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

Conference · Tue Oct 01 04:00:00 EDT 1985 · IEEE Trans. Nucl. Sci.; (United States)

OSTI ID:6337976

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 Laboratory, Upton, NY
• OSTI ID: 6337976
• Report Number(s): CONF-850504-
• Conference Information: Journal Name: IEEE Trans. Nucl. Sci.; (United States) Journal Volume: NS-32:5
• 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
AMPLITUDES
ANALYTICAL SOLUTION
BEAM DYNAMICS
BOLTZMANN-VLASOV EQUATION
CAVITIES
DAMPING
DIFFERENTIAL EQUATIONS
ELECTROMAGNETIC FIELDS
ELECTRON RINGS
EQUATIONS
FOKKER-PLANCK EQUATION
INSTABILITY
NONLINEAR PROBLEMS
OSCILLATION MODES
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
RESONANCE
SYNCHROTRON OSCILLATIONS