Nonlinear Dynamics of Single Bunch Instability

Conference · Fri Sep 09 04:00:00 EDT 2011 · Conf.Proc.C970512:1635,1997

OSTI ID:1024174

Stupakov, G V; Breizman, B N; Pekker, M S

A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping rings at SLAC with a new low-impedance vacuum chamber revealed new interesting features of the instability. In some cases, after initial exponential growth, the instability eventually saturated at a level that remained constant through the accumulation cycle. In other regimes, relaxation-type oscillations were measured in nonlinear phase of the instability. In many cases, the instability was characterized by a frequency close to the second harmonic of the synchrotron oscillations. Several attempts have been made to address the nonlinear stage of the instability based on either computer simulations or some specific assumptions regarding the structure of the unstable mode. An attempt of a more general consideration of the problem is carried out in this paper. We adopt an approach recently developed in plasma physics for analysis of nonlinear behavior of weakly unstable modes in dynamic systems. Assuming that the growth rate of the instability is much smaller than its frequency, we find a time dependent solution to Vlasov equation and derive an equation for the complex amplitude of the oscillations valid in the nonlinear regime. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations.

• Research Organization: SLAC National Accelerator Laboratory (SLAC)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 1024174
• Report Number(s): SLAC-PUB-14582
• Conference Information: Journal Name: Conf.Proc.C970512:1635,1997
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
ACCELERATORS
AMPLITUDES
Accelerators
ACCSYS
BOLTZMANN-VLASOV EQUATION
COMPUTERIZED SIMULATION
DAMPING
DIFFUSION
HARMONICS
INSTABILITY
NUMERICAL SOLUTION
OSCILLATIONS
PHYSICS
PLASMA
STANFORD LINEAR ACCELERATOR CENTER
SYNCHROTRON OSCILLATIONS
SYNCHROTRON RADIATION