Magneto-Fluid Dynamics Seminar

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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.