• T. Katayama
  GSI, Darmstadt
• T. Kikuchi
  Nagaoka University of Technology, Nagaoka, Niigata
• R. Maier, D. Prasuhn, R. Stassen, H. Stockhorst
  FZJ, Jülich
• I.N. Meshkov
  JINR, Dubna, Moscow Region

The stochas­tic cool­ing is em­ployed to re­duce the mo­men­tum spread of ac­cel­er­at­ed 2 GeV pro­ton beam at COSY. In ad­di­tion the bar­ri­er volt­ages are suc­cess­ful­ly used to com­pen­sate the mean en­er­gy loss of the beam due to the thick in­ter­nal tar­get such as pel­let tar­get. To an­a­lyze the ex­per­i­men­tal re­sults at COSY, we have de­vel­oped the par­ti­cle track­ing code which sim­u­late the par­ti­cle be­hav­ior under the in­flu­ences of stochas­tic cool­ing force, Schot­tky dif­fu­sion, ther­mal dif­fu­sion and IBS ef­fects. The syn­chrotron mo­tion due to the RF fields are in­clud­ed with 4th order sym­plec­tic way. The sim­u­la­tion re­sults are well in agree­ment with the ob­served cool­ing pro­cess for the case of bar­ri­er volt­age as well as RF field of har­mon­ic num­ber=1. In the pre­sent paper, the sys­tem­at­ic anal­y­sis of the ex­per­i­men­tal re­sults with use of the de­vel­oped track­ing codes are de­scribed. In ad­di­tion the pro­cess of short bunch for­ma­tion at the heavy ion col­lid­er at NICA pro­ject is in­ves­ti­gat­ed with use of the stochas­tic cool­ing. In that case the strong IBS ef­fects are main lim­it­ing fac­tor of mak­ing and keep­ing the short bunch as well as the space charge ef­fects. De­tails of the sim­u­la­tion study will be pre­sent­ed.

• T. Katayama, M. Steck
  GSI, Darmstadt
• T. Kikuchi
  Nagaoka University of Technology, Nagaoka, Niigata
• R. Maier, D. Prasuhn, R. Stassen, H. Stockhorst
  FZJ, Jülich
• I.N. Meshkov
  JINR, Dubna, Moscow Region

An­ti-pro­ton beam ac­cu­mu­la­tion at CERN and FNAL has been per­formed with use of stochas­tic stack­ing in the mo­men­tum space. Thus ac­cu­mu­lat­ed beam has a large mo­men­tum spread and re­sul­tant­ly large ra­di­al beam size with large dis­per­sion ring. In the pre­sent pro­posed sce­nario, beams from the pre-cool­ing ring are in­ject­ed into the lon­gi­tu­di­nal empty space pre­pared by the bar­ri­er volt­ages and sub­se­quent­ly the stochas­tic cool­ing is ap­plied. After the well cool­ing, bar­ri­er volt­ages will pre­pare again the empty space for the next beam in­jec­tion. We have sim­u­lat­ed the stack­ing pro­cess up to 100 stack­ing with use of the bunched beam track­ing code in­clud­ing the stochas­tic cool­ing force and the dif­fu­sion force such as Schot­tky dif­fu­sion term, ther­mal dif­fu­sion, IBS ef­fects. The syn­chrotron mo­tion by bar­ri­er volt­ages are in­clud­ed with 4th order sym­plec­tic method. Ex­am­ples of the ap­pli­ca­tion to 3 GeV an­ti-pro­ton beam for the HESR ring in FAIR pro­ject are pre­sent­ed as well as the ac­cu­mu­la­tion of heavy ion beam 3.5 GeV/u Au, at the NICA col­lid­er at JINR pro­ject.

• H. Stockhorst, R. Maier, D. Prasuhn, R. Stassen
  FZJ, Jülich
• T. Katayama
  GSI, Darmstadt

Nu­mer­i­cal stud­ies of lon­gi­tu­di­nal fil­ter and time-of-flight (TOF) cool­ing sug­gest that the strong mean en­er­gy loss due to an in­ter­nal Pel­let tar­get in the High En­er­gy Stor­age Ring (HESR) at the FAIR fa­cil­i­ty can be com­pen­sat­ed by cool­ing and op­er­a­tion of a bar­ri­er buck­et (BB) cav­i­ty. In this con­tri­bu­tion de­tailed ex­per­i­ments at COSY to com­pen­sate the mean en­er­gy loss are pre­sent­ed. The in­ter­nal Pel­let tar­get was sim­i­lar to that being used by the PANDA ex­per­i­ment at the HESR. A BB cav­i­ty was op­er­at­ed and ei­ther TOF or fil­ter stochas­tic mo­men­tum cool­ing was ap­plied to cool a pro­ton beam. Ex­per­i­men­tal com­par­isons be­tween the fil­ter and TOF cool­ing method are dis­cussed. Mea­sure­ments to de­ter­mine the mean en­er­gy loss which is used in the sim­u­la­tion codes are out­lined. The ex­per­i­ments proved that the mean en­er­gy loss can be com­pen­sat­ed with a BB cav­i­ty. Re­sults are com­pared with nu­mer­i­cal track­ing sim­u­la­tions which in­clude the syn­chrotron mo­tion in a bar­ri­er buck­et as well as in an h = 1 cav­i­ty and stochas­tic mo­men­tum cool­ing. A de­tailed dis­cus­sion of the track­ing sim­u­la­tion code will be out­lined in a sep­a­rate con­tri­bu­tion to this con­fer­ence.

• T. Kikuchi, N. Harada, T. Sasaki, H. Tamukai
  Nagaoka University of Technology, Nagaoka, Niigata
• J. Dietrich, R. Maier, D. Prasuhn, R. Stassen, H. Stockhorst
  FZJ, Jülich
• T. Katayama
  GSI, Darmstadt

A small mo­men­tum spread of pro­ton beam has to be re­al­ized and kept in a stor­age ring dur­ing an ex­per­i­ment with a dense in­ter­nal tar­get such as a pel­let tar­get. A stochas­tic cool­ing alone does not com­pen­sate the mean en­er­gy loss by the in­ter­nal tar­get. Bar­ri­er buck­et op­er­a­tion will co­op­er­ate ef­fec­tive­ly the en­er­gy loss. In ad­di­tion, the fur­ther small mo­men­tum spread can be re­al­ized with use of an elec­tron cool­ing. In the pre­sent study, the sim­u­la­tion re­sults on the si­mul­ta­ne­ous use of stochas­tic cool­ing and elec­tron cool­ing at COSY are pre­sent­ed.

• D.M. Welsch, A. Lehrach, B. Lorentz, R. Maier, D. Prasuhn, R. Tölle
  FZJ, Jülich

The High-En­er­gy Stor­age Ring (HESR) is part of the up­com­ing Fa­cil­i­ty for An­tipro­ton and Ion Re­search (FAIR). The HESR will pro­vide an­tipro­tons in the mo­men­tum range from 1.5 to 15 GeV/c for the in­ter­nal tar­get ex­per­i­ment PANDA. The de­mand­ing re­quire­ments of PANDA in terms of beam qual­i­ty and lu­mi­nos­i­ty to­geth­er with a lim­it­ed pro­duc­tion rate of an­tipro­tons call for a long beam life time and a min­i­mum of beam loss. Thus, a suf­fi­cient­ly large dy­nam­ic aper­ture of the HESR is cru­cial. To pro­vide this, a chro­matic­i­ty cor­rec­tion scheme for the HESR has been de­vel­oped to re­duce tune spread and thus to min­i­mize the emit­tance growth caused by be­ta­tron res­o­nances. The chro­matic­i­ty cor­rec­tion scheme has been op­ti­mized through dy­nam­ic aper­ture cal­cu­la­tions. The es­ti­mat­ed field er­rors of the HESR dipole and quadrupole mag­nets have been in­clud­ed in the non-lin­ear beam dy­nam­ics stud­ies. The ion op­ti­cal set­tings of the HESR have been im­proved using dy­nam­ic aper­ture cal­cu­la­tions and fre­quen­cy map anal­y­sis tech­nique. In this pre­sen­ta­tion com­pre­hen­sive beam sim­u­la­tions are pre­sent­ed and pre­dic­tions of long-term sta­bil­i­ty based on short-term par­ti­cle track­ing and orbit dif­fu­sion dis­cussed.