Understanding how magnetic fields impact plasma transport is essential for improving the efficiency of thermonuclear fusion power plants. To address the transport problem, both plasma fluid equations and Maxwell’s equations must be solved. To solve these equations, it is necessary to derive closure relations that allow the system to be closed. Previous closure models are useful for describing the behavior of high-collisionality plasma but are not effective at low collisionality. To obtain closure relations valid for low collisionality, the first-order drift kinetic equation must be solved.
This study presents methods for numerically obtaining parallel closures for NIMROD code by deriving a system of parallel moment equations from the drift kinetic equation in an axisymmetric magnetic field. Two methods are introduced: one uses two-dimensional finite elements in the poloidal plane of a tokamak. The other is a hybrid method that reduces memory burden by using the Fourier method over the poloidal angle of the tokamak to obtain closures, and then converting them back to the finite element basis. The obtained closures show convergence with an increasing number of moments and accurately resolve the drift kinetic equation, making this approach effective for incorporating kinetic effects into fluid simulations for nuclear fusion devices
