Alexei Beklemishev

Helical plasma thruster

A new scheme of plasma thruster is proposed. It is based on axial acceleration of rotating magnetized plasmas in magnetic field with helical corrugation. The idea is that the propellant ionization zone can be placed into the local magnetic well, so that initially the ions are trapped. The E × B rotation is provided by an applied radial electric field that makes the setup similar to a magnetron discharge. Then, from the rotating plasma viewpoint, the magnetic wells of the helically corrugated field look like axially moving mirror traps. Specific shaping of the corrugation can allow continuous acceleration of trapped plasma ions along the magnetic field by diamagnetic forces. The accelerated propellant is expelled through the expanding field of magnetic nozzle. By features of the acceleration principle, the helical plasma thruster may operate at high energy densities but requires a rather high axial magnetic field, which places it in the same class as the VASIMR® rocket engine.

The Exact Radiation‐Reaction Equation for a Classical Charged Particle

An unsolved problem of classical mechanics and classical electrodynamics is related to the search of the exact relativistic equations of motion for a classical charged point‐particle subject to the force produced by the action of its EM self‐field. The problem is related to the conjecture that for a classical charged point‐particle there should exist a relativistic equation of motion (RR equation) which results both non‐perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non‐asymptotic, i.e., it does not depend on any infinitesimal parameter. In this paper we intend to propose a novel solution to this well known problem, and in particular that the RR equation is necessarily variational. The approach is based on two key elements: 1) the adoption of the relativistic hybrid synchronous Hamilton variational principle recently pointed out (Tessarotto et al., 2006). Its basic feature is that it can be expressed in princi...

Generalized Grad‐Shafranov Equation for Gravitational Hall‐MHD Equilibria

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. In addition, for the description of equilibria occurring close to compact stars, the effect of space‐time curvature is expected to become significant. Extending previous approaches, holding for ...

Axi-symmetric Gravitational MHD Equilibria in the Presence of Plasma Rotation

In this paper, extending the investigation developed in an earlier paper (Cremaschini et al., 2008), 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:1) the formulation of the kinetic treatment of G‐Hall‐MHD equilibria. Based on the identification of the relevant first integrals of motion, we show that an explicit representation can be given for the equilibrium kinetic distribution function. For each species this is represented as a superposition of suitable generalized Maxwellian distributions;2) the determination of the constraints to be placed on the fluid fields for the existence of the kinetic equilibria. In particular, this permits a uniqu...

On the validity of the LAD and LL classical radiation‐reaction equations

The search of the correct equation of motion for a classical charged particle under the action of its electromagnetic (EM) self‐field, the so‐called radiation‐reaction equation of motion, remains elusive to date. In this paper we intend to point out why this is so. The discussion is based on the direct construction of the EM self‐potentials produced by a charged spherical particle under the action of an external EM force. In particular we intend to analyze basic features of the LAD (Lorentz‐Abraham‐Dirac) and the LL (Landau‐Lifschitz) equations. Both are shown to lead to incorrect or incomplete results.

Generalized covariant gyrokinetic dynamics of magnetoplasmas

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 (Beklemishev et al., 1999–2005). 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 (Tessarotto et al., 2007) which permits to satisfy exactly the physical realizability condition for the four‐vel...

Relativistic kinetic theory of magnetoplasmas

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.