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Title: Diffusive processes in a stochastic magnetic field

Abstract

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a moremore » quantitative (though not entirely deductive) treatment than in earlier works.« less

Authors:
; ; ; ; ;  [1]
  1. Association Euratom-Etat Belge sur la Fusion, Physique Statistique et Plasmas, Code Postal 231, Universite Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe, 1050 Bruxelles (Belgium)
Publication Date:
OSTI Identifier:
44835
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Additional Journal Information:
Journal Volume: 51; Journal Issue: 5; Other Information: PBD: May 1995
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; PLASMA CONFINEMENT; DIFFUSION; MAGNETIC FIELDS; STOCHASTIC PROCESSES; FLUCTUATIONS; CORRELATION FUNCTIONS; INTEGRAL EQUATIONS

Citation Formats

Wang, H, Vlad, M, Vanden Eijnden, E, Spineanu, F, Misguich, J H, Balescu, R, and Association Euratom-Commissariat a l`Energie Atomique sur la Fusion, Departement de Recherches sur la Fusion Controle, Centre d`Etudes de Cadarache, 13108 Saint-Paul-lez-Durance Cedex. Diffusive processes in a stochastic magnetic field. United States: N. p., 1995. Web. doi:10.1103/PhysRevE.51.4844.
Wang, H, Vlad, M, Vanden Eijnden, E, Spineanu, F, Misguich, J H, Balescu, R, & Association Euratom-Commissariat a l`Energie Atomique sur la Fusion, Departement de Recherches sur la Fusion Controle, Centre d`Etudes de Cadarache, 13108 Saint-Paul-lez-Durance Cedex. Diffusive processes in a stochastic magnetic field. United States. doi:10.1103/PhysRevE.51.4844.
Wang, H, Vlad, M, Vanden Eijnden, E, Spineanu, F, Misguich, J H, Balescu, R, and Association Euratom-Commissariat a l`Energie Atomique sur la Fusion, Departement de Recherches sur la Fusion Controle, Centre d`Etudes de Cadarache, 13108 Saint-Paul-lez-Durance Cedex. Mon . "Diffusive processes in a stochastic magnetic field". United States. doi:10.1103/PhysRevE.51.4844.
@article{osti_44835,
title = {Diffusive processes in a stochastic magnetic field},
author = {Wang, H and Vlad, M and Vanden Eijnden, E and Spineanu, F and Misguich, J H and Balescu, R and Association Euratom-Commissariat a l`Energie Atomique sur la Fusion, Departement de Recherches sur la Fusion Controle, Centre d`Etudes de Cadarache, 13108 Saint-Paul-lez-Durance Cedex},
abstractNote = {The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.},
doi = {10.1103/PhysRevE.51.4844},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
number = 5,
volume = 51,
place = {United States},
year = {1995},
month = {5}
}