Restricted Lie point symmetries and reductions for ideal magnetohydrodynamics equilibria

Abstract

Restricted Lie point symmetries are derived for the axially symmetric steady solutions to the ideal magnetohydrodynamics equations. The symmetries transform vectors of magnetic field B and plasma velocity V linearly with coefficients depending on a function u(z, r). A reduction of the eight MHD equilibrium equations to a single second-order partial differential equation for the function u(z, r) is obtained. Analogous Lie point symmetries and reduction are derived for the translationally invariant MHD equilibria. Applications of the symmetry transforms are indicated.