New exact plasma equilibria with axial and helical symmetry

Abstract

We derive new exact closed-form solutions of magnetohydrodynamics equations, with and without dynamics, which model astrophysical jets and other prolonged plasma configurations. The solutions are obtained in static and dynamic incompressible equilibrium settings, in axial and helical symmetry assumptions, and are given in terms of Whittaker, Coulomb, and Heun special functions. For each symmetry, two distinct families of physical solutions arise, corresponding to two distinct pressure profiles. One pressure profile models plasmas supported by an external pressure and is suitable for the description of plasma configurations in a medium, such as atmosphere. The second profile features higher pressure inside the plasma domain and can model plasmas residing in a vacuum. Examples of static and dynamic solutions in axially and helically symmetric settings, including solutions with boundary current sheets, are presented and discussed.