Fractional kinetics for relaxation and superdiffusion in a magnetic field

被引:124
作者
Chechkin, AV
Gonchar, VY
Szydlowski, M
机构
[1] Kharkov Inst Phys & Technol, Natl Sci Ctr, Inst Theoret Phys, UA-61108 Kharkov, Ukraine
[2] Jagiellonian Univ, Astron Observ, PL-30244 Krakow, Poland
关键词
D O I
10.1063/1.1421617
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
Fractional Fokker-Planck equation is proposed for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. It is assumed that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide one with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly nonequilibrium plasmas of solar systems and thermonuclear devices. The fractional kinetic equation is solved, the properties of the solution are studied, and analytical results are compared with those of numerical simulation based on the solution of the Langevin equations with a noise source having Levy stable probability density. It is found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field. (C) 2002 American Institute of Physics.
引用
收藏
页码:78 / 88
页数:11
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