Analytical description of stationary ideal MHD flows with constant total pressure

TL;DR

This paper analytically describes stationary ideal MHD flows with constant total pressure, revealing their geometric structure and providing explicit solutions with functional arbitrariness.

Contribution

It introduces a curvilinear coordinate system simplifying MHD equations and characterizes flows with constant total pressure using translational magnetic surfaces.

Findings

Contact magnetic surfaces are translational surfaces.

Explicit solutions with functional arbitrariness are constructed.

Symmetry transformations act as scaling in the coordinate system.

Abstract

Incompressible stationary flows of ideal plasma are observed. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations performs as a scaling transformation for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Explicit examples of solutions with constant total pressure possessing a significant functional arbitrariness are given.