Regularized magnetic islands. I. Hyperviscosity and profile functions

Abstract

The problem of the magnetic island profile functions is analyzed. An idea is suggested that discontinuities of the profile function derivatives at the island separatrix, which appear in simplified plasma models, can be eliminated by means of more complete description, i.e., the profile functions can be regularized. As an example, the regularization of the electrostatic potential profile function is considered for the case of a slab geometry when its formation is governed by the perpendicular viscosity. It is shown that for regularization of such a profile function one should keep in the viscosity expression the terms with higher derivatives of the velocity, usually referred to as hyperviscosity terms. A model expression for the hyperviscosity is derived by the Grad-type method. Physically, the regularization is related to the appearance of a part of the profile function localized in the Larmor transition layer near the island separatrix.