Covariant descriptions of the relativistic guiding-center dynamics

Beklemishev, A. D.; Tessarotto, Massimo

doi:10.1063/1.873736

Cited by 29 publications

(70 citation statements)

References 14 publications

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“…Results similar to those in this Appendix were obtained earlier for particle motion in a dc magnetic field [3,35,41], oscillations in nonrelativistic high-frequency waves [8,93], and laser-driven relativistic electron dynamics in vacuum [16,24,25]. In the main text, we make use of the general form of the theorem (A6), which contains the earlier results as particular cases.…”

Section: Acknowledgmentsmentioning

confidence: 91%

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Positive and negative effective mass of classical particles in oscillatory and static fields

Dodin

Fisch

2008

Phys. Rev. E

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A classical particle oscillating in an arbitrary high-frequency or static field effectively exhibits a modified rest mass m eff derived from the particle averaged Lagrangian. Relativistic ponderomotive and diamagnetic forces, as well as magnetic drifts, are obtained from the m eff dependence on the guiding center location and velocity. The effective mass is not necessarily positive and can result in backward acceleration when an additional perturbation force is applied. As an example, adiabatic dynamics with m|| > 0 and m|| < 0 is demonstrated for a wave-driven particle along a dc magnetic field, m|| being the effective longitudinal mass derived from m eff . Multiple energy states are realized in this case, yielding up to three branches of m|| for a given magnetic moment and parallel velocity.

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Section: Acknowledgmentsmentioning

confidence: 91%

“…(14); thus additional strong fields, if any, are as well embedded here. Derivation of timedependent and fully relativistic magnetic drifts [40,41] using the effective mass formalism should be possible, too, but remains out of the scope of the present paper.…”

Section: Static Magnetic Fieldmentioning

confidence: 99%

Positive and negative effective mass of classical particles in oscillatory and static fields

Dodin

Fisch

2008

Phys. Rev. E

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“…A basic prerequisite for the formulation of a consistent relativistic kinetic for strongly magnetized plasmas in astrophysical problems, is the formulation of single-particle dynamics in the context of a relativistic, fully covariant, formulation of gyrokinetic theory [2,3,4]. As is well known, this regards the so-called "gyrokinetic problem", i.e., the description of the dynamics of a charged particle in the presence of suitably "intense" electromagnetic (EM) fields realized by means of appropriate perturbative expansions for its equations of motion.…”

Section: Introductionmentioning

confidence: 99%

“…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 [3]. 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.…”

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confidence: 99%

Relativistic kinetic theory of magnetoplasmas

Beklemishev¹,

Nicolini

Tessarotto³

2005

AIP Conference Proceedings

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Abstract.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 [1]. 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 [3]. 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.

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“…Indeed the result applies to BH having, in principle, arbitrary shape of the event horizon. The description adopted is purely classical both for the falling particles (charged or neutral [17,18,19,20]) and for the gravitational field and is based on the relativistic collisionless Boltzmann equation and/or the Vlasov equation respectively for neutral and charged particles. A key aspect of our formalism is the definition of suitable boundary conditions for the kinetic distribution function in order to take into account the presence of the event horizon.…”

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confidence: 99%

H-theorem for a relativistic plasma around black holes

Nicolini

Tessarotto

2006

Physics of Plasmas

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We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The formulation is based on a relativistic kinetic description for classical particles in the presence of an event horizon. An H-theorem is established which holds for arbitrary models of black holes and is valid also in the presence of contracting event horizons. PACS: 65.40.Gr 04.70.Bw 04.70.Dy. PACS numbers:The remarkable mathematical analogy between the laws of thermodynamics and black hole (BH) physics following from classical general relativity still escapes a complete and satisfactory interpretation. In particular it is not yet clear whether this analogy is merely formal or leads to an actual identification of physical quantities belonging to apparently unrelated framework. The analogous quantities are E ↔ M , T ↔ ακ and S ↔ (1/8πα)A, where A and κ are the area and the surface gravity of the BH, while α is a constant. A immediate hint to believe in the thermodynamical nature of BH comes from the first analogy which actually regards a unique physical quantity: the total energy. However, at the classical level there are obstacles to interpret the surface gravity as the BH temperature since a perfectly absorbing medium, discrete or continuum, which is by definition unable to emit anything, cannot have a temperature different from absolute zero. An reconciliation was partially achieved by in 1975 by Hawking [1], who showed, in terms of quantum particle pairs nucleation, the existence of a thermal flux of radiation emitted from the BH with a black body spectrum at temperature T = κ/2πk B (Hawking BH radiation model). The last analogy results the most intriguing, since the area A should essentially be the logarithm of the number of microscopic states compatible with the observed macroscopic state of the BH, if we identify it with the Boltzmann definition. In such a context, a further complication arise when one strictly refers to the internal microstates of the BH, since for the infinite red shift they are inaccessible to an external observer. An additional difficulty with the identification S ↔ (1/8πα)A, however, follows from the BH radiation model, since it predicts the existence of contracting BH for which the radius of the BH may actually decrease. To resolve this difficulty a modified constitutive equation for the entropy was postulated [2,3], in order to include the contribution of the matter in the BH exterior, by setting(S ′ denoting the so-called Bekenstein entropy) where S is the entropy carried by the matter outside the BH andidentifies the contribution of the BH. As a consequence a generalized second lawwas proposed [2, 3] which can be viewed as nothing more than the ordinary second law of thermodynamics applied to a system containing a BH. From this point of view one notices that, by assumption and in contrast to the first term S, S bh cannot be interpreted, in a proper ...

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Covariant descriptions of the relativistic guiding-center dynamics

Cited by 29 publications

References 14 publications

Positive and negative effective mass of classical particles in oscillatory and static fields

Positive and negative effective mass of classical particles in oscillatory and static fields

Relativistic kinetic theory of magnetoplasmas

H-theorem for a relativistic plasma around black holes

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