss beyond ±6 MeV is 200 pA. – Small but, maybe, not negligible. We will look more carefully. Scattering on residual gas (elastic) – Total loss beyond 1 cm aperture at 100 MeV is 1 pA – Negligible Bremsstrahlung on residual gas – Total loss beyond ±6 MeV is < 0.1 pA – Negligible (A. Fedotov, G. Wang) 8

9. MeRHIC - CSR effect after passing 10 arcs with local bending radius of 6.2m and 1 arc with 7.2m (100MeV is not included) 9 rms bunch length  s =2mm (no shielding)  s =4mm (no shielding)  s =2mm (h=2cm)  s =2mm (h=1cm) Energy loss: -  E, MeV 83.22.1e-58e-18 -  E/E (relative energy loss, at 100MeV – our lowest energy arc) 0.080.03 RMS energy spread  E rms, MeV 5.72.26  E/E) rms (relative energy spread, at 100MeV) 0.060.02 Shielding suppression factor =P coh (shielded)/ P coh ( unshielded) 2.6e-61e-18 A. Fedotov

10. Some issues with CSR One experiment did not show expected theoretical reduction (with shielding) even in energy loss due to CSR. 2. Another experiment studied synchrotron radiation rather than effects on the beam – also some issue were reported, like disagreement with theory for small gap sizes, etc. While there seems to be a clear picture about suppression of CSR power loss with shielding, effect of shielding on energy spread is less transparent. Transient effects. Simple, well-controlled experiment is desired to address these issues. ATF@BNL is ideally suited for such an experiment. A. Fedotov

11. ATF@BNL proposal (April 2009) Team: A. Fedotov, D. Kayran, V. Litvinenko (C-AD, BNL), P. Muggli (USC), V. Yakimenko (ATF, BNL), others Experimental goal: To have a quantitative study of CSR suppression with shielding due to vacuum chamber. Measurements will be compared with detailed simulations of CSR which will including shielding and transient effects. A. Fedotov

12. Experiment description Construct and install a system of two vertical plates with controllable gap between the plates to be placed inside the vacuum chamber of bending magnet. Beam parameters will be chosen to enhance CSR effect without shielding. Energy loss and energy spread will be measured for various values of the gap between the plates. Measurements will be done both for Gaussian and square-shape longitudinal beam profiles. Measurements will be compared with detailed simulations. Experiment: approved May 2009 Constructed: September 2009 Measurements: ongoing A. Fedotov

13. Work in progress V. Yakimenko, APEX09, November 2009

14. Electron beam fluctuations The correlation relation leads to a Lorentz distribution frequency spectrum 1/(α 2 ω 0 2 +ω 2 ), ω 0 is the RHIC revolution frequency More realistic than white noise. Reduction factor R A quad example: α = 0.06 Q = 0.685 R = 0.06 (C. Montag, M. Blaskiewicz) 14 Ion emittance growth for fluctuations in electron bunch charge/emittance steering fluctuations

15. Conclusion Main Linac design nearly developed – Constant gradient: weak identical quads, similar arcs, sufficiently high BBU threshold – Scaled gradient: higher BBU threshold, baseline No showstoppers have been found in beam dynamics studies. Work to do – Linac details – Ion trapping and countermeasures – Check CSR issues – Electron Noise, what is the spectrum? 15