Cooling Scenarios Recycler

1
Cooling Scenarios _at_ Recycler

• Alexey Burov
• DOE Review
• July 2003

2
Introduction

• Recycler 3 km, 8.9 GeV/c, 40 p 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) p 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

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 10 p µm
• 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

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 4 µm/hr (eff. pressure only
  2x of Accumulator), and lt10 of total phase space
  dilution, MI can get 2E12 pbars in 36?3 eVs.
• For 8 µm/hr, MI gets 1.4E12 pbars
• Conclusion
• With SC only (no EC), benefits of Recycler
  integration are marginal.

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.

6
Efficiency of Coalescing in MI
Efficiency of coalescing, , as a function of
the initial phase space area (by I. Kourbanis).
7
S-Cooling, Gas Heating and Lifetime
dependence of the lifetime on the beam emittance
(by V. Lebedev)
8
E-Cool Tools Goals
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.

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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
  ECSC
• IBS diffusion can be neglected for proper
  compression (checked by Bjorken-Mtingwa
  formulae).
• Several scenarios are presented to show a space
  of possibilities.

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IBS

• (Phase space diffusion) ? (bunching)2 x
  (momentum diffusion).
• With more compression, IBS diffusion goes down
  due to
• bunching2
• vz/vx gets closer to equilibrium (Fig. below with
  red as direct B-M calculation).

12
Small emittance, nominal e-current
13
Small emittance vacuum for e-current
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Nominal emittance, nominal e-current
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Nominal emittance vacuum for e-current
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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.

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.

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