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Title: Covariant formulation of spatially non-symmetric 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 well-defined 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 non-symmetric kinetic equilibria can actually be determined, an example being provided by Gaussian-like distributions. As an application, the physical mechanisms related to the occurrence of a non-vanishing equilibrium fluid 4-flowmore » are investigated.« less

Authors:
;  [1];  [1];  [2]
  1. Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava (Czech Republic)
  2. (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, E-mail: 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 non-symmetric kinetic equilibria in magnetized astrophysical plasmas. United States: N. p., 2014. Web. doi:10.1063/1.4874324.
Cremaschini, Claudio, E-mail: claudiocremaschini@gmail.com, Stuchlík, Zdeněk, Tessarotto, Massimo, & Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste. Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas. United States. doi:10.1063/1.4874324.
Cremaschini, Claudio, E-mail: 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 non-symmetric kinetic equilibria in magnetized astrophysical plasmas". United States. doi:10.1063/1.4874324.
@article{osti_22252869,
title = {Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas},
author = {Cremaschini, Claudio, E-mail: 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 well-defined 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 non-symmetric kinetic equilibria can actually be determined, an example being provided by Gaussian-like distributions. As an application, the physical mechanisms related to the occurrence of a non-vanishing equilibrium fluid 4-flow 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/non-existence of spatially non-symmetric kinetic equilibria has remained unsolved in plasma theory. For collisionless magnetized plasmas, this involves the construction of stationary solutions of the Vlasov-Maxwell equations. In this paper, the issue is addressed for non-relativistic plasmas both in astrophysical and laboratory contexts. The treatment is based on a Lagrangian variational description of single-particle dynamics. Starting point is a non-perturbative 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 bi-Maxwellian equilibriamore » are proved to exist. These are shown to recover, under suitable assumptions, a Chapman-Enskog form which permits an analytical treatment of the corresponding fluid moments. In particular, the constrained posed by the Poisson and the Ampere equations are analyzed, both for quasi-neutral and non-neutral plasmas. The conditions of existence of the corresponding non-symmetric kinetic equilibria are investigated. As a notable feature, both astrophysical and laboratory plasmas are shown to exhibit, under suitable conditions, a kinetic dynamo, whereby the equilibrium magnetic field can be self-generated by the equilibrium plasma currents.« less
  • The properties of transverse waves parallel propagating in magnetized plasmas with arbitrary composition and thermally anisotropic, are investigated on the basis of relativistic Vlasov-Maxwell equations. The transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear (transverse) plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. Further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct transverse dispersionmore » relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the dispersion relations are expressed in terms of plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light, c{yields}{infinity}, does the nonrelativistic dispersion relations reduce to the standard noncovariant dispersion relations.« less
  • This Letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic- and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfven waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfven waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind.more » Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.« less
  • A Comment on the Letter by G. G. Howes et al., Phys. Rev. Lett. 100, 065004 (2008). The authors of the Letter offer a Reply.
  • This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulent motions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to themore » ion cyclotron frequency. The turbulence is assumed to be forced at some system-specific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the 'inertial range' above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvenic fluctuations and a passive cascade of density and magnetic-field-strength fluctuations. The former are governed by the reduced magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvenic component (in the collisional limit, these compressive fluctuations become the slow and entropy modes of the conventional MHD). In the 'dissipation range' below ion gyroscale, there are again two cascades: the kinetic-Alfven-wave (KAW) cascade governed by two fluid-like electron reduced magnetohydrodynamic (ERMHD) equations and a passive cascade of ion entropy fluctuations both in space and velocity. The latter cascade brings the energy of the inertial-range fluctuations that was Landau-damped at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for all of these cascades. The relationship between the theoretical models proposed in this paper and astrophysical applications and observations is discussed in detail.« less