Modelling of heat transport in magnetised plasmas using non-aligned coordinates

We present discretisation schemes for the heat diffusion equation in strongly magnetised plasmas in 2-d Cartesian and 3-d cylindrical geometry. The algorithms described do not use field-aligned coordinates, but show, nevertheless, a strong reduction of the pollution of perpendicular heat flux caused by parallel heat conduction, compared to standard finite element or other finite difference formulations. Results for test examples show independence of the numerical error from χ∥ for values of χ∥/χ⊥ up to 109 in plane and 1012 in periodic cylinder geometry (simulating toroidal connection). The algorithms appear particularly well suited for dynamic MHD calculations, where the effort of using exactly aligned coordinates becomes prohibitive.