A variational approach to resistive relativistic plasmas
A variational approach to resistive relativistic plasmas
We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general 'relabeling' invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358
Hawke, I.
fc964672-c794-4260-a972-eaf818e7c9f4
Andersson, N.
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Comer, G.L.
f2c1746c-8638-4268-94f0-e5d4375f0358
Hawke, I.
fc964672-c794-4260-a972-eaf818e7c9f4
Andersson, N., Comer, G.L. and Hawke, I.
(2017)
A variational approach to resistive relativistic plasmas.
Classical and Quantum Gravity, 34 (12), [125001].
(doi:10.1088/1361-6382/aa6b37).
Abstract
We develop an action principle to construct the field equations for a multi-fluid system containing charge-neutral fluids, plasmas, and dissipation (via resistive interactions), by combining the standard, Maxwell action and minimal coupling of the electromagnetic field with a recently developed action for relativistic dissipative fluids. We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for both the charge-neutral fluids and currents making up the plasmas. Using basic linear algebra techniques, we show that a general 'relabeling' invariance exists for the abstract matter spaces. With the field equations in place, a phenomenological model for the resistivity is developed, using as constraints charge conservation and the Second Law of Thermodynamics. A minimal model for a system of electrons, protons, and heat is developed using the Onsager procedure for incorporating dissipation.
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Accepted/In Press date: 4 April 2017
e-pub ahead of print date: 22 May 2017
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Local EPrints ID: 412264
URI: http://eprints.soton.ac.uk/id/eprint/412264
ISSN: 0264-9381
PURE UUID: 20854a3b-e404-4259-bed9-5fce079bab7b
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Date deposited: 14 Jul 2017 16:31
Last modified: 16 Mar 2024 05:22
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G.L. Comer
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