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

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.