Diffusive processes in a stochastic magnetic field

Hai Da Wang, M. Vlad, E. Vanden Eijnden, F. Spineanu, J. H. Misguich, R. Balescu

Research output: Contribution to journalArticle

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 more quantitative (though not entirely deductive) treatment than in earlier works.

Original languageEnglish (US)
Pages (from-to)4844-4859
Number of pages16
JournalPhysical Review E
Volume51
Issue number5
DOIs
StatePublished - 1995

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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    Wang, H. D., Vlad, M., Vanden Eijnden, E., Spineanu, F., Misguich, J. H., & Balescu, R. (1995). Diffusive processes in a stochastic magnetic field. Physical Review E, 51(5), 4844-4859. https://doi.org/10.1103/PhysRevE.51.4844