MARFE onset conditions and stability

The MARFE stability is considered on closed magnetic held lines in a config uration having an X-point. The model incorporates both perpendicular and pa rallel transport and takes into account the flux expansion in the vicinity of the X-point. The stability analysis can be reduced to a standard eigenva lue problem for the temperature perturbation. The ballooning representation of the perturbation is shown to be essentially a method to separate radial and poloidal variables and to reduce the two-dimensional heat conduction e quation with periodic metric coefficients to a one-dimensional equation in a ballooning space. The effect of the toroidal magnetic topology on the mar fe stability is investigated. It is shown that the flux expansion near the X-point has a destabilizing effect. The competing stabilizing effect is ass ociated with the 'steepening' of the ballooning perturbation both in radial direction (between the magnetic surfaces) and perpendicular to the magneti c field lines on the magnetic surfaces. The main result of the work argues that in the stability analyses both parallel and perpendicular heat fluxes must be taken into account and can not be omitted without change in the spe ctrum of the anisotropic heat conduction equation. (C) 1999 Elsevier Scienc e B.V. All rights reserved.