Saturation of a longitudinal instability due to nonlinearity of the wake field

Conference · Tue Jan 01 04:00:00 EST 1985

OSTI ID:5735188

Krinsky, S

Self-sustained synchrotron oscillations are observed in electron storage rings. In general the theoretical description of the saturation of an instability for large oscillation amplitude is a difficult problem, and techniques have not yet been developed which yield analytic approximations to the appropriate nonlinear Vlasov or Fokker-Planck equations. In this paper, a single point bunch interacting with the wake field from a single resonant mode of an rf cavity is considered, and the averaging method of Bogoliubov and Mitropolsky is used to study the saturation of the initial exponential growth of the oscillation amplitude, due to the nonlinearity of the wake field. The determination of the limiting amplitude of oscillation is discussed both in the presence and in the absence of radiation damping.

• Research Organization: Brookhaven National Lab., Upton, NY (USA)
• DOE Contract Number: AC02-76CH00016
• OSTI ID: 5735188
• Report Number(s): BNL-36430; CONF-850504-82; ON: DE85012514
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200 -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
430400* -- Particle Accelerators-- Storage Rings
BEAM DYNAMICS
BEAMS
DIFFERENTIAL EQUATIONS
ELECTRON BEAMS
EQUATIONS
EQUATIONS OF MOTION
FOKKER-PLANCK EQUATION
LEPTON BEAMS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
STORAGE RINGS