Hyper-resistivity and electron thermal conductivity due to destroyed magnetic surfaces in axisymmetric plasma equilibria

Abstract

In order to model the effects of small-scale current-driven magnetic fluctuations in a mean-field theoretical description of a large-scale plasma magnetic field B(x,t), a space and time dependent hyper-resistivity Λ(x,t) can be incorporated into the Ohm’s law for the parallel electric field E⋅B. Using Boozer coordinates, a theoretical method is presented that allows for a determination of the hyper-resistivity Λ(ψ) functional dependence on the toroidal magnetic flux ψ for arbitrary experimental steady-state Grad-Shafranov axisymmetric plasma equilibria, if values are given for the parallel plasma resistivity η(ψ) and the local distribution of any auxiliary plasma current. Heat transport in regions of plasma magnetic surfaces destroyed by resistive tearing modes can then be modeled by an electron thermal conductivity ke(ψ)=(ɛ02me/e2)Λ(ψ), where e and me are the electron charge and mass, respectively, while ɛ0 is the permittivity of free space. An important result obtained for axisymmetric plasma equilibria is that the ψψ−component of the metric tensor of Boozer coordinates is given by the relation gψψ(ψ)≡∇ψ⋅∇ψ=[μ0G(ψ)][μ0I(ψ)]/ι(ψ), with μ0 the permeability of free space, G(ψ) the poloidal current outside a magnetic surface, I(ψ) the toroidal current inside a magnetic surface, and ι(ψ) the rotational transform.