Linear Vlasov Analysis for Stability of a Bunched Beam
- SLAC
The authors study the linearized Vlasov equation for a bunched beam subject to an arbitrary wake function. Following Oide and Yokoya, the equation is reduced to an integral equation expressed in angle-action coordinates of the distorted potential well. Numerical solution of the equation as a formal eigenvalue problem leads to difficulties, because of singular eigenmodes from the incoherent spectrum. The authors rephrase the equation so that it becomes non-singular in the sense of operatory theory, and has only regular solutions for coherent modes. They report on a code that finds thresholds of instability by detecting zeros of the determinant of the system as they enter the upper-half frequency plane, upon increase of current. Results are compared with a time-domain integration of the nonlinear Vlasov equation with a realistic wake function for the SLC damping rings. There is close agreement between the two calculations.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)
- Sponsoring Organization:
- USDOE Office of Science (US)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 829709
- Report Number(s):
- SLAC-PUB-10648
- Country of Publication:
- United States
- Language:
- English
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