Linear Vlasov analysis for stability of a bunched beam
- LBNL Library
We 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. We rephrase the equation so that it becomes non-singular in the sense of operator theory, and has only regular solutions for coherent modes. We 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:
- Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
- Sponsoring Organization:
- USDOE Director. Office of Science. Office of High Energy Physics. DE-AC03-76SF00515. DE-AC03-76SF00098. DE-FG03-993441104 (US)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 827098
- Report Number(s):
- LBNL--55806
- Country of Publication:
- United States
- Language:
- English
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