A Newton-Krylov Method for Simultaneous Semi-Implicit Time-advance of Extended MHD with Kinetic Closures

The Chapman-Enskog like drift kinetic equations [1] provide kinetic closures to fluid equations and extends to the long mean free path regime of magnetized plasmas. Tight coupling between the fluid equations and drift kinetic equations demands a careful treatment of the time-centering to implicitly advance the full system of equations over large time steps. The fluid advance in NIMROD is numerically stabilized by a semi-implicit approach to allow for timesteps large compared to the compressional Alfven wave propagation time. In this approach, the center-of-mass flow is staggered in time from the remaining fluid quantities. Building on the success of this leap-frog method we center the electron and ion velocity distribution functions such that one is advanced simultaneously with the ion flow and the other is advanced simultaneously with the remaining fluid quantities. Preliminary results are presented that focus on the collisional effects of the Spitzer thermalization problem and the collisional/free-streaming effects of temperature flattening across a growing magnetic island.

[1] J. J. Ramos, Phys Plasmas 17, 082502 (2010); J. J. Ramos, Phys Plasmas 18, 102506 (2011).