Alexei Beklemishev | Novosibirsk State University (original) (raw)

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Papers by Alexei Beklemishev

A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic e... more A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic equation and the phase-independent expressions for charge and current densities, is derived for an arbitrary four-dimensional coordinate system. The guiding-center dynamics of charged particles and the gyrokinetic transformation are obtained accurate through second order of the ratio of the Larmor radius to the gradient length. The wave-terms (kρ ∼ 1) are described in the second-order approximation with respect to the amplitude of the wave. The same approximations are used in the derivation of the gyrophase-averaged charge and current densities. Averaging is explicit.

A crucial issue in relativistic plasma, particularly relevant in the astrophysical context, is th... more 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

AIP Conference Proceedings, 2008

In this paper, extending the investigation developed in an earlier paper , we pose the problem of... more In this paper, extending the investigation developed in an earlier paper , we pose the problem of the kinetic description of gravitational Hall-MHD equilibria which may arise in accretion disks (AD) plasmas close to compact objects. When intense EM and gravitational fields, generated by the central object, are present, a convenient approach can be achieved in the context of the Vlasov-Maxwell description. In this paper the investigation is focused primarily on the following two aspects:

AIP Conference Proceedings, 2008

The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fu... more The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non-relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense, so that AD plasmas are likely to be locally non-neutral and therefore characterized by the presence of Hall currents. This suggests therefore that such equilibria should be described in the framework of the Hall-MHD theory. Extending previous approaches, holding for non-rotating plasmas or based on specialized single-species model equilibria which ignore the effect of space-time curvature, the purpose of this work is the formulation of a generalized Grad-Shafranov (GGS) equation suitable for the investigation of G-Hall-MHD equilibria in AD's where non-relativistic plasmas are present. For this purpose the equilibria are assumed to be generated by a strong axisymmetric stellar magnetic field and by the gravitating plasma characterizing the AD.

AIP Conference Proceedings, 2008

A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurrin... more A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurring typically in the vicinity of massive stellar objects (black holes, neutron stars, active galactic nuclei, etc.), is the accurate description of single-particle covariant dynamics, based on gyrokinetic theory . Provided radiation-reaction effects are negligible, this is usually based on the assumption that both the space-time metric and the EM fields (in particular the magnetic field) are suitably prescribed and are considered independent of single-particle dynamics, while allowing for the possible presence of gravitational/EM perturbations driven by plasma collective interactions which may naturally arise in such systems. The purpose of this work is the formulation of a generalized gyrokinetic theory based on the synchronous variational principle recently pointed out which permits to satisfy exactly the physical realizability condition for the four-velocity. The theory here developed includes the treatment of nonlinear perturbations (gravitational and/or EM) characterized locally, i.e., in the rest frame of a test particle, by short wavelength and high frequency. Basic feature of the approach is to ensure the validity of the theory both for large and vanishing parallel electric field. It is shown that the correct treatment of EM perturbations occurring in the presence of an intense background magnetic field generally implies the appearance of appropriate four-velocity corrections, which are essential for the description of single-particle gyrokinetic dynamics.

AIP Conference Proceedings, 2005

Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifest... more 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 [2], 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.

Radiation damping of the motion of charged particles in relativistic, optically thin plasmas is d... more Radiation damping of the motion of charged particles in relativistic, optically thin plasmas is described within the framework of the covariant gyrokinetic theory . It involves description of the collisionless single-particle dynamics as well as the Vlasov and Maxwell equations both written in the covariant formulation. The damping causes corrections to the phase-space trajectory of the particle, as well as to the form of the kinetic equation itself, due to the failure of conditions of the Liouville theorem. Both effects result independent of the gyrophase, which is retained as an ignorable variable. In addition, the applicability range of the covariant gyrokinetic theory is extended to describe short-wavelength perturbations with the background of zero parallel electric field. The presented theory is suitable for description of magnetized, relativistic, collisionless plasmas in the context of astrophysical or laboratory problems. Non-uniquenes of the gyrokinetic representation and consequences thereof are discussed.

Fusion Science and Technology

One of the most important subjects of the GDT research program is MHD-stability and transversal t... more One of the most important subjects of the GDT research program is MHD-stability and transversal transport of high pressure two-component plasma. Positive influence of radial electric field on the plasma confinement was demonstrated in previous experiments on the GDT in regimes without any special MHD stabilizers. In recent experiments it was observed that stable plasma confinement always corresponds to intermittent distribution of biasing potential on limiters and plasma dumps. It was shown that enhancement of plasma confinement time corresponds to the radial electric field in the range of 15 - 40 V/cm and one induces the sheared plasma rotation. Regime with grounding of all radial electrodes was typically unstable with plasma confinement time two times lower than gas dynamic flow time. Therefore sheared rotation can stabilize MHD modes of high β two-component plasma in the GDT experiment. It is also shown that contact between plasma and radial electrodes is essential but can not co...

Physics of Fluids B: Plasma Physics, 1992

Physics of Fluids B: Plasma Physics, 1992

ABSTRACT

Physics of Plasmas, 1999

ABSTRACT

Astronomy and Astrophysics, 2004

A fundamental aspect of many plasma-related astrophysical problems is the kinetic description of ... more A fundamental aspect of many plasma-related astrophysical problems is the kinetic description of magnetized relativistic plasmas in intense gravitational fields, such as in accretion disks around compact gravitating bodies. The goal of this paper is to formulate a gyrokinetic description for a Vlasov-Maxwell plasma within the framework of general relativity. A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic equation and corresponding expressions for the four-current density, is derived for an arbitrary four-dimensional coordinate system. General relativity effects are taken into account via the tetrad formalism. The guiding-center dynamics of charged particles and the gyrokinetic transformation are obtained accurate to the second order of the ratio of the Larmor radius to the nonuniformity scale length. The wave terms with arbitrary wavelength (kρ L ∼ 1) are described in the second-order (nonlinear) approximation with respect to the amplitude of the wave. The same approximations are used in the derivation of the gyrophase-averaged Maxwell equations. The derivation is based on the perturbative Lagrangian approach with a fully relativistic, four-dimensional covariant formulation. Its results improve on existing limitations of the gyrokinetic theory.

A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic e... more A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic equation and the phase-independent expressions for charge and current densities, is derived for an arbitrary four-dimensional coordinate system. The guiding-center dynamics of charged particles and the gyrokinetic transformation are obtained accurate through second order of the ratio of the Larmor radius to the gradient length. The wave-terms (kρ ∼ 1) are described in the second-order approximation with respect to the amplitude of the wave. The same approximations are used in the derivation of the gyrophase-averaged charge and current densities. Averaging is explicit.

A crucial issue in relativistic plasma, particularly relevant in the astrophysical context, is th... more 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

AIP Conference Proceedings, 2008

In this paper, extending the investigation developed in an earlier paper , we pose the problem of... more In this paper, extending the investigation developed in an earlier paper , we pose the problem of the kinetic description of gravitational Hall-MHD equilibria which may arise in accretion disks (AD) plasmas close to compact objects. When intense EM and gravitational fields, generated by the central object, are present, a convenient approach can be achieved in the context of the Vlasov-Maxwell description. In this paper the investigation is focused primarily on the following two aspects:

AIP Conference Proceedings, 2008

The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fu... more The consistent theoretical description of gravitational Hall-MHD (G-Hall-MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non-relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense, so that AD plasmas are likely to be locally non-neutral and therefore characterized by the presence of Hall currents. This suggests therefore that such equilibria should be described in the framework of the Hall-MHD theory. Extending previous approaches, holding for non-rotating plasmas or based on specialized single-species model equilibria which ignore the effect of space-time curvature, the purpose of this work is the formulation of a generalized Grad-Shafranov (GGS) equation suitable for the investigation of G-Hall-MHD equilibria in AD's where non-relativistic plasmas are present. For this purpose the equilibria are assumed to be generated by a strong axisymmetric stellar magnetic field and by the gravitating plasma characterizing the AD.

AIP Conference Proceedings, 2008

A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurrin... more A basic prerequisite for the investigation of relativistic astrophysical magnetoplasmas, occurring typically in the vicinity of massive stellar objects (black holes, neutron stars, active galactic nuclei, etc.), is the accurate description of single-particle covariant dynamics, based on gyrokinetic theory . Provided radiation-reaction effects are negligible, this is usually based on the assumption that both the space-time metric and the EM fields (in particular the magnetic field) are suitably prescribed and are considered independent of single-particle dynamics, while allowing for the possible presence of gravitational/EM perturbations driven by plasma collective interactions which may naturally arise in such systems. The purpose of this work is the formulation of a generalized gyrokinetic theory based on the synchronous variational principle recently pointed out which permits to satisfy exactly the physical realizability condition for the four-velocity. The theory here developed includes the treatment of nonlinear perturbations (gravitational and/or EM) characterized locally, i.e., in the rest frame of a test particle, by short wavelength and high frequency. Basic feature of the approach is to ensure the validity of the theory both for large and vanishing parallel electric field. It is shown that the correct treatment of EM perturbations occurring in the presence of an intense background magnetic field generally implies the appearance of appropriate four-velocity corrections, which are essential for the description of single-particle gyrokinetic dynamics.

AIP Conference Proceedings, 2005

Recently, an increasing interest in astrophysical as well as laboratory plasmas has been manifest... more 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 [2], 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.

Radiation damping of the motion of charged particles in relativistic, optically thin plasmas is d... more Radiation damping of the motion of charged particles in relativistic, optically thin plasmas is described within the framework of the covariant gyrokinetic theory . It involves description of the collisionless single-particle dynamics as well as the Vlasov and Maxwell equations both written in the covariant formulation. The damping causes corrections to the phase-space trajectory of the particle, as well as to the form of the kinetic equation itself, due to the failure of conditions of the Liouville theorem. Both effects result independent of the gyrophase, which is retained as an ignorable variable. In addition, the applicability range of the covariant gyrokinetic theory is extended to describe short-wavelength perturbations with the background of zero parallel electric field. The presented theory is suitable for description of magnetized, relativistic, collisionless plasmas in the context of astrophysical or laboratory problems. Non-uniquenes of the gyrokinetic representation and consequences thereof are discussed.

Fusion Science and Technology

One of the most important subjects of the GDT research program is MHD-stability and transversal t... more One of the most important subjects of the GDT research program is MHD-stability and transversal transport of high pressure two-component plasma. Positive influence of radial electric field on the plasma confinement was demonstrated in previous experiments on the GDT in regimes without any special MHD stabilizers. In recent experiments it was observed that stable plasma confinement always corresponds to intermittent distribution of biasing potential on limiters and plasma dumps. It was shown that enhancement of plasma confinement time corresponds to the radial electric field in the range of 15 - 40 V/cm and one induces the sheared plasma rotation. Regime with grounding of all radial electrodes was typically unstable with plasma confinement time two times lower than gas dynamic flow time. Therefore sheared rotation can stabilize MHD modes of high β two-component plasma in the GDT experiment. It is also shown that contact between plasma and radial electrodes is essential but can not co...

Physics of Fluids B: Plasma Physics, 1992

Physics of Fluids B: Plasma Physics, 1992

ABSTRACT

Physics of Plasmas, 1999

ABSTRACT

Astronomy and Astrophysics, 2004

A fundamental aspect of many plasma-related astrophysical problems is the kinetic description of ... more A fundamental aspect of many plasma-related astrophysical problems is the kinetic description of magnetized relativistic plasmas in intense gravitational fields, such as in accretion disks around compact gravitating bodies. The goal of this paper is to formulate a gyrokinetic description for a Vlasov-Maxwell plasma within the framework of general relativity. A closed set of relativistic gyrokinetic equations, consisting of the collisionless gyrokinetic equation and corresponding expressions for the four-current density, is derived for an arbitrary four-dimensional coordinate system. General relativity effects are taken into account via the tetrad formalism. The guiding-center dynamics of charged particles and the gyrokinetic transformation are obtained accurate to the second order of the ratio of the Larmor radius to the nonuniformity scale length. The wave terms with arbitrary wavelength (kρ L ∼ 1) are described in the second-order (nonlinear) approximation with respect to the amplitude of the wave. The same approximations are used in the derivation of the gyrophase-averaged Maxwell equations. The derivation is based on the perturbative Lagrangian approach with a fully relativistic, four-dimensional covariant formulation. Its results improve on existing limitations of the gyrokinetic theory.