Comparison between Fokker-Planck Equation and Vlasov Equation in the Research of the Mode Coupling Theory

  • Mode coupling theory successfully explains the microwave instability, and the Vlasov equation is the basic of the theory. Fokker-Planck equation describes the distribution of the particles in bunch, which includes damping effect and the quantum excitation effect. We compare the Fokker-Planck equation with the Vlasov equation in the aspects of the origin, physics meaning, solution, and also introduce the method of polynomial expansion to solve the equation.
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  • [1] . Sacherer F .IEEE Trans. Nucl. Science NS-24,1977,(3):13932. Chao A .Physics of Collective Beam Instabilities in High Energy Accelerator.New York:Wiley,19933. Oide K ,Yokoya K .Longitudinal Single Bunch Instability in Electron Storage Rings,KEK Preprint 90–10,19904. Podobedov B V ,Siemann R H .Sawtooth Instability Studies in the Stanford Linear Collider Damping Rings,PAC97,1997,2:16295. Pauluhn A .Stochastic Beam Dynamicsin Storage Rings,DESY 93—138,19936. Suzuki T .Part. Accel.1983,14:917. CHEN Bo,Longitudinal Collective Instability of Nonlinear Hamiltonian Systemsina Circular Accelerator, Ph. D thesis,1995,SLAC8. Heifets S ,Chao A .Study of Microwave Instability,SLAC-PUB-7390,19969. Zorzano M P ,Mais H .Numerical Solution for Fokker Planck Equation in Accelerators, PAC97,1997,2:1825
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GE Jun, GUO Zhi-Yuan and LIN Yu-Zheng. Comparison between Fokker-Planck Equation and Vlasov Equation in the Research of the Mode Coupling Theory[J]. Chinese Physics C, 2003, 27(3): 268-272.
GE Jun, GUO Zhi-Yuan and LIN Yu-Zheng. Comparison between Fokker-Planck Equation and Vlasov Equation in the Research of the Mode Coupling Theory[J]. Chinese Physics C, 2003, 27(3): 268-272. shu
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Received: 2002-03-18
Revised: 1900-01-01
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Comparison between Fokker-Planck Equation and Vlasov Equation in the Research of the Mode Coupling Theory

    Corresponding author: GE Jun,
  • Department of Engineering Physics, Tsinghua University, Beijing 100084, China2 Institute of High Energy Physics, CAS, Beijing 100039, China

Abstract: Mode coupling theory successfully explains the microwave instability, and the Vlasov equation is the basic of the theory. Fokker-Planck equation describes the distribution of the particles in bunch, which includes damping effect and the quantum excitation effect. We compare the Fokker-Planck equation with the Vlasov equation in the aspects of the origin, physics meaning, solution, and also introduce the method of polynomial expansion to solve the equation.

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