Ideal MHD Equilibrium of a Weakly Toroidal Plasma Column with Elongated Cross Section. Part 2: Force-Free Fields

摘要

Solutions of the ideal MHD equations are obtained describing the equilibrium of a weakly toroidal plasma with an elliptic cross section surrounded by a force-free magnetic field with constant ratio between current density and magnetic field strength. The force-free field parameter causes the stagnation points to recede along the major axis of the ellipse. Above a certain value of the force-free field parameter stagnation points do not exist, so that the compression ratio of the plasma column is no longer limited. The analysis was carried out to first order in the force-free field parameter as well as to second order for an estimate of the error.