LANGEVIN EQUATION VERSUS KINETIC-EQUATION - SUBDIFFUSIVE BEHAVIOR OF CHARGED-PARTICLES IN A STOCHASTIC MAGNETIC-FIELD

被引:62
作者
BALESCU, R [1 ]
WANG, HD [1 ]
MISGUICH, JH [1 ]
机构
[1] CEA FUS, ASSOC EURATOM, DRFC, CTR ETUD CADARACHE, F-13108 ST PAUL LES DURANCE, FRANCE
关键词
D O I
10.1063/1.870855
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
The running diffusion coefficient D(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. © 1994 American Institute of Physics.
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页码:3826 / 3842
页数:17
相关论文
共 34 条
  • [1] [Anonymous], 1989, FOKKERPLANCK EQUATIO
  • [2] Balescu R., 1975, EQUILIBRIUM NONEQUIL
  • [3] BALESCU R, 1988, TRANSPORT PROCESSES, V1, pCH5
  • [4] A MODEL FOR COLLISION PROCESSES IN GASES .1. SMALL AMPLITUDE PROCESSES IN CHARGED AND NEUTRAL ONE-COMPONENT SYSTEMS
    BHATNAGAR, PL
    GROSS, EP
    KROOK, M
    [J]. PHYSICAL REVIEW, 1954, 94 (03): : 511 - 525
  • [5] Braginskii S., 1965, REV PLASMA PHYS, V1, P205, DOI DOI 10.1088/0741-3335/47/10/005
  • [6] Bykov A. M., 1992, Soviet Physics - JETP, V74, P462
  • [7] Cercignani C., 1989, BOLTZMANN EQUATION I
  • [8] Stochastic problems in physics and astronomy
    Chandrasekhar, S
    [J]. REVIEWS OF MODERN PHYSICS, 1943, 15 (01) : 0001 - 0089
  • [9] CHANDRASEKHAR S, 1989, SELECTED PAPERS, V3, P180
  • [10] SELF-CONSISTENT MODEL OF STOCHASTIC MAGNETIC-FIELDS
    DIAMOND, PH
    DUPREE, TH
    TETREAULT, DJ
    [J]. PHYSICAL REVIEW LETTERS, 1980, 45 (07) : 562 - 565