SELF-CONSISTENT KINETIC MODEL FOR 2-DIMENSIONAL CUSPED AND MINIMUM-B TYPE EQUILIBRIA

Plane quadrupolar cusp containment is studied in terms of the Vlasov equation for ions and electrons. The treatment applies both with and without a constant magnetic field component normal to the considered plane (respectively, minimum-B type and pure-cusp type confinement.) Under certain assumptions, the problem reduces to an elliptic nonlinear partial differential equation of the second order with Dirichlet boundary conditions, which is investigated numerically using standard relaxation methods. Solutions are found with cusp width as small as the electron Larmor radius; if the field lines are short-circuited, however, the smallest cusp width is of the order of the ion Larmor radius. The plasma outflow through the cusps is also computed, and the results are discussed.