• T. Sen
  Fermilab, Batavia

Syn­chro-be­ta­tron res­o­nances can lead to emit­tance growth and the loss of lu­mi­nos­i­ty. We con­sid­er the de­tailed dy­nam­ics of a bunch near such a low order res­o­nance driv­en by cross­ing an­gles at the col­li­sion points. We char­ac­ter­ize the na­ture of dif­fu­sion and find that it is anoma­lous and sub-dif­fu­sive. This af­fects both the shape of the beam dis­tri­bu­tion and the time scales for growth. Pre­dic­tions of a sim­pli­fied anoma­lous dif­fu­sion model are com­pared with di­rect sim­u­la­tions.

• H.J. Kim, T. Sen
  Fermilab, Batavia
• W. Fischer
  BNL, Upton, Long Island, New York

In order to avoid the ef­fects of long-range beam-beam in­ter­ac­tions which pro­duce beam blow-up and de­te­ri­o­rate beam life time, a com­pen­sa­tion scheme with cur­rent car­ry­ing wires has been pro­posed. Two long-range beam-beam com­pen­sators were in­stalled in RHIC rings in 2006. The ef­fects of the com­pen­sators have been ex­per­i­men­tal­ly in­ves­ti­gat­ed. An in­di­ca­tion was ob­served that the com­pen­sators are ben­e­fi­cial to beam life time in mea­sure­ments per­formed in RHIC dur­ing 2009. In this paper, we re­port the ef­fects of wire com­pen­sator on beam loss and emit­tance for pro­ton-pro­ton beams at col­li­sion en­er­gy.

• H.J. Kim, T. Sen
  Fermilab, Batavia

In­creas­ing the lu­mi­nos­i­ty re­quires high­er beam in­ten­si­ty and often fo­cus­ing the beam to small­er sizes at the in­ter­ac­tion points. The ef­fects of head-on in­ter­ac­tions be­come even more sig­nif­i­cant. The head-on in­ter­ac­tion in­tro­duces a tune spread due to a dif­fer­ence of tune shifts be­tween small and large am­pli­tude par­ti­cles. A low en­er­gy elec­tron beam so called elec­tron lens is ex­pect­ed to im­prove in­ten­si­ty life­time and lu­mi­nos­i­ty of the col­lid­ing beams by re­duc­ing the be­ta­tron tune shift and spread. In this paper we dis­cuss the re­sults of beam sim­u­la­tions with the elec­tron lens in RHIC.

• T. Sen, C.M. Bhat, H.J. Kim, J.-F. Ostiguy
  Fermilab, Batavia

We in­ves­ti­gate the dy­nam­ics of lon­gi­tu­di­nal­ly flat bunch­es cre­at­ed with a sec­ond har­mon­ic cav­i­ty in a high en­er­gy col­lid­er. We study Lan­dau damp­ing in a sec­ond har­mon­ic cav­i­ty with an­a­lyt­i­cal and nu­mer­i­cal meth­ods. The lat­ter in­clude par­ti­cle track­ing and evo­lu­tion of the phase space den­si­ty. The re­sults are in­ter­pret­ed in the con­text of pos­si­ble ap­pli­ca­tion to the LHC.

• H.J. Kim, T. Sen
  Fermilab, Batavia

Beam col­li­sions with a cross­ing angle at the in­ter­ac­tion point are often nec­es­sary in col­lid­ers to re­duce the ef­fects of par­a­sitic col­li­sions which in­duce emit­tance growth and de­crease beam life­time. The cross­ing angle re­duces the ge­o­met­ri­cal over­lap of the beams and hence the lu­mi­nos­i­ty. Crab cav­i­ty offer a promis­ing way to com­pen­sate the cross­ing angle and to re­al­ize ef­fec­tive head-on col­li­sions. More­over, the crab cross­ing mit­i­gates the syn­chro-be­ta­tron res­o­nances due to the cross­ing angle. A crab cav­i­ty ex­per­i­ment in SPS is pro­posed as a proof of prin­ci­ple be­fore de­cid­ing on a full crab-cav­i­ty im­ple­men­ta­tion in the LHC. In this paper, we in­ves­ti­gate the ef­fects of a sin­gle crab cav­i­ty on beam dy­nam­ics in the SPS and life time.