Development and Implementation of a Resistive Hall MHD Extension to the Gorgon Code

Hall MHD becomes significant in low-density regions of Z-pinches where the ion inertial length is comparable to the characteristic scale length [1]. We present a new method to include the Hall term and anisotropic conductivity in the extended MHD code Gorgon. The Hall term is challenging to model in low-density regions due to the electron drift velocity becoming unphysically large. To mitigate this a vacuum cut-off density is used.  This method includes the Hall term as part of the conductivity tensor [2]. With this casting a more intuitive understanding of the formation of force free currents is gained. Force free currents may be significant for MagLIF instability growth [3]. Using Gorgon we have reproduced the results of whistler wave and Hall drift wave test problems. We investigate extending a Magnetic Rayleigh-Taylor test problem [1], including the Hall term, to include regions below the vacuum cut-off density. We also study the effects of Hall on MRT growth on Z-pinches such as Hall driven shear flow.

[1] J. D. Huba and D. Winske, Phys. Plasmas 5, 2305 (1998).

[2] E. M. Epperlein and M. G. Haines, Phys. Fluids 29, 1029 (1986).

[3] C. E. Seyler, M. R. Martin, and N. D. Hamlin, Phys. Plasmas 25, 062711 (2018).