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

GE Jun; GUO Zhi-Yuan; LIN Yu-Zheng

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2003, Vol. 27> Issue(3) : 268-272

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

Department of Engineering Physics, Tsinghua University, Beijing 100084, China2 Institute of High Energy Physics, CAS, Beijing 100039, China

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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.

References

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. 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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沈阳化工大学材料科学与工程学院沈阳 110142

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

Received Date: 2002-03-18
Accepted Date: 1900-01-01
Available Online: 2003-03-05

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.