Numerical modeling of diffusive heat transport across magnetic islands and local stochastic field

Q Yu

doi:10.1063/1.2206788

Abstract

The heat diffusion across magnetic islands is studied numerically and compared with analytical results. For a single island, the enhanced radial heat diffusivity, χr, due to the parallel transport along the field lines is increased over a region of about the island width w. The maximum enhanced heat conductivity at the rational surface is proportional to w2(χ‖χ⊥)1∕2 for sufficiently high values of χ‖∕χ⊥, where χ‖∕χ⊥ is the ratio between the parallel and the perpendicular heat diffusivity. For low ratios of χ‖∕χ⊥, however, the maximum value of χr is proportional to w4χ‖. In a locally stochastic magnetic field, χr is again proportional to w4χ‖ for low χ‖∕χ⊥, which is in agreement with the analytical results. With increasing χ‖∕χ⊥,χr is dominated first by the additive effect of individual islands and then by the field ergodicity.

Highlights

Magnetic islands generally exist in laboratory and space plasmas, caused either by resonant helical magnetic field perturbations in fusion devices or by the tearing mode type instabilities, driven by an unfavorable plasma current density gradient [1,2,3], the perturbed bootstrap current [4,5,6,7,8,9], or the electron temperature gradient [10,11]
Eq (A14) rather than Eq (12), the Fluid regime result. In this case only these magnetic field perturbations with their rational surfaces being sufficiently close to the observation point r have a significant contribution to χr, and the heat diffusion is essentially determined by the additive effects of these individual islands satisfying (r-rs,k)/wc,k
The heat diffusion consists of three regimes: (a) the quasi-linear regime w/wc>wc

Summary

Introduction

Magnetic islands generally exist in laboratory and space plasmas, caused either by resonant helical magnetic field perturbations (finite error fields) in fusion devices or by the tearing mode type instabilities, driven by an unfavorable plasma current density gradient [1,2,3], the perturbed bootstrap current [4,5,6,7,8,9], or the electron temperature gradient [10,11]. The resulting degradation of plasma energy confinement due to the fast parallel transport along the field lines is found to be determined by the island width, the minor radius of the rational surface and the local equilibrium plasma pressure gradient [15]. In addition to the numerical problem, the parallel heat flux is much more complicated for a sufficiently high χ||/χ⊥ It is of the classical form only in a narrow region around the rational surface or the island’s x-point [28]. When two neighboring islands overlap, the local magnetic field becomes stochastic In this case, for low ratios of χ||/χ⊥, the radial heat transport is found to be dominated by the additive effect of individual islands. The normalization scheme is as followings: the length is normalized to a, the magnetic field to B0t, and Te to Te0(r=0)

Modelling results

Comparison with analytical theories

Discussion and summary