Nonsingular Integral Equation for Stability of a Bunched Beam
- SLAC
The linearized Vlasov equation for longitudinal motion of a bunched beam leads to a singular integral equation, the singularity being associated with the tune spectrum of the single-particle motion. A discretization for numerical solution of the equation in this form is not well justified. A simple change of the unknown function gives an equation that can more readily be approximated by a matrix equation. In contrast to the usual approach (Oide-Yokoya) the equation for eigen-frequencies does not have a continuum of solutions corresponding to single-particle frequencies, but only a few solutions corresponding to coherent modes.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)
- Sponsoring Organization:
- USDOE Office of Science (US)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 826786
- Report Number(s):
- SLAC-PUB-10358
- Country of Publication:
- United States
- Language:
- English
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