Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Zpinches
Abstract
In this study, it is shown that the twofluid 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 underresolved stiff source terms constrain the dynamics of a set of hyperbolic equations to give the correct asymptotic solution. When applied to the collisional twofluid 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 extendedMHD physics. This relaxation formulation offers an efficient way to implicitly advance the Hall term and naturally simulate a plasmavacuum interface without invoking phenomenological models. The relaxation model is implemented as an extendedMHD code, which is used to analyze pulsed power loads such as wire arrays and ablating foils. Twodimensional simulations of pulsed power loads are compared for extendedMHD and MHD. For these simulations, it is also shown that the relaxation model properly recovers the resistiveMHD 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. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1114998
 Alternate Identifier(s):
 OSTI ID: 1076490
 Grant/Contract Number:
 FC0302NA00057
 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 1070664X
 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 Zpinches. 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 Zpinches. United States. doi:10.1063/1.3543799.
Seyler, C. E., and Martin, M. R. Fri .
"Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Zpinches". United States. doi:10.1063/1.3543799.
@article{osti_1114998,
title = {Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Zpinches},
author = {Seyler, C. E. and Martin, M. R.},
abstractNote = {In this study, it is shown that the twofluid 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 underresolved stiff source terms constrain the dynamics of a set of hyperbolic equations to give the correct asymptotic solution. When applied to the collisional twofluid 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 extendedMHD physics. This relaxation formulation offers an efficient way to implicitly advance the Hall term and naturally simulate a plasmavacuum interface without invoking phenomenological models. The relaxation model is implemented as an extendedMHD code, which is used to analyze pulsed power loads such as wire arrays and ablating foils. Twodimensional simulations of pulsed power loads are compared for extendedMHD and MHD. For these simulations, it is also shown that the relaxation model properly recovers the resistiveMHD limit.},
doi = {10.1063/1.3543799},
journal = {Physics of Plasmas},
number = 1,
volume = 18,
place = {United States},
year = {2011},
month = {1}
}
DOI: 10.1063/1.3543799
Web of Science
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