Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows

Abstract

In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation (PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.