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Dynamics of collisional particles in a fluctuating magnetic field

Published online by Cambridge University Press:  13 March 2009

F. Spineanu  and
M. Vlad
F. Spineanu
Affiliation:
Association EURATOM-Etat Beige stir la Fusion, Physique Statistique et Plasmas, CP 231, Université Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe, 1050 Bruxelles, Belgium, and Association EURATOM-CEA sur la Fusion, DRFC, Centre d'Etudes de Cadarache, 13108 Saint-Paul-Iez-Durance Cedex, France
M. Vlad
Affiliation:
Association EURATOM-Etat Beige stir la Fusion, Physique Statistique et Plasmas, CP 231, Université Libre de Bruxelles, Campus Plaine, Boulevard du Triomphe, 1050 Bruxelles, Belgium, and Association EURATOM-CEA sur la Fusion, DRFC, Centre d'Etudes de Cadarache, 13108 Saint-Paul-Iez-Durance Cedex, France
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Abstract

The equations of motion of a test particle in a stochastic magnetic field and interacting through collisions with a plasma are Langevin-type equations. Under reasonable assumptions on the statistical properties of the random processes (field and collisional velocity fluctuations), we perform an analytical calculation of the mean-square displacement (MSD) of the particle. The basic nonlinearity in the problem (Lagrangian argument of the random field) yields complicated averages, which we carry out using a functional formalism. The result is expressed as a series, and we find the conditions for its convergence, i.e. the limits of validity of our approach (essentially, we must restrict attention to non-chaotic regimes). Further, employing realistic bounds (spectral cut-off and limited time of observation), we derive an explicit formula for the MSD. We show that from this unique expression, we can obtain several previously known results.

Type
Research Article
Information
Journal of Plasma Physics , Volume 54 , Issue 3 , December 1995 , pp. 333 - 371
Copyright
Copyright © Cambridge University Press 1995

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