Time-dependent closures for plasma fluid equations

Two approaches to calculating time-dependent parallel closures for plasma fluid equations are presented. Both solve a lowest-order drift kinetic equation that includes time dependence, free streaming, and an exact treatment of the linearized Coulomb collision operator. The first approach extends the theory of Chang and Callen \footnote{ Z. Chang and J. D. Callen, {\it Phys. Fluids B} {\bf 4} (5), 1167 (1992).} by including additional moments in the treatment of the collision operator as well as initial value effects for the distribution function. Time-dependent equations for the closures are derived via inverse Laplace/Fourier transforms of single pole approximations to the pseudotransport equations. The second approach entails a continuum solution to the drift kinetic equation using 2-D finite elements for the velocity space variables. As enhancements to the first approach, this method allows for arbitrary geometry as well as the full Coulomb collision operator.