Electronic edition ISSN 1574-0579

The role of the CUSP velocity in magnetohydrodynamics flows

Manuel Núñez

Depto. Análisis Matemático, Universidad de Valladolid 47011 Valladolid, Spain

Abstract
An extremely important phenomenon in the study of magnetohydrodynamic equilibria is its elliptic or hyperbolic character, as well as the transition between the two. We consider plane field-aligned magnetohydrodynamic flows, which may be described by a single ordinary differential equation on the density. The trailing cusp velocity not only governs the character of the equation, but its very essence: this equation turns out to be singular when the flow velocity equals the cusp velocity, whereas the Alfven and sound speeds do not present any problem. There exists a number of arbitrary functions in this equation, including the Lame coefficients of the curvilinear coordinates associated with the streamlines and the ratio of the magnetic field to the momentum. By integrating this equation with several different parameters we observe that most solutions really hit the cusp line and cannot be extended beyond a certain interval. Tangential discontinuities may occur. Figs 4, Refs 22.