Pseudo-classical transport I: The particle and energy flux

The transport of particles and energy that accompanies the trapping of electrons by a finite amplitude drift wave is calculated. Starting from the drift kinetic equation, it is shown that, in the limit of small collision frequency, the electron entropy source is stationary with respect to variations in the electron distribution function. This variational principal is employed, together with the full Fokker–Planck collision operators, to evaluate the electron transport coefficients and, hence, the flux of particles and energy across the magnetic field. Explicit expressions for the particle and energy flux are obtained in terms of the parameters of the plasma-wave system. These expressions should be used in place of the usual quasi-linear expressions for the particle and energy flux when the autocorrelation time of the wave spectrum is sufficient to permit the trapping of electrons by individual waves. These pseudo-classical transport rates are found to be smaller than the quasi-linear expressions that they replace.