Cooling Scenarios @ Recycler

1. Cooling Scenarios @ Recycler Alexey Burov DOE Review July 2003

2. Introduction • Recycler: 3 km, 8.9 GeV/c, 40π mm mrad ring for cooling and stacking of pbars from the Accumulator. • The goal is to stack (2-6)E12 pbars inside (100-30) eVs and (10-7)π mm mrad with flux (20-45)E10 pbars/hr (tougher numbers – electron cooling goal). • Both electron cooling (EC) and stochastic cooling (SC) are supposed to do the job. • Requires: • Good vacuum • Good MI shielding • Suppression of longitudinal IBS diffusion Alexey Burov

3. Stochastic Cooling Only • Before EC gets functioning, what can be done with SC only? • SC: (0.5-1)(1-2) GHz for ||; 2-4 GHz for . • Scenario: • batches arrive from Accumulator every 3-4 hours; • stacked longitudinally inside ~100 eVs and cooled transversely against gas diffusion to be inside 10πμm; • IBS-driven longitudinal emittance growth is suppressed with proper bunching. • Modeling: • Longitudinal: Fokker-Planck equation where both friction and diffusion include SC and IBS terms. • Transverse: SC – gas diffusion equilibrium Alexey Burov

4. Stochastic Cooling Only: Results • Losses: longitudinal (efficiency of coalescing in MI is a function of the initial phase space) and transverse (finite lifetime due to gas scattering). • Results: • For as good vacuum as 4μm/hr (eff. pressure only 2x of Accumulator), and <10% of total phase space dilution, MI can get 2E12 pbars in 363 eVs. • For 8μm/hr, MI gets 1.4E12 pbars • Conclusion: With SC only (no EC), benefits of Recycler integration are marginal. Alexey Burov

5. Longitudinal Distribution Longitudinal evolution after the last injection (SC-IBS equilibrium). Black: before the injection, red: just after, all other: changes after every ¾ hour. The number of particles 3E12, the total time is 3 hours. Alexey Burov

6. Efficiency of Coalescing in MI Efficiency ofcoalescing, %, as a function of the initial phase space area (by I. Kourbanis). Alexey Burov

7. S-Cooling, Gas Heating and Lifetime dependence of thelifetime on the beam emittance (by V. Lebedev) Alexey Burov

8. E-Cool+ Tools & Goals Alexey Burov

9. Cooling Process • Every repetition interval, a new pbar batch is injected in RR. • The batch can be either kept separated from the accumulated stack for one more repetition interval, or immediately merged with the stack. • A reason for separation is batch transverse stochastic pre-cooling (BSC), which would make the following EC more effective. To make BSC faster, the batch phase space can be deliberately inflated. The goal for BSC is to make batch and stack emittances equal. • EC may be off for the batch. • After BSC, the batch is merged with the stack, and a new batch is injected on its place. • The stack is both e-cooled and s-cooled (, gated, for tail pbars). • The stack is properly compressed ||, to suppress longitudinal IBS emittance growth ( IBS is weak for RR). • After the merger, the stack phase space is increased by the batch. EC has to cool it down to design value (30 eVs) for rep. time (1 hr). • Transverse EC acts against gas diffusion. • To prevent core over-cooling, e-beam can be deliberately misalign. Alexey Burov

10. Cooling Simulations • The whole process is modeled by Monte-Carlo simulations. • SC: cooling + diffusion. • EC: cooling rates are functions of 3 pbar actions for given e-beam parameters (currentlength, radius, effective temperature). • EC rates have been analytically calculated by averaging of the friction power over pbar phases and e-beam angle distribution, assuming it Gaussian (5D integrals). • Two-stage simulation: 1. BSC and 2. after-merger EC+SC • IBS diffusion can be neglected for proper compression (checked by Bjorken-Mtingwa formulae). • Several scenarios are presented to show a space of possibilities. Alexey Burov

11. IBS (Phase space diffusion)  (bunching)^2 x (momentum diffusion). With more compression, || IBS diffusion goes down due to • bunching^2 • vz/vx gets closer to equilibrium (Fig. below with red as direct B-M calculation). Alexey Burov

12. Small emittance, nominal e-current Alexey Burov

13. Small emittance: vacuum for e-current Alexey Burov

14. Nominal emittance, nominal e-current Alexey Burov

15. Nominal emittance: vacuum for e-current Alexey Burov

16. Space Charge and Coherent Instabilities • The space charge tune shift for max number of stacked pbars, small emittance scenario is as high as 0.08, which is not far from the conventional limit 0.10-0.15 . • There is no Landau damping up to frequencies • Thus, a broadband feedback up to SC lower frequency is required. • Growth time due to resistive wall is calculated as 300 turns at lowest frequency. Alexey Burov

17. Conclusions • Pbar stacking goals require to be inside a certain volume in the space of parameters (vacuum, e-current, e-angles, s-cool, acceptance, …). • For moderately good vacuum eff pressure = 4x AA  pencil beam lifetime = 200 hr and good alignment rms e-angle (1D) = 0.2 mrad e-current = 0.5 A is sufficient. • For better vacuum, current requirements are reduced. • The stack bunching varies during cooling. E-current may be either DC or pulse with the same pattern. • For the same e-current, e-angles and vacuum, the stack emittance can be as any value between 3 and 10 mm mrad. Discussions with D. McGinnis and V. Lebedev were essential for this work. Alexey Burov

18. Alexey Burov