TURBULENT DIFFUSION PARTICLE ORBITS AND FIELD FLUCTUATIONS IN A PLASMA IN A MAGNETIC FIELD

A universal relationship is deduced between diffusion coefficients, electric field spectra, and averaged Liouville orbit functions for a turbulent plasma in a magnetic field. This relation is a generalization of a similar relation previously derived by Dupree from completely different considerations. In particular, the solution of the Vlasov equation is avoided. Aside from generality and rigor, the present result differs from Dupree's in that the latter involves Vlasov orbit functions whereas the former involves Liouville orbit functions. The Liouville orbit function is easily evaluated by expanding in terms of the cumulants (semi-invariants) of the moments of the exact particle orbits. Dupree's results are thus produced without having to solve the nonlinear Vlasov equation. The present results can be viewed as an extension of Spitzer's diffusion formula to strong plasma turbulence. Conditions for the validity of the diffusion expression are determined, and corrections are made for mode frequencies in excess of gyrofrequencies.