dorsal/arxiv
View SchemaFractional Kinetics for Relaxation and Superdiffusion in Magnetic Field
| Authors | A. Chechkin, V. Gonchar, M. Szydlowski |
|---|---|
| Categories | |
| ArXiv ID | physics/0107018 |
| URL | https://arxiv.org/abs/physics/0107018 |
| DOI | 10.1063/1.1421617 |
Abstract
We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We 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.
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"abstract": "We propose fractional Fokker-Planck equation for the kinetic description of\nrelaxation and superdiffusion processes in constant magnetic and random\nelectric fields. We assume that the random electric field acting on a test\ncharged particle is isotropic and possesses non-Gaussian Levy stable\nstatistics. These assumptions provide us with a straightforward possibility to\nconsider formation of anomalous stationary states and superdiffusion processes,\nboth properties are inherent to strongly non-equilibrium plasmas of solar\nsystems and thermonuclear devices. We solve fractional kinetic equations, study\nthe properties of the solution, and compare analytical results with those of\nnumerical simulation based on the solution of the Langevin equations with the\nnoise source having Levy stable probability density. We found, in particular,\nthat the stationary states are essentially non-Maxwellian ones and, at the\ndiffusion stage of relaxation, the characteristic displacement of a particle\ngrows superdiffusively with time and is inversely proportional to the magnetic\nfield.",
"arxiv_id": "physics/0107018",
"authors": [
"A. Chechkin",
"V. Gonchar",
"M. Szydlowski"
],
"categories": [
"physics.plasm-ph"
],
"doi": "10.1063/1.1421617",
"title": "Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field",
"url": "https://arxiv.org/abs/physics/0107018"
},
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