Title :
Single bunch monopole instability
Author :
Podobedov, Boris ; Heifets, Sam
Author_Institution :
Linear Accel. Center, Stanford Univ., CA, USA
Abstract :
We study single bunch stability with respect to monopole longitudinal oscillations in electron storage rings. Our analysis is different from the standard approach based on the linearized Vlasov equation. Rather, we reduce the full nonlinear Fokker-Planck equation to a Schrodinger-like equation which is subsequently analyzed by perturbation theory. We show that the Haissinski solution (1973) may become unstable with respect to monopole oscillations and derive a stability criterion in terms of the ring impedance
Keywords :
Fokker-Planck equation; electron accelerators; particle beam bunching; particle beam stability; perturbation theory; storage rings; Schrodinger-like equation; electron storage rings; full nonlinear Fokker-Planck equation; monopole longitudinal oscillations; monopole oscillations; perturbation theory; ring impedance; single bunch monopole instability; single bunch stability; stability criterion; Differential equations; Electrons; Impedance; Linear accelerators; Nonlinear equations; Potential well; Stability criteria; Stochastic processes; Storage rings; Synchrotron radiation;
Conference_Titel :
Particle Accelerator Conference, 1999. Proceedings of the 1999
Conference_Location :
New York, NY
Print_ISBN :
0-7803-5573-3
DOI :
10.1109/PAC.1999.794215
