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:
-
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
- 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. 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. 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 = {Fri Jan 14 00:00:00 EST 2011},
month = {Fri Jan 14 00:00:00 EST 2011}
}
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