1. Alexei Fedotov, 02/02/12 1 Potentials for luminosity improvement for low-energy RHIC (with electron cooling) February 2, 2012

2. Alexei Fedotov, 02/02/12 2 Beam dynamics luminosity limits for RHIC operation at low energies Some fundamental limitations come from: Intra-beam Scattering (IBS): Strong IBS growth at lowest energies- can be counteracted by Electron cooling Beam-beam: Becomes significant limitation for RHIC parameters only at  > 20. Space-charge: At lowest energies, ultimate limitation on achievable ion beam peak current is expected to be given by space-charge effects.

3. Alexei Fedotov, 02/02/12 3 Luminosity limitation by space-charge and beam-beam Luminosity expressed through beam-beam parameter  Luminosity expressed through space-charge tune shift  Q: Single-bunch luminosity (shown for  *=10 m) limitation of Au ions in RHIC: 1) magenta line – limitation due to beam-beam parameter of 0.015 (such values could not be reached without exceeding space-charge limit first) 2) limited by space-charge tune spread  Q sc =0.03 (blue, lower curve), 0.05 (red, solid line) and 0.1 (black, upper dash curve). Ratio of space-charge tune spread to beam-beam spread at low-energies in RHIC for rms bunch length 2 m (red) and 1 m (blue, upper dash line).

4. Alexei Fedotov, 02/02/12 Cooling of bunches with nominal length (1-2 m rms): Improvement comes mostly from counteracting IBS and longer stores. Expect larger gain for higher energies. 4

5. Alexei Fedotov, 02/02/12 5 With e-cooling at 3.85 GeV/n (sqrt[s]=7.7) factor 3 (in average Luminosity) x 1.5 (duty factor between stores, assumes 6-7 minutes between fills)=4.5 with cooling no cooling

6. Alexei Fedotov, 02/02/12 6 E-cooling benefits with nominal bunch length 1.Electron cooling can provide significant luminosity improvement for low-energy RHIC operation: - sqrt[s] < 11 GeV/n : factor 3-6 - sqrt[s]=11-16 GeV/n: about factor of 6 - sqrt[s]=16-20 GeV/n: factor 6-10 (additional factor at higher energies comes from cooling of transverse emittance to the space charge limit and decrease of  *) 2. Electron cooling offers longer stores with relatively constant luminosity. 3. Present choice of the cooler with electron energy up to 5MeV will extend cooling all the way up to present injection energy with heavy ions. As such, if needed, pre-cooling of transverse and/or longitudinal emittance can be done for high- energy program as well. At least factor of 3-6 gain in luminosity for all low energies with nominal bunch length (1-2 m rms, 28 MHz RF)

7. Alexei Fedotov, 02/02/12 Additional gain in luminosity is possible if one can tolerated operation with longer bunches (9MHz RF) for lowest energies: Since we are limited by space-charge, we cannot cool transverse emittance at lowest energy points of interest (sqrt[s] < 11 GeV/n). If bunch length is relaxed, we can now cool transverse emittance which in turn allows to reduce  *. Losses on transverse acceptance will be minimized as well. 7

8. Alexei Fedotov, 02/02/12 8 Luminosity limitation by space-charge Luminosity expressed through space-charge tune shift  Q sc : When also limited by transverse acceptance (which is the case for RHIC lowest energy points): f(  s /  *) f(  s /  *)*(  s /  *) hour-glass function

9. Alexei Fedotov, 02/02/12 Projection for luminosity improvement 9 Projection of total (without vertex cut) luminosity for 111 bunches of Au ions in RHIC with electron cooling and long bunches (for  s /  *=3) for the space-charge tune spread  Q sc =0.05 (red, solid curve) and 0.1 (blue, dash curve), and without cooling  Q sc =0.05,  s /  *=1/3 (magenta). Magenta (without cooling) – is optimistic projection which does not include losses on transverse acceptance and assumes very short stores to maximize average luminosity. Expect to get within factor of 2 of this line. Assumes acceptance limitation <  =4 (if <  =6, such drop in luminosity would start at  =6). expect with cooling

10. Alexei Fedotov, 02/02/12 10 E-cooling benefits and longer bunch length Operation with longer bunches allows to get more benefits from cooling at lowest energy points as well: (additional factor comes from cooling of transverse emittance to the space charge limit and decrease of  *) About factor of 10 gain in total luminosity for all low energies with longer bunch length. Some gain will be upset if detector length is not optimized for longer bunches.

11. Alexei Fedotov, 02/02/12 Electron cooler for Low-energy RHIC 11 1.Available working DC accelerator Pelletron from FNAL – suitable for cooling: < sqrt[s]=20 GeV/n: requires 3-4 years from the start of the project with full commitment of needed resources from C-AD. 2.RF-gun bunched beam electron cooler - can be designed to go above sqrt[s]=20 GeV/n: longer time scale and R&D needed. Different approaches are possible:

12. Alexei Fedotov, 02/02/12 12 Low-E RHIC Electron cooler @IR4: Q3 E-cooler: Recycler’s 6MV Pelletron (FNAL) RHIC beams

13. Alexei Fedotov, 02/02/12 13 Status of Pelletron-based (FNAL) cooler for RHIC Cost estimate of the project June 2010 (done) Estimate of C-AD manpower December 2010 (done) Feasibility study completed December 2010 (done) Start of the project ? January 2011 – did not start Due to significant resources required from C-AD, project is put on hold until decisions by Experiments are made at what energies significant increase in luminosity is required for future low-energy program at RHIC. October 2011: FNAL was informed that C-AD does not plan to start the project until needs from Experiments are fully established. March 2012: FNAL will start to decommission cooling section without assumption that it will be used for RHIC. For luminosity improvement need 3-4 years from the start of the project assuming full commitment of all needed resources from C-AD.