# Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field Source: [Fractional Kinetics for Relaxation and Superdiffusion in Magnetic Field]() Collection index: [llms.txt]() Data updated: 2025-10-24T10:49:15.477Z Authors: A. Chechkin, V. Gonchar, M. Szydlowski (2) \_\_INSTITUTION\_3\_\_ Institute of Theoretical Physics, Kharkov, Ukraine, (2) Jagiellonian University, Cracow, Poland) Published: 2001-07-09T07:38:54.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()