Parallel closures and transport for toroidal plasmas in the collisionless limit

Although the general moment method [1] provides an accurate description of Coulomb collision effects in solving the kinetic equation, it requires a large number of moments to obtain convergent solutions at low collisionality. Therefore, we directly solve a reduced drift kinetic equation with a Krook-type model collision operator to obtain parallel closures in the collisionless limit. The distribution function is expressed by velocity-dependent kernel weighted integrals of closure drives. Taking closure moments and solving a coupled system for Fourier coefficients, we express the closure coefficients in terms of drive coefficients. Using the closures we solve the momentum balance equation to calculate the parallel flows and the bootstrap current. The formalism is valid for arbitrary aspect ratios of toroidal geometry.

[1] J.-Y. Ji and E. D. Held, Phys. Plasmas 13, 102103 (2006); 21, 042102 (2014).