The establishment of the electrostatic field in a stellarator

A particle-in-cell transport simulation has been developed to model the evolution of electrostatic potentials in stellarators. The analysis is done by decomposing a poloidal cross-section. The code uses a rectangular grid, one axis of which corresponds to the poloidal angle and the other to the minor radius. In the former direction, periodic boundary conditions are applied. In the latter, a reflecting boundary is used on the ''inside'' and an absorbing boundary on the ''outside''. The toroidal angle corresponds to the third coordinate. An analytic vacuum stellarator field was used in the simulation to observe the evolution of the surfaces of constant electric potential. In this case, the configuration is iota=3, 7 field periods. The e=3 nature of the surfaces is clearly evident. The surfaces are followed for the same toridal angle and thus the vertical deflection is a measure of the rotational transform, which is seen to monotonically increase, and has a value of .6 at the outside edge. The surfaces are seen to be similar, but not identical, to the magnetic surfaces