A bounce-averaged Monte Carlo transport code for Elmo Bumpy Torus

We present the development of a bounce-averaged Monte Carlo code for transport in the toroidally confined plasma in Elmo Bumpy Torus (EBT). We begin with a review of basic plasma transport theory applicable to this problem and then describe the basic ideas of the calculation of diffusion coefficients by the Monte Carlo method. The method is generalized for use in cylindrically symmetric situations, and the special difficulties present in a plasma are described, along with suitable methods of handling these difficulties.

The first calculation is a simple application of the method to resonant ion diffusion in EBT, a situation in which only one velocity space dimension and only two configuration space dimensions are required. The Monte Carlo results are shown to agree with the analytic theory in a highly idealized regime where the theory should be valid.

The bulk of the work presented here is the development of a much more general Monte Carlo code suitable for examining many different transport processes in EBT. Since the drift and transport motion in EBT occur on a much slower time scale than the parallel streaming motion, the plasma properties and all the important three-dimensional geometrical effects are accurately represented by a bounce-averaged description, leaving two configuration space coordinates and two velocity space dimensions. The two configuration space dimensions are developed as general curvilinear coordinates (α_N, β) that describe the surfaces of constant plasma pressure in EBT. A differential Coulomb collision operator that describes changes in both velocity space directions (the total energy &epsillon; and a "pitch-angle" variable λ) is bounce averaged and discretized for Monte Carlo use. The bounce-averaged guiding-center equations of motion in (α_N, β, &epsillon;, λ)) space are presented in terms of the longitudinal adiabatic invariant J, and a suitably fast and accurate scheme for the numerical solution of the equations of motion is described.

The general Monte Carlo code is used to calculate nonresonant electron diffusion coefficients in a large aspect ratio EBT device, and a comparison is made with the theory. We present diffusion coefficients in a regime where the theory is valid and show that the Monte Carlo method produces correct results. We also present new results in regimes where no analytic theory exists.