Treatment of the long range coherent beam-beam with the Vlasov equation

Technical Report · Tue Oct 01 00:00:00 EDT 1985

DOI:https://doi.org/10.2172/6733100· OSTI ID:6733100

Forest, E

In a previous SSC-report (SSC-32), we explained how one could get some analytical results in the study of dipole beam-beam collisions. We examined three cases. We solved exactly for the stability condition in the presence of head-on collisions (h.o.). Then we studied the change in these conditions as we add long-range collisions (l.r.). We obtained analytical results which agreed very well with the exact computer solution. The purpose of this paper is to extend to the l.r. collisions a calculation due to Chao and Ruth. This calculation reported in SLAC-PUB-3400/AP-37 (SLAC-37) used the Vlasov equation in the study of h.o. collisions. They looked at the effect of modes up to octupole order. In their formalism the ribbon beams are represented by two distribution functions {Psi} and {Phi}.

• Research Organization: Lawrence Berkeley Lab., CA (USA). SSC Central Design Group
• Sponsoring Organization: DOE/ER
• DOE Contract Number: AC02-89ER40486
• OSTI ID: 6733100
• Report Number(s): SSC-51; ON: DE90014011; TRN: 90-023108
• Country of Publication: United States
• Language: English

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430200* - Particle Accelerators- Beam Dynamics
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