# Magneto-Fluid Dynamics Seminar

#### Extended MHD for High Energy Density Plasmas: Methods and Simulation Results

**Speaker:**
Charles E. Seyler, Laboratory of Plasma Studies, School of Electrical and Computer Engineering, Cornell University

**Location:**
Warren Weaver Hall 905

**Date:**
Tuesday, March 20, 2018, 11 a.m.

**Synopsis:**

In this talk I will introduce an extended magnetohydrodynamical model (XMHD)

and discuss the importance of correctly including the dynamics of the low-density

plasma that can be orders of magnitude lower in density than the target or load

material in high-energy density (HED) experiments. Including the low-density

plasma component in these experiments requires the Hall term in the Generalized

Ohm’s Law, if one is to correctly model the physics. However, the Hall term is

notoriously difficult to include in the MHD range of frequencies due to the strong

dispersive (stiff) and nonlinear character. We have developed a method that handles

the stiff nature of the equations that we call a hyperbolic relaxation method, which

is local in the spatial discretization. The basic idea is that a specific semi-implicit

time stepping algorithm applied to the full GOL (including electron inertia) and

Maxwell-Ampere law (including displacement current) is shown to relax to the Hall-

MHD Ohm’s law (without electron inertia) and Ampere’s law (without displacement

current) in the limit of large time steps. The method naturally includes standard

resistive MHD when the density is sufficiently high, without the need for a global

implicit solve of the resistive diffusion equation. Most importantly, inclusion of the

Hall term allows for a much more physical transition to the vacuum that is

problematic for resistive MHD. We will present the relaxation method, the

implementation in the PERSEUS code, and simulation results of HED experiments

that highlight the importance of low-density plasma dynamics and the necessity of

the Hall term.