Existence and Properties of an Collisions
The equilibrium phase distribution of stored colliding electron beams is studied from the viewpoint of Vlasov-Fokker-Planck (VFP) theory. Numerical integration of the VFP system in one degree of freedom revealed a nearly Gaussian equilibrium with non-diagonal covariance matrix. This result is reproduced approximately in an analytic theory based on linearization of the beam-beam force. Analysis of an integral equation for the equilibrium distribution, without linearization, establishes the existence of a unique equilibrium at sufficiently small current. The role of damping and quantum noise is clarified through a new representation of the propagator of the linear Fokker-Planck equation with harmonic force.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Energy Research (ER) (US)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 784879
- Report Number(s):
- SLAC-PUB-8778; TRN: US0108662
- Resource Relation:
- Other Information: PBD: 15 Feb 2001
- Country of Publication:
- United States
- Language:
- English
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