An exact helical wave solution to the equations of magnetohydrodynamics

Abstract

An exact solution to the equations of motion in an ideally conducting medium in the magnetohydrodynamic approximation, is obtained. It is seen that the solution describes the propagation of a helical magnetosonic wave parallel to the direction of a uniform magnetic field. In general the wave propagates as (x+at2+bt+c) and, when the acceleration a is due solely to a gravitational force, it is seen that the motion depends on a periodic function of this. The relevance of the solution to magnetospheric studies is discussed.