Exact solutions for axisymmetric nonlinear magnetohydrodynamic equilibria of aligned magnetic field and plasma flow with applications to astrophysics and plasma confinement devices

The steady state equations of magnetohydrodynamic (MHD) flows for an inviscid fluid of high electrical conductivity are considered for an axisymmetric case, in which the physical quantities are independent of the coordinate phi of a cylindrical coordinate system (r,phi,z). The magnetic field is taken to be aligned to the plasma velocity, i.e., the magnetic lines of force and the streamlines of the velocity field coincide. Two classes of exact solutions are obtained. The obtained solutions are smooth everywhere and satisfy all necessary physical conditions, in which they have applications in astrophysics as well as plasma confinement devices, e.g., tokamak and reversed field pinch.