Langevin equation versus kinetic equation: Subdiffusive behavior of charged particles in a stochastic magnetic field

Journal Article · Thu Dec 01 00:00:00 EST 1994 · Physics of Plasmas; (United States)

DOI:https://doi.org/10.1063/1.870855· OSTI ID:6635910

Balescu, R; Wang, H ^[1]; Misguich, J H ^[2]

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1. Association Euratom---Etat Belge sur la Fusion, Physique Statistique et Plasmas, CP 231, Universite Libre de Bruxelles, Campus Plaine, Bd. du Triomphe, 1050 Bruxelles (Belgium)
2. Association Euratom---C.E.A. sur la Fusion, DRFC, Centre d'Etudes de Cadarache, 13108 Saint-Paul-lez-Durance Cedex (France)

The running diffusion coefficient [ital D]([ital t]) is evaluated for a system of charged particles undergoing the effect of a fluctuating magnetic field and of their mutual collisions. The latter coefficient can be expressed either in terms of the mean square displacement (MSD) of a test particle, or in terms of a correlation between a fluctuating distribution function and the magnetic field fluctuation. In the first case a stochastic differential equation of Langevin type for the position of a test particle must be solved; the second problem requires the determination of the distribution function from a kinetic equation. Using suitable simplifications, both problems are amenable to exact analytic solution. The conclusion is that the equivalence of the two approaches is by no means automatically guaranteed. A new type of object, the hybrid kinetic equation'' is constructed: it automatically ensures the equivalence with the Langevin results. The same conclusion holds for the generalized Fokker--Planck equation. The (Bhatnagar--Gross--Krook) (BGK) model for the collisions yields a completely wrong result. A linear approximation to the hybrid kinetic equation yields an inexact behavior, but represents an acceptable approximation in the strongly collisional limit.

• OSTI ID: 6635910
• Journal Information: Physics of Plasmas; (United States), Vol. 1:12; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
CHARGED PARTICLES
KINETIC EQUATIONS
DIFFUSION
DISTRIBUTION FUNCTIONS
FOKKER-PLANCK EQUATION
LANGEVIN EQUATION
MAGNETIC FIELDS
STOCHASTIC PROCESSES
TEST PARTICLES
TURBULENCE
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
700330* - Plasma Kinetics
Transport
& Impurities- (1992-)