Solution of the Fokker-Planck equation for charged particle transport in one space dimension

In the study of charged particle transport in plasmas, numerical techniques for solving the Fokker-Planck equation have been developed which closely parallel those used in neutron transport. This was a natural step since the theory and methods of neutron transport have been well developed. Moreover a line of treatment has been developed tailored to the specific requirements of transport in mirror machines. This approach involves the assumption that the distribution function remain constant along a guiding center orbit. Diffusion techniques have been developed in which sequential moments of the transport equation are taken so as to generate a set of coupled equations. Here a method is developed which treats the transport operator according to the standard diamond differencing techniques of neutron transport, but treats the collision term by a method designed to take advantage of the form of the Fokker-Planck collision operator. This latter method makes use of matrix factorization techniques. In the absence of applied external fields, this method conserves particles rigorously. Deterministic methods run into difficulty in the treatment of magnetized plasmas in cases in which the guiding-center approximation does not apply. Thus, there are some situations in which one is driven to Monte Carlo techniques which are not a subject of this paper