Local neoclassical calculations using a Hermite-Laguerre velocity-space basis with advanced collision operators

Abstract

We present radially local neoclassical (NC) calculations based on a Hermite-Laguerre (HL) velocity-space polynomial expansion combined with advanced linearized collision operators, including the exact Fokker-Planck-Landau (FPL) operator. The implementation is verified against the NC code SFINCS using both a multi-species Lenard-Bernstein-Dougherty-like (LBD) operator and the FPL operator, the NC fluxes agreeing to within 3% in the Pfirsch-Schlüter regime. The accuracy of the HL basis is then assessed by convergence studies against the Legendre-Laguerre (LG) basis. At an equal number of spectral coefficients, neither basis is uniformly more accurate. In the plateau regime, the LG basis is more accurate on the particle and heat fluxes, which are sensitive to the trapped-passing boundary, whereas the HL basis is more accurate on the bootstrap current, carried by the parallel flow. In the banana regime, both bases converge slowly. Finally, we compare the LBD and the original (OS) and improved Sugama (IS) operators against the FPL operator. The IS operator retrieves the NC fluxes to within 6% over four decades of collisionality, whereas the LBD operator overestimates the ion heat flux by a factor of 2.6 to 4.7. The OS operator overestimates the ion heat flux by 4 to 33%, while retrieving the particle flux and the bootstrap current to within 9% and 18%, respectively. The convention adopted for the LBD collision frequency also changes the bootstrap current by up to two orders of magnitude. The present work extends the use of the HL basis, previously used in turbulent calculations, to NC physics and, to the knowledge of the author, these are the first NC calculations using the HL basis.