Orbit-averaged guiding-center Fokker-Planck operator for numerical applications

Abstract

A guiding-center Fokker-Planck operator is derived in a coordinate system that is well suited for the implementation in a numerical code. This differential operator is transformed such that it can commute with the orbit-averaging operation. Thus, in the low-collisionality approximation, a three-dimensional Fokker-Planck evolution equation for the orbit-averaged distribution function in a space of invariants is obtained. This transformation is applied to a collision operator with nonuniform isotropic field particles. Explicit neoclassical collisional transport diffusion and convection coefficients are derived, and analytical expressions are obtained in the thin orbit approximation. To illustrate this formalism and validate our results, the bootstrap current is analytically calculated in the Lorentz limit. © 2010 American Institute of Physics.