Neoclassical conductivity and bootstrap current formulas for general axisymmetric equilibria and arbitrary collisionality regime

Abstract

Expressions for the neoclassical resistivity and the bootstrap current coefficients in terms of aspect ratio and collisionality are widely used in simulating toroidal axisymmetric equilibria and transport evolution. The formulas used are in most cases based on works done 15–20 years ago, where the results have been obtained for large aspect ratio, small or very large collisionality, or with a reduced collision operator. The best expressions to date and to our knowledge are due to Hirshman [S. P. Hirshman, Phys. Fluids 31, 3150 (1988)] for arbitrary aspect ratio in the banana regime and Hinton–Hazeltine [F. L. Hinton and R. D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976)] for large aspect ratio and arbitrary collisionality regime. A code solving the Fokker–Planck equation with the full collision operator and including the variation along the magnetic field line, coupled with the adjoint function formalism, has been used to calculate these coefficients in arbitrary equilibrium and collisionality regimes. The coefficients have been obtained for a wide variety of plasma and equilibrium parameters and a comprehensive set of formulas, which have been fitted to the code results within 5%, is proposed for evaluating the neoclassical conductivity and the bootstrap current coefficients. This extends previous works and also highlights inaccuracies in the previous formulas in this wide plasma parameter space.