Antiproton Stacking and Cooling

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					Cooling Scenarios @ Recycler



       Alexey Burov
       DOE Review
        July 2003
                       Introduction

 Recycler: 3 km, 8.9 GeV/c, 40 π 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              2
                 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 π 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



                              Alexey Burov                      3
             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 <10% 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.




                               Alexey Burov                        4
                                             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.


                                                        Evolution After Last Injection




                                   0.8



                                   0.6
          Distrib ution Function




                                   0.4



                                   0.2



                                    0



                                   0.2
                                         0    20   40   60      80        100      120   140   160   180
                                                               Act ion, eV sec




                                                                Alexey Burov                               5
                  Efficiency of Coalescing in MI




Efficiency of coalescing, %, as a function of the initial phase space area (by I. Kourbanis).


                                            Alexey Burov                                        6
                     S-Cooling, Gas Heating and Lifetime

         2W                                                                                                  mx  my
 1 
  
              , with M c  f 0 F ( f 0 / f 0 ) ln( f max / f min ) / W                         s  Ls
                                                                                               
         NM c                                                                                               mx   my
                                                 1

                      Relative beam lifetime




                                                0.1




                                               0.01
                                                      0    10             20             30         40
                                                          Normilized 95% emittance [mm mrad]




                    dependence of the lifetime on the beam emittance (by V. Lebedev)




                                                                        Alexey Burov                                     7
                   E-Cool+ Tools & Goals



Transverse stochastic cooling band (effective)        2.5 – 3.5 GHz
Batch transverse emittances at injection, 95% norm    10  mm mrad
Repetition time                                       1 hour
Pbars flux                                            45 1010 /hour
Pbars in the stack, up to                             600 1010
Stack longitudinal 95% phase area                     30 eVs
E-cooling length                                      20 m
Electron current                                      0.5 A
Electron 1D rms angle in the cooler                   0.22 mrad
Electron beam radius / pbar rms size                  2.5
Beta-function in the e-cooler                         22 m




                                       Alexey Burov                    8
                          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                            9
                    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                        10
                                                       IBS
(Phase space diffusion)  (bunching)^2 x (momentum diffusion).
With more compression, || IBS diffusion goes down due to
a)   bunching^2
b)   vz/vx gets closer to equilibrium (Fig. below with red as direct B-M
     calculation).


                                              IBS longitudinal heating
                         1


                        0.8
         d/dt(dp/p)^2




                        0.6


                        0.4


                        0.2



                              0   0.2   0.4      0.6    0.8       1      1.2   1.4   1.6
                                                       vz/vx




                                                         Alexey Burov                      11
         Small emittance, nominal e-current
Electron current                                        0.5 A
Electron beam radius                                    2.7 mm
Stack 95% normalized emittance                          3  mm mrad
Transverse diffusion (norm. 95% emittance growth)       8  mm mrad /hour
Batch 95% longitudinal phase space, inflated to         60 eVs




                                               Alexey Burov                 12
Small emittance: vacuum for e-current
Electron current                                      0.25 A
Electron beam radius                                  2.7 mm
Stack 95% normalized emittance                        3  mm mrad
Transverse diffusion (norm. 95% emittance growth)     5.6  mm mrad /hour
Batch 95% longitudinal phase space, inflated to       60 eVs




                                              Alexey Burov                  13
Nominal emittance, nominal e-current
 Electron current                                    0.5 A
 Electron beam radius                                5.0 mm
 Stack 95% normalized emittance                      10  mm mrad
 Transverse diffusion (norm. 95% emittance growth)   8  mm mrad /hour
 Batch 95% longitudinal phase space, inflated to     30 eVs




                                     Alexey Burov                        14
Nominal emittance: vacuum for e-current
 Electron current                                      0.25 A
 Electron beam radius                                  5.0 mm
 Stack 95% normalized emittance                        10  mm mrad
 Transverse diffusion (norm. 95% emittance growth)     5.6  mm mrad /hour
 Batch 95% longitudinal phase space, inflated to       30 eVs




                                        Alexey Burov                         15
       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

                            0 .3  
                   f  f0               0.7 GHz
                           ( p / p )

 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                     16
                          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                 17
Alexey Burov   18

				
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posted:5/2/2013
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