Some improvements in the theory of plasma relaxation

Eliezer Hameiri

Research output: Contribution to journalArticle

Abstract

Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.

Original languageEnglish (US)
Article number044503
JournalPhysics of Plasmas
Volume21
Issue number4
DOIs
StatePublished - 2014

Fingerprint

entropy
conservation
parallel flow
fluids
mass flow
Mach number
magnetohydrodynamics
energy
magnetic fields
temperature

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Some improvements in the theory of plasma relaxation. / Hameiri, Eliezer.

In: Physics of Plasmas, Vol. 21, No. 4, 044503, 2014.

Research output: Contribution to journalArticle

Hameiri, Eliezer. / Some improvements in the theory of plasma relaxation. In: Physics of Plasmas. 2014 ; Vol. 21, No. 4.
@article{c06ad90b6a4a44da97a53243b8e7c197,
title = "Some improvements in the theory of plasma relaxation",
abstract = "Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.",
author = "Eliezer Hameiri",
year = "2014",
doi = "10.1063/1.4871391",
language = "English (US)",
volume = "21",
journal = "Physics of Plasmas",
issn = "1070-664X",
publisher = "American Institute of Physics Publising LLC",
number = "4",

}

TY - JOUR

T1 - Some improvements in the theory of plasma relaxation

AU - Hameiri, Eliezer

PY - 2014

Y1 - 2014

N2 - Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.

AB - Taylor's relaxation theory is extended to plasmas with mass flow by using the cross helicity as a conserved quantity, similar to the magnetic helicity. Indeed, it is shown that the conservation of the cross helicity in magnetohydrodynamics is the result of the conservation of two magnetic-like helicities in two-fluid plasmas. In addition, the usually ignored toroidal flux is also held to be conserved. We also view plasma relaxation as attaining a maximum entropy state rather than Taylor's minimum energy state, but prove that maximizing the entropy subject to a given amount of energy is equivalent to minimizing the energy subject to a given amount of entropy. The resulting relaxed state is similar to the one discussed by Finn and Antonsen [Phys. Fluids 26, 3540 (1983)], and involves flow parallel to the magnetic field and constant temperature, but non-constant pressure. We show how to construct an asymptotic solution to the relaxed state based on the smallness of the Alfven Mach number of the flow.

UR - http://www.scopus.com/inward/record.url?scp=84899019188&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899019188&partnerID=8YFLogxK

U2 - 10.1063/1.4871391

DO - 10.1063/1.4871391

M3 - Article

VL - 21

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 4

M1 - 044503

ER -