Progress in the kinetic modeling of collisionless two-dimensional bounded plasma systems

Elsewhere, a two-dimensional slab model was developed for calculating self-consistent dc states of a collisionless single-ended Q-machine in which the potential distribution decreases monotonically in the axial direction (i.e., the direction of the constant applied magnetic field). This method combines trajectory integration of the Vlasov equation for each particle species (electrons and ions) and a well-known Poisson solver into a numerical iteration scheme yielding the two-dimensional self-consistent potential and space-charge distributions. In the present contribution, the method is used to calculate the dc states of a ''long'' system (i.e., several hundred Debye lengths), and typical potential and space-charge distributions are shown. In addition, related ion and electron velocity distribution functions are presented for a position near the plasma-vacuum transition region, where the largest potential and electric-field gradients occur. These results demonstrate that our method is well capable of describing the complex fine structure of the distribution functions. Finally, a comparison is made between electron trajectories obtained in the guiding-center approximation used by us and the numerically exact electron trajectories, which shows that the approximation is good even in the plasma-vacuum transition region. (author) 6 refs., 4 figs