Equilibria for the Vlasov-Maxwell system related to plasma confinement

Abstract

By working in a setting of azimuthal and $z$-directional invariance, we reduce the existence of electrically neutral, magnetically driven, equilibria of the two-species Vlasov-Maxwell (VM) equation to a second-order ODEs in the radial variable. In contrast to previous works, we consider specific situations that correspond physically to $z$-pinch, $\theta$-pinch, and screw-pinch equilibria in plasma physics. Semi-explicit solutions in these situations are provided.