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Title: Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches

Abstract

In this study, it is shown that the two-fluid model under a generalized Ohm’s law formulation and the resistive magnetohydrodynamics (MHD) can both be described as relaxation systems. In the relaxation model, the under-resolved stiff source terms constrain the dynamics of a set of hyperbolic equations to give the correct asymptotic solution. When applied to the collisional two-fluid model, the relaxation of fast time scales associated with displacement current and finite electron mass allows for a natural transition from a system where Ohm’s law determines the current density to a system where Ohm’s law determines the electric field. This result is used to derive novel algorithms, which allow for multiscale simulation of low and high frequency extended-MHD physics. This relaxation formulation offers an efficient way to implicitly advance the Hall term and naturally simulate a plasma-vacuum interface without invoking phenomenological models. The relaxation model is implemented as an extended-MHD code, which is used to analyze pulsed power loads such as wire arrays and ablating foils. Two-dimensional simulations of pulsed power loads are compared for extended-MHD and MHD. For these simulations, it is also shown that the relaxation model properly recovers the resistive-MHD limit.

Authors:
 [1];  [2]
  1. School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
  2. Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1114998
Alternate Identifier(s):
OSTI ID: 1076490
Grant/Contract Number:  
FC03-02NA00057
Resource Type:
Published Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Name: Physics of Plasmas Journal Volume: 18 Journal Issue: 1; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; magnetohydrodynamics; electrical resistivity; current density; electric fields; speed of light

Citation Formats

Seyler, C. E., and Martin, M. R. Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches. United States: N. p., 2011. Web. doi:10.1063/1.3543799.
Seyler, C. E., & Martin, M. R. Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches. United States. doi:https://doi.org/10.1063/1.3543799
Seyler, C. E., and Martin, M. R. Fri . "Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches". United States. doi:https://doi.org/10.1063/1.3543799.
@article{osti_1114998,
title = {Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches},
author = {Seyler, C. E. and Martin, M. R.},
abstractNote = {In this study, it is shown that the two-fluid model under a generalized Ohm’s law formulation and the resistive magnetohydrodynamics (MHD) can both be described as relaxation systems. In the relaxation model, the under-resolved stiff source terms constrain the dynamics of a set of hyperbolic equations to give the correct asymptotic solution. When applied to the collisional two-fluid model, the relaxation of fast time scales associated with displacement current and finite electron mass allows for a natural transition from a system where Ohm’s law determines the current density to a system where Ohm’s law determines the electric field. This result is used to derive novel algorithms, which allow for multiscale simulation of low and high frequency extended-MHD physics. This relaxation formulation offers an efficient way to implicitly advance the Hall term and naturally simulate a plasma-vacuum interface without invoking phenomenological models. The relaxation model is implemented as an extended-MHD code, which is used to analyze pulsed power loads such as wire arrays and ablating foils. Two-dimensional simulations of pulsed power loads are compared for extended-MHD and MHD. For these simulations, it is also shown that the relaxation model properly recovers the resistive-MHD limit.},
doi = {10.1063/1.3543799},
journal = {Physics of Plasmas},
number = 1,
volume = 18,
place = {United States},
year = {2011},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1063/1.3543799

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Cited by: 23 works
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