Study of Particle Diffusion in a Stochastic Magnetic Field: DIA Approximation and Beyond


M.Taguchi

College of Industrial Technology, Nihon University, Narashino, Chiba 275-0005, Japan

The anomalous particle-diffusion coefficient in a stochastic magnetic field is described by the time integral of the two-point Lagrangian correlation of the stochastic velocity. Calculation of this Lagrangian correlation is not an easy work since we need the information of particle trajectories in the stochastic magnetic field. Many authors have proposed various methods and approximations of calculating this diffusion coefficient.
Firstly, this work will show what we can say about the diffusion coefficient in a framework of the DIA approximation. Starting with a kinetic equation in the presence of magnetic fluctuations, we derive a closed set of equations for an ensemble-averaged distribution function and a response function to an infinitesimal external perturbation. Employing the model collisions used by Eijnden and Balescu [1] and using a functional integral method, we obtain a second-order ordinary differential equation for the cross-field running diffusion coefficient. This equation is the extension of that in [1] in the following points: (1) Inclusion of the shear effect of mean magnetic field. (2) Applicable to the diffusion of fast particles. Solving this differential
equation, we can easily obtain the particle diffusion coefficient as a function of the amplitude,
and the parallel and perpendicular correlation lengths of fluctuating magnetic field, the collision frequency and so on. Secondly, we will incorporate the idea of the decorrelation
trajectory proposed by Vlad et al. [2] into our functional integral formulation. The resulting diffusion coefficient includes the effect of particle trapping in the stochastic magnetic field, which can not be taken into account in the DIA approximation.

References

[1]E. V. Eijnden and R. Balescu, Phys. Plasmas 3(1996)874.
[2]M. Vlad, F. Spineanu, J. H. Misguich, and R. Balescu, Rhys. Rev. E 58(1998)7359.


This work is partially supported by a Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science.