Integral Equation for the Equilibrium State of Colliding Electron Beams
We study a nonlinear integral equation for the equilibrium phase distribution of stored colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model of the beam-beam interaction in one degree of freedom. We expect no difficulty in generalizing the argument to more realistic models.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (US)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 808677
- Report Number(s):
- SLAC-PUB-9577; TRN: US0302560
- Resource Relation:
- Other Information: PBD: 11 Nov 2002
- Country of Publication:
- United States
- Language:
- English
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