Covariant formulation of spatially nonsymmetric kinetic equilibria in magnetized astrophysical plasmas
Abstract
Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidences suggest that magnetized plasmas of this type are collisionless and can persist for long times (e.g., with respect to a distant observer, coordinate, time), while exhibiting geometrical structures characterized by the absence of welldefined spatial symmetries. In this paper, the problem is posed whether such configurations can correspond to some kind of kinetic equilibrium. The issue is addressed from a theoretical perspective in the framework of a covariant Vlasov statistical description, which relies on the method of invariants. For this purpose, a systematic covariant variational formulation of gyrokinetic theory is developed, which holds without requiring any symmetry condition on the background fields. As a result, an asymptotic representation of the relativistic particle magnetic moment is obtained from its formal exact solution, in terms of a suitably defined invariant series expansion parameter (perturbative representation). On such a basis, it is shown that spatially nonsymmetric kinetic equilibria can actually be determined, an example being provided by Gaussianlike distributions. As an application, the physical mechanisms related to the occurrence of a nonvanishing equilibrium fluid 4flowmore »
 Authors:
 Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ74601 Opava (Czech Republic)
 (Italy)
 Publication Date:
 OSTI Identifier:
 22252869
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 5; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASTROPHYSICS; ASYMPTOTIC SOLUTIONS; ELECTROMAGNETIC FIELDS; EQUILIBRIUM; EXACT SOLUTIONS; MAGNETIC MOMENTS; PLASMA; RELATIVISTIC RANGE; SERIES EXPANSION; SYMMETRY; VARIATIONAL METHODS
Citation Formats
Cremaschini, Claudio, Email: claudiocremaschini@gmail.com, Stuchlík, Zdeněk, Tessarotto, Massimo, and Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste. Covariant formulation of spatially nonsymmetric kinetic equilibria in magnetized astrophysical plasmas. United States: N. p., 2014.
Web. doi:10.1063/1.4874324.
Cremaschini, Claudio, Email: claudiocremaschini@gmail.com, Stuchlík, Zdeněk, Tessarotto, Massimo, & Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste. Covariant formulation of spatially nonsymmetric kinetic equilibria in magnetized astrophysical plasmas. United States. doi:10.1063/1.4874324.
Cremaschini, Claudio, Email: claudiocremaschini@gmail.com, Stuchlík, Zdeněk, Tessarotto, Massimo, and Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste. 2014.
"Covariant formulation of spatially nonsymmetric kinetic equilibria in magnetized astrophysical plasmas". United States.
doi:10.1063/1.4874324.
@article{osti_22252869,
title = {Covariant formulation of spatially nonsymmetric kinetic equilibria in magnetized astrophysical plasmas},
author = {Cremaschini, Claudio, Email: claudiocremaschini@gmail.com and Stuchlík, Zdeněk and Tessarotto, Massimo and Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste},
abstractNote = {Astrophysical plasmas in the surrounding of compact objects and subject to intense gravitational and electromagnetic fields are believed to give rise to relativistic regimes. Theoretical and observational evidences suggest that magnetized plasmas of this type are collisionless and can persist for long times (e.g., with respect to a distant observer, coordinate, time), while exhibiting geometrical structures characterized by the absence of welldefined spatial symmetries. In this paper, the problem is posed whether such configurations can correspond to some kind of kinetic equilibrium. The issue is addressed from a theoretical perspective in the framework of a covariant Vlasov statistical description, which relies on the method of invariants. For this purpose, a systematic covariant variational formulation of gyrokinetic theory is developed, which holds without requiring any symmetry condition on the background fields. As a result, an asymptotic representation of the relativistic particle magnetic moment is obtained from its formal exact solution, in terms of a suitably defined invariant series expansion parameter (perturbative representation). On such a basis, it is shown that spatially nonsymmetric kinetic equilibria can actually be determined, an example being provided by Gaussianlike distributions. As an application, the physical mechanisms related to the occurrence of a nonvanishing equilibrium fluid 4flow are investigated.},
doi = {10.1063/1.4874324},
journal = {Physics of Plasmas},
number = 5,
volume = 21,
place = {United States},
year = 2014,
month = 5
}

The problem posed by the possible existence/nonexistence of spatially nonsymmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas, this involves the construction of stationary solutions of the VlasovMaxwell equations. In this paper, the issue is addressed for nonrelativistic plasmas both in astrophysical and laboratory contexts. The treatment is based on a Lagrangian variational description of singleparticle dynamics. Starting point is a nonperturbative formulation of gyrokinetic theory, which allows one to construct 'a posteriori' with prescribed order of accuracy an asymptotic representation for the magnetic moment. In terms of the relevant particle adiabatic invariants generalized biMaxwellian equilibriamore »

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