New three-dimensional simulation models for cylindrical and toroidal plasmas

A new class of three-dimensional particle simulation models using finite-size particles has been developed which is useful for studying plasma behavior in large, cylindrical, and toroidal systems. The model makes use of the combination of eigenfunction expansion in one direction and the multipole expansion on a two-dimensional spatial grid for solving the Maxwell equations and for pushing particles. For a toroidal system, the Poisson equation is solved by using the cubic spline technique in the radial direction. It is shown that, using presently available computers, full three-dimensional simulations may be carried out for real plasma devices such as tokamaks or pinch devices where only several eigenmodes are required in the axial direction. Results of the simulations for the thermal fluctuations are shown to agree with the theoretical predictions for both cylindrical and toroidal systems.