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On the magnetohydrodynamic limits of the ideal two-fluid plasma equations

Shen, Naijian and Li, Yuan and Pullin, D. I. and Samtaney, Ravi and Wheatley, Vincent (2018) On the magnetohydrodynamic limits of the ideal two-fluid plasma equations. Physics of Plasmas, 25 (12). Art. No. 122113. ISSN 1070-664X. http://resolver.caltech.edu/CaltechAUTHORS:20190102-092233851

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Abstract

The two-fluid plasma equations describing a magnetized plasma, originating from truncating moments of the Vlasov-Boltzmann equation, are increasingly used to describe an ion-electron plasma whose transport phenomena occur on a time scale slower and a length scale longer than those of particle collisions. A similar treatment under more stringent constraints gives the single-fluid magnetohydrodynamic (MHD) equations for low-frequency macroscopic processes. Since both stem from kinetic theory, the two-fluid plasma and MHD equations are necessarily related to each other. Such a connection is often established via ad hoc physical reasoning without a firm analytical foundation. Here, we perform a sequence of formal expansions for the dimensionless ideal two-fluid plasma equations with respect to limiting values of the speed-of-light c, the ion-to-electron mass ratio M, and the plasma skin depth d_S. Several different closed systems of equations result, including separate systems for each limit applied in isolation and those resulting from limits applied in combination, which correspond to the well-known Hall-MHD and single-fluid ideal MHD equations. In particular, it is shown that while the zeroth-order description corresponding to the c→∞ limit, with M and dS fixed, is strictly charge neutral, it nonetheless uniquely determines the perturbation charge non-neutrality at the first order. Furthermore, the additional M→∞ limit is found to be not required to obtain the single-fluid MHD equations despite being essential for the Hall-MHD system. The hierarchy of systems presented demonstrates how plasmas can be appropriately modeled in situations where only one of the limits applies, which lie in the parameter space in between where the two-fluid plasma and Hall-MHD models are appropriate.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/1.5067387DOIArticle
https://doi.org/10.1063/1.5094930DOIErratum
ORCID:
AuthorORCID
Shen, Naijian0000-0002-0533-8081
Li, Yuan0000-0003-2865-4877
Samtaney, Ravi0000-0002-4702-6473
Additional Information:© 2018 AIP Publishing. (Received 17 October 2018; accepted 2 December 2018; published online 26 December 2018) This work was supported by the KAUST Office of Sponsored Research under Award No. URF/1/3418-01.
Group:GALCIT
Funders:
Funding AgencyGrant Number
King Abdullah University of Science and Technology (KAUST)URF/1/3418-01
Record Number:CaltechAUTHORS:20190102-092233851
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190102-092233851
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91976
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:02 Jan 2019 19:42
Last Modified:09 Apr 2019 17:11

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