Longitudinal instabilities with a non-harmonic rf potential
We consider the longitudinal instabilities of a bunched beam subject to a non-harmonic rf potential. Assuming the unperturbed bunch to be described by a Maxwell-Boltzmann distribution, our treatment is based upon the linearized Vlasov equation. The formalism developed is exact, and in particular, correctly describes the effect of the dependence on amplitude of the synchrotron oscillation frequency. We discuss the fast blowup limit, and extend Wang and Pellegrini's treatment of the microwave instability to include the case of a non-Gaussian bunch. Next, within the short bunch approximation, we derive the dispersion relation describing the Landau damping of the coupled bunch modes, resulting from the use of a Landau cavity.
- Research Organization:
- Brookhaven National Lab., Upton, NY (USA)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 6443214
- Report Number(s):
- BNL-32764; CONF-830311-89; ON: DE83010428
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
ACCELERATORS
BEAM BUNCHING
BEAM DYNAMICS
BOLTZMANN-VLASOV EQUATION
DAMPING
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
EQUATIONS
EQUATIONS OF MOTION
INSTABILITY
LANDAU DAMPING
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SYNCHROTRON OSCILLATIONS