Kinetic closures for unmagnetized and magnetized plasmas

Parallel and perpendicular closures with cyclotron resonance effects retained for the five-moment (density, temperature, and flow velocity) fluid equations are derived by solving the kinetic equation with the Bhatnagar–Gross–Krook operator in Fourier space. For parallel propagation, the parallel closures are reduced to those of Ji et al. [Phys. Plasmas 20, 082121 (2013)]. The closures when combined to the fluid equations reproduce the fully kinetic dispersion relation that can be directly derived from the kinetic equation. The closures for the five-moment fluid system can be utilized to derive closures for the extended fluid system, which is demonstrated by deriving closures for the ten-moment system consisting of density, flow velocity, temperature, and viscosity tensor equations.