Extended MHD Modelling with the Ten-Moment Equations

High-order moment fluid equations for simulation of plasmas are presented. The ten-moment equations are a two-fluid model in which time dependent equations are used to advance the pressure tensor. With the inclusion of the full pressure tensor Finite Larmor Radius (FLR) effects are captured. Further, Hall-effects are captured correctly by including the full electron momentum equation. Hall and FLR effects are important to understand stability of compact toroids like Field Reversed Configurations (FRCs) and also to detailed understanding of small scale instabilities in current carrying plasmas. The effects of collisions are discussed. Solutions to a Riemann problem for the ten-moment equations are presented. The ten-moment equations show complex dispersive solutions which come about from the source terms. The model is validated with the GEM fast magnetic reconnection challenge problem.