Plasma Transport in Stochastic Magnetic Fields. II: Principles and Problems of Test Electron Transport

Abstract

A model stochastic differential equation is considered which describes guiding center electron motion in a statistically specified spectrum of turbulent magnetic fluctuations. The fluctuation intensity is assumed to satisfy the Chirikov criterion (resonance overlap) for onset of stochasticity. In this limit typical lines diffuse and are adequately described by a quasilinear diffusion coefficient D/sub m/. However, quasilinear theory does not describe an important mechanism for loss of particle correlations: particles collisionally diffuse from one line to an adjacent one which diverges rapidly from the first, carrying the particles away. The scale length L/sub K/ for line divergence is related to the inverse of the Kolmogorov-Sinai entropy. An attempt is made to determine L/sub K/ from a simplified Eulerian vertex renormalization. The exponentiation length which emerges is L/sub K/ approximately L/sub s/(anti k/sup 2//sub theta/D''/sub m/L/sub s/)/sup -1/3/, where L/sub s/ is the shear length, k bar/sub theta/ is a typical azimuthal wavenumber, and D''/sub m/ is of order D/sub m/. In a particular limit of weak shear, the particle diffusion coefficient can then be estimated as D approximately DELTA r/sup 2//tau/sub c/, where ..delta..r/sup 2/ approximately D/sub m/z(tau/sub c/), z(tau) is the distance traveled along the lines in time tau,more » and for static fluctuations tau/sub c/ approximately tau(L/sub delta/), where L/sub delta/ is L/sub K/ multiplied by a logarithmic factor involving the perpendicular collisional diffusion coefficient.« less