Application of the Fokker-Planck equation to particle-beam injection into [ital e][sup [minus]] storage rings
- Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (United States)
Nonlinear forces in the longitudinal accelerating field---or in the transverse magnetic fields---lead to filamentation of the injected emittance and to the decoherence of the center-of-mass motion. The dynamics of the particle distribution function in the presence of synchrotron radiation is governed by the Fokker-Planck equation. We derive the time evolution of the distribution function after injection as an approximate solution to the Fokker-Planck equation. The approximation assumes the injected emittance to be considerably larger than the equilibrium emittance, which is fulfilled for a certain class of storage rings, e.g., damping rings. In the limit of no quantum excitation, this distribution function will then be an exact solution. Higher moments of the distribution can be expressed in combinations of elementary functions and agree very well with multiparticle simulations.
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6037302
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 48:2; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
STORAGE RINGS
BEAM EMITTANCE
BEAM BUNCHING
BEAM INJECTION
DAMPING
DISTRIBUTION FUNCTIONS
FOKKER-PLANCK EQUATION
NONLINEAR PROBLEMS
BEAM DYNAMICS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
430302* - Particle Accelerators- Injection & Extraction Systems
430400 - Particle Accelerators- Storage Rings