• J.-L. Vay, E. Cormier-Michel, W.M. Fawley, C.G.R. Geddes
  LBNL, Berkeley, California

Nu­mer­i­cal sim­u­la­tion of some sys­tems con­tain­ing charged par­ti­cles with high­ly rel­a­tivis­tic di­rect­ed mo­tion can be speed­ed up dra­mat­i­cal­ly by choice of the prop­er Lorentz-boost­ed frame*. Or­ders of mag­ni­tude speedup has been demon­strat­ed for sim­u­la­tions from first prin­ci­ples of laser-plas­ma ac­cel­er­a­tor, free elec­tron laser, and par­ti­cle beams in­ter­act­ing with elec­tron clouds. We sum­ma­rize the tech­nique and the most re­cent ex­am­ples. We then ad­dress the ap­pli­ca­tion of the Lorentz-boost­ed frame ap­proach to co­her­ent syn­chrotron ra­di­a­tion (CSR), which can be strong­ly pre­sent in bunch com­pres­sor chi­canes. CSR is par­tic­u­lar­ly rel­e­vant to the next gen­er­a­tion of x-ray light sources and dif­fi­cult to sim­u­late in the lab frame be­cause of the large ratio of scale lengths. It can in­crease both the in­co­her­ent and co­her­ent lon­gi­tu­di­nal en­er­gy spread, ef­fects that often lead to an in­crease in trans­verse emit­tance. We use the WARP code** to sim­u­late CSR emis­sion around dipole sim­ple bends. We pre­sent some scal­ing ar­gu­ments for the pos­si­ble com­pu­ta­tion­al speed up fac­tor in the boost­ed frame and ini­tial 3D sim­u­la­tion re­sults for some stan­dard CSR test cases.

* J.-L. Vay, Phys. Rev. Lett. 98 (2007) 130405
** D.P. Grote, A. Friedman, J.-L. Vay, and I. Haber, AIP Conf. Proc. 749 (2005), 55.

• G. Penn, J.-L. Vay
  LBNL, Berkeley, California

The prop­a­ga­tion of TE waves is sen­si­tive to the pres­ence of an elec­tron cloud pri­mar­i­ly through phase shifts gen­er­at­ed by the al­tered di­elec­tric func­tion, but can also lead to po­lar­iza­tion changes and other ef­fects, es­pe­cial­ly in the pres­ence of mag­net­ic fields. These ef­fects are stud­ied the­o­ret­i­cal­ly and also through sim­u­la­tions using WARP-POSINST. Full elec­tro­mag­net­ic sim­u­la­tions are per­formed for Ces­r­TA pa­ram­e­ters, and used as a bench­mark for sim­pli­fied phase shift es­ti­mates that are also im­ple­ment­ed in WARP/POSINST. Non­lin­ear ef­fects such as elec­tron heat­ing are also ex­am­ined.

• M. Venturini, M.A. Furman, G. Penn, R. Secondo, J.-L. Vay
  LBNL, Berkeley, California
• R. De Maria, Y. Papaphilippou, G. Rumolo
  CERN, Geneva

One of the op­tions under con­sid­er­a­tion for a fu­ture up­grade of the LHC in­jec­tor com­plex in­cludes the re­place­ment of PS with PS2 (a longer cir­cum­fer­ence and high­er en­er­gy ring). Ef­forts are cur­rent­ly un­der­way to de­sign the new ma­chine and char­ac­ter­ize the beam dy­nam­ics. Elec­tron cloud ef­fects rep­re­sent a po­ten­tial­ly se­ri­ous lim­i­ta­tion to the achieve­ment of the up­grade goals. We re­port on on­go­ing nu­mer­i­cal stud­ies aim­ing at es­ti­mat­ing the e-cloud den­si­ty thresh­old for the oc­cur­rence of sin­gle bunch in­sta­bil­i­ties or sig­nif­i­cant degra­da­tion of the beam emit­tance. We pre­sent se­lect­ed re­sults ob­tained in the more fa­mil­iar quasi-stat­ic ap­prox­i­ma­tion and/or in the Lorentz-boost­ed frame.

• J.-L. Vay, J.M. Byrd, M.A. Furman, G. Penn, R. Secondo, M. Venturini
  LBNL, Berkeley, California
• J.D. Fox, C.H. Rivetta
  SLAC, Menlo Park, California

Elec­tron clouds im­pose lim­i­ta­tions on cur­rent ac­cel­er­a­tors that may be more se­vere for fu­ture ma­chines, un­less ad­e­quate mea­sures of mit­i­ga­tion are taken. Re­cent­ly, it has been pro­posed to use feed­back sys­tems op­er­at­ing at high fre­quen­cy (in the GHz range) to damp sin­gle-bunch trans­verse co­her­ent os­cil­la­tions that may oth­er­wise be am­pli­fied dur­ing the in­ter­ac­tion of the beam with am­bi­ent elec­tron clouds. We have used the sim­u­la­tion pack­age WARP-POSINST to study the growth rate and fre­quen­cy pat­terns in space-time of the elec­tron cloud driv­en trans­verse in­sta­bil­i­ty in the CERN SPS ac­cel­er­a­tor with, or with­out, an ide­al­ized feed­back model for damp­ing the in­sta­bil­i­ty. We will pre­sent our lat­est sim­u­la­tion re­sults, con­trast them with ac­tu­al mea­sure­ments and dis­cuss the im­pli­ca­tions for the de­sign of the ac­tu­al feed­back sys­tem.

Slides

• J.D. Fox, A. Bullitt, T. Mastorides, G. Ndabashimiye, C.H. Rivetta, O. Turgut, D. Van Winkle
  SLAC, Menlo Park, California
• J.M. Byrd, M.A. Furman, J.-L. Vay
  LBNL, Berkeley, California
• R. De Maria
  BNL, Upton, Long Island, New York
• W. Höfle, G. Rumolo
  CERN, Geneva

The SPS at high in­ten­si­ties ex­hibits trans­verse sin­gle-bunch in­sta­bil­i­ties with sig­na­tures con­sis­tent with an Ecloud driv­en in­sta­bil­i­ty. We pre­sent re­cent MD data from the SPS, de­tails of the in­stru­ment tech­nique and spec­tral anal­y­sis meth­ods which help re­veal com­plex ver­ti­cal mo­tion that de­vel­ops with­in a sub­set of the in­ject­ed bunch trains. The beam mo­tion is de­tect­ed via wide-band ex­po­nen­tial taper striplines and delta-σ hy­brids. The raw sum and dif­fer­ence data is sam­pled at 50 GHz with 1.8 GHz band­width. Slid­ing win­dow FFT tech­niques and RMS mo­tion tech­niques show the de­vel­op­ment of large ver­ti­cal tune shifts on por­tions of the bunch of near­ly 0.025 from the base tune of 0.185. Re­sults are pre­sent­ed via spec­tro­grams and rms bunch slice tra­jec­to­ries to il­lus­trate de­vel­op­ment of the un­sta­ble beam and time scale of de­vel­op­ment along the in­ject­ed bunch train. The study shows that the grow­ing un­sta­ble mo­tion oc­cu­pies a very broad fre­quen­cy band of 1.2 GHz. These mea­sure­ments are com­pared to nu­mer­i­cal sim­u­la­tion re­sults, and the sys­tem pa­ram­e­ter im­pli­ca­tions for an Ecloud feed­back sys­tem are out­lined.