Stochastic diffusivity and heat transport in the presence of a radial dependence of the perturbed magnetic field in the reversed field pinch

Abstract

Stochastic diffusivity in the presence of island overlapping can be numerically estimated following the radial evolution of an ensemble of magnetic field lines, starting from a given initial position, when they have travelled for a length of the order of the perturbed magnetic field correlation length along the main magnetic field. In this paper we show that, caused by the radial dependence of the magnetic perturbation and due to the short correlation length in reversed field pinches (RFPs), different `local' diffusion rates at different radii originate.The numerical results describing the stochastic diffusion process, obtained for typical RFP configurations and magnetic field perturbations, are presented and compared with an analytical WKB approximated solution of the relevant one-dimensional Fokker-Planck diffusion equation. The magnetic diffusivity profile is then inserted into a heat diffusion equation for the electrons in which the heat flux is balanced by the ohmic input power. In this way the electron temperature profile is numerically obtained in collisionless and collisional regimes.