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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 equilibria 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., Comment: 15 pages

This paper is concerned with the kinetic treatment of quasi-stationary axisymmetric collisionless accretion disc plasmas. The conditions of validity of the kinetic description for non-relativistic magnetized and gravitationally-bound plasmas of this type are discussed. A classification of the possible collisionless plasma regimes which can arise in these systems is proposed, which can apply to accretion discs around both stellar-mass compact objects and galactic-center black holes. Two different classifications are determined, which are referred to respectively as energy-based and magnetic field-based classifications. Different regimes are pointed out for each plasma species, depending both on the relative magnitudes of kinetic and potential energies and the magnitude of the magnetic field. It is shown that in all cases, there can be quasi-stationary Maxwellian-like solutions of the Vlasov equation. The perturbative approach outlined here permits unique analytical determination of the functional form for the distribution function consistent, in each kinetic regime, with the explicit inclusion of finite Larmor radius-diamagnetic and/or energy-correction effects., Comment: 13 pages

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 evidence 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., Comment: 16 pages

Non-ideal fluids are generally subject to the occurrence of non-isotropic pressure tensors, whose determination is fundamental in order to characterize their dynamical and thermodynamical properties. This requires the implementation of theoretical frameworks provided by appropriate microscopic and statistical kinetic approaches in terms of which continuum fluid fields are obtained. In this paper the case of non-relativistic magnetized fluids forming equilibrium toroidal structures in external gravitational fields is considered. Analytical solutions for the kinetic distribution function are explicitly constructed, to be represented by a Chapman-Enskog expansion around a Maxwellian equilibrium. In this way, different physical mechanisms responsible for the generation of non-isotropic pressures are identified and proved to be associated with the kinetic constraints imposed on single and collective particle dynamics by phase-space symmetries and magnetic field. As a major outcome, the validity of a polytropic representation for the kinetic pressure tensors corresponding to each source of anisotropy is established, whereby directional pressures exhibit a specific power-law functional dependence on fluid density. The astrophysical relevance of the solution for the understanding of fluid plasma properties in accretion-disc environments is discussed., Comment: 16 pages

The kinetic description of relativistic plasmas in the presence of time-varying and spatially non-uniform electromagnetic fields is a fundamental theoretical issue both in astrophysics and plasma physics. This refers, in particular, to the treatment of collisionless and strongly-magnetized plasmas in the presence of intense radiation sources. In this paper the problem is investigated in the framework of a covariant gyrokinetic treatment for Vlasov-Maxwell equilibria. The existence of a new class of kinetic equilibria is pointed out, which occur for spatially-symmetric systems. These equilibria are shown to exist in the presence of non-uniform background EM fields and curved space-time. In the non-relativistic limit this feature permits the determination of kinetic equilibria even for plasmas in which particle energy is not conserved due to the occurrence of explicitly time-dependent EM fields. Finally, absolute stability criteria are established which apply in the case of infinitesimal symmetric perturbations that can be either externally or internally produced., Comment: 8 pages

A largely unsolved theoretical issue in controlled fusion research is the consistent \textit{kinetic} treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchalleged to date. The goal of this paper is to address the problem within the framework of Vlasov-Maxwell description. The gyrokinetic treatment of charged particles dynamics is adopted for the construction of asymptotic solutions for the quasi-stationary species kinetic distribution functions. These are expressed in terms of the particle exact and adiabatic invariants. The theory relies on a perturbative approach, which permits to construct asymptotic analytical solutions of the Vlasov-Maxwell system. In this way, both diamagnetic and energy corrections are included consistently into the theory. In particular, by imposing suitable kinetic constraints, the existence of generalized bi-Maxwellian asymptotic kinetic equilibria is pointed out. The theory applies for toroidal rotation velocity of the order of the ion thermal speed. These solutions satisfy identically also the constraints imposed by the Maxwell equations, i.e. quasi-neutrality and Ampere's law. As a result, it is shown that, in the presence of non-uniform fluid and EM fields, these kinetic equilibria can sustain simultaneously toroidal differential rotation, quasi-stationary finite poloidal flows and temperature anisotropy., Comment: Accepted for publication in Physics of Plasmas

A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively-inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and conditions leading to particle trapping phenomena. With this solution one can treat temperature anisotropy, toroidal and poloidal flow velocities and finite Larmor-radius effects. An asymptotic expansion for the distribution function permits analytic evaluation of all of the relevant fluid fields. Basic theoretical features of the solution and their astrophysical implications are discussed. As an application, the possibility of describing the dynamics of slowly time-varying accretion flows and the self-generation of magnetic field by means of a \textquotedblleft kinetic dynamo effect\textquotedblright\ is discussed. Both effects are shown to be related to intrinsically-kinetic physical mechanisms., Comment: Accepted version for Physics of Plasmas

A theoretical treatment is presented of kinetic equilibria in accretion discs around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axi-symmetric and to be acted on by gravitational and electromagnetic fields; in this paper, the particular case is considered where the magnetic field admits a family of toroidal magnetic surfaces, which are locally mutually-nested and closed. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by primarily toroidal differential rotation and temperature anisotropy. It is conjectured that kinetic equilibria of this type can exist which are able to sustain both toroidal and poloidal electric current densities, the latter being produced via finite Larmor-radius effects associated with the temperature anisotropy. This leads to the possibility of existence of a new kinetic effect - referred to here as a \textquotedblleft kinetic dynamo effect\textquotedblright\ - resulting in the self-generation of toroidal magnetic field even by a stationary plasma, without any net radial accretion flow being required. The conditions for these equilibria to occur, their basic theoretical features and their physical properties are all discussed in detail., Comment: 13 pages, 1 figure Accepted for publication in Physics of Plasmas

The gyrokinetic description of particle dynamics faces a basic difficulty when a special type of canonical variables is sought, i.e., the so-called \textit{gyrokinetic canonical variables}. These are defined in such a way that two of them are respectively identified with the gyrophase-angle, describing the fast particle gyration motion around magnetic field lines, and its canonically conjugate momentum. In this paper we intend to discuss the conditions of existence for these variables., Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008)

A crucial issue in relativistic plasma, particularly relevant in the astrophysical context, is the description of highly magnetized plasmas based on a covariant formulation of gyrokinetic dynamics. An interesting case in question is that in which the background electric field (produced either by the same plasma of by other sources) results suitably small (or vanishing) with respect to the magnetic field, while at the same time short-wavelength EM perturbations can be present. The purpose of this work is to extend the relativistic gyrokinetic theory developed by Beklemishev \textit{et al.} [1999-2005] to include, in particular, also the treatment of such a case. We intend to show that this requires the development of a perturbative expansion involving simultaneously both the particle 4-position vector and the corresponding \textit{4-velocity vector}. For this purpose a synchronous form of the relativistic Hamilton variational principle is adopted., Comment: Communication presented at the 25th International Symposium on Rarefied Gas Dynamics, St. Petersburg, Russia, July 21-28, 2006

Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifested in reference to the existence of relativistic flows, related in turn to the production of intense electric fields in magnetized systems. Such phenomena require their description in the framework of a consistent relativistic kinetic theory, rather than on relativistic MHD equations, subject to specific closure conditions. The purpose of this work is to apply the relativistic single-particle guiding-center theory developed by Beklemishev and Tessarotto, including the nonlinear treatment of small-wavelength EM perturbations which may naturally arise in such systems. As a result, a closed set of relativistic gyrokinetic equations, consisting of the collisionless relativistic kinetic equation, expressed in hybrid gyrokinetic variables, and the averaged Maxwell's equations, is derived for an arbitrary four-dimensional coordinate system., Comment: 6 pages, 1 figure. Contributed to the Proceedings of the 24th International Symposium on Rarefied Gas Dynamics, July 10-16, 2004 Porto Giardino Monopoli (Bari), Italy

The well-known gyrokinetic problem regards the perturbative expansion related to the dynamics of a charged particle subject to fast gyration motion due to the presence of a strong magnetic field. Although a variety of approaches have been formulated in the past to this well known problem, surprisingly a purely canonical approach based on Lie transform methods is still missing. This paper aims to fill in this gap and provide at the same time new insight in Lie-transform approaches., Comment: 6 pages, 1 figure. Contributed to the Proceedings of the 24th International Symposium on Rarefied Gas Dynamics, July 10-16, 2004 Porto Giardino Monopoli (Bari), Italy