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An unsolved problem of classical mechanics and classical electrodynamics is 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 to point out 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 principle in terms of arbitrary "hybrid" variables (i.e., generally non-Lagrangian and non-Hamiltonian variables); 2) the variational treatment of the EM self-field, taking into account the exact particle dynamics., Contributed paper at RGD26 (Kyoto, Japan, July 2008)

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 unique determination of the functional form of the species number densities and of the fluid partial pressures, in terms of suitably prescribed flux functions., Contributed paper at RGD26 (Kyoto, Japan, July 2008)

An interesting issue in fluid dynamics is represented by the possible existence of inverse kinetic theories (IKT) which are able to deliver, in a suitable sense, the complete set of fluid equations which are associated to a prescribed fluid. From the mathematical viewpoint this involves the formal description of a fluid by means of a classical dynamical system which advances in time the relevant fluid fields. The possibility of defining an IKT for the 3D incompressible Navier-Stokes equations (INSE), recently investigated (Ellero \textit{et al}, 2004-2007) raises the interesting question whether the theory can be applied also to thermofluids, in such a way to satisfy also the second principle of thermodynamics. The goal of this paper is to prove that such a generalization is actually possible, by means of a suitable \textit{extended phase-space formulation}. We consider, as a reference test, the case of non-isentropic incompressible thermofluids, whose dynamics is described by the Fourier and the incompressible Navier-Stokes equations, the latter subject to the conditions of validity of the Boussinesq approximation., Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008)

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-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., Comment: Contributed paper at RGD26 (Kyoto, Japan, July 2008)

On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V = 7.2 , K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: R T = 788.4 ± 0.6 km ( 1 - σ error bar). This implies a density of ρ = 1.711 ± 0.005 g cm −3 using the value G M = ( 2.343 ± 0.006 ) × 10 11 m 3 s −2 derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362–374]. We do not detect any significant difference between equatorial and polar radii, in the limit r eq − r po = − 1.3 ± 2.1 km , in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: Δ α T cos ( δ T ) = − 108 ± 13 mas and Δ δ T = − 62 ± 7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: Δ α U cos ( δ U ) = − 100 ± 25 mas and Δ δ U = − 85 ± 25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of Δ α T cos ( δ T ) = − 127 ± 20 mas and Δ δ T = − 97 ± 13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10–20 nbar. More specifically, we find an upper limit of 13 nbar ( 1 - σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO2 atmosphere. We also provide an upper limit of 8 nbar for a possible CH4 atmosphere, and 22 nbar for pure N2, again at the 1 - σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54 ± 0.03 mas (corresponding to 7.5 ± 0.4 km projected at Titania). With a distance of 170 ± 25 parsecs, this corresponds to a radius of 9.8 ± 0.2 solar radii for HIP 106829, typical of a K0 III giant.

International audience; Context: In 2003, the Sun and the Earth passed through both the equatorial plane of Jupiter and therefore the orbital planes of its main satellites. Aims: During this period, mutual eclipses and occultations were observed and we present the data collected. Methods: Light curves of mutual eclipses and occultations were recorded by the observers of the international campaign PHEMU03 organized by the Institut de mécanique céleste, Paris, France. Results: We completed 377 observations of 118 mutual events from 42 sites and the corresponding data are presented in this paper. For each observation, information about the telescope, receptor, site, and observational conditions are provided. Conclusions: This paper gathers all data and indicates a first estimate of its precision. This catalogue of these rare events should constitute an improved basis for accurate astrometric data useful in the development of dynamical models.

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.

The physical mechanism responsible for driving accretion flows in astrophysical accretion disks is commonly thought to be related to the development of plasma instabilities and turbulence. A key question is therefore the determination of consistent equilibrium configurations for accretion-disk plasmas and investigation of their stability properties. In the case of collisionless plasmas kinetic theory provides the appropriate theoretical framework. This paper presents a kinetic description of low-frequency and long-wavelength axisymmetric electromagnetic perturbations in non-relativistic, strongly-magnetized and gravitationally-bound axisymmetric accretion-disk plasmas in the collisionless regime. The analysis, carried out within the framework of the Vlasov-Maxwell description, relies on stationary kinetic solutions of the Vlasov equation which allow for the simultaneous treatment of non-uniform fluid fields, stationary accretion flows and temperature anisotropies. It is demonstrated that, for such solutions, no axisymmetric unstable perturbations can exist occurring on characteristic time and space scales which are long compared with the Larmor gyration time and radius. Hence, these stationary configurations are actually stable against axisymmetric kinetic instabilities of this type. As a fundamental consequence, this rules out the possibility of having the axisymmetric magneto-rotational or thermal instabilities to arise in these systems.

Magnetic fields are a distinctive feature of accretion disc (AD) plasmas around compact objects (i.e., black holes and neutron stars) and they play a decisive role in their dynamical evolution. Of particular interest for the structure of ADs and their dynamical properties is the interaction between the magnetic field and the accreting plasma. The magnetic field can modify the velocity profile of the disc introducing species-dependent rotational frequencies. Moreover, from the microscopic point of view, the same field is a natural source of phase-space anisotropies, allowing for the existence of characteristic symmetries, which influence the dynamics of charged particles in the AD plasma. These features are important both for the kinetic description of AD plasmas and their influence on the collective plasma interactions. In this paper, basic issues concerned with the origin and structure of magnetic fields in collisionless astrophysical AD plasmas are discussed, with particular reference to the stationary dynamo phenomenon, which leads to the selfgeneration of the magnetic field appearing in these systems. More precisely, the problem is addressed here of the generation of both the poloidal and toroidal components of the AD magnetic field as a consequence of plasma currents produced purely by diamagnetic collisionless kinetic mechanisms, which are characterized by a slow-time variation.

An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite-size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the self-field generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self-4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on the Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e., point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed, respectively, in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.

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., 13 pages, 1 figure Accepted for publication in Physics of Plasmas

Magnetic fields are a distinctive feature of accretion disc plasmas around compact objects (i.e., black holes and neutron stars) and they play a decisive role in their dynamical evolution. A fundamental theoretical question related with this concerns investigation of the so- called gravitational MHD dynamo effect, responsible for the self-generation of magnetic fields in these systems. Experimental observations and theoretical models, based on fluid MHD descrip- tions of various types support the conjecture that accretion discs should be characterized by coherent and slowly time-varying magnetic fields with both poloidal and toroidal components. However, the precise origin of these magnetic structures and their interaction with the disc plasmas is currently unclear. The aim of this paper is to address this problem in the context of kinetic theory. The starting point is the investigation of a general class of Vlasov-Maxwell kinetic equilibria for axi-symmetric collisionless magnetized plasmas characterized by tempera- ture anisotropy and mainly toroidal flow velocity. Retaining finite Larmor-radius effects in the calculation of the fluid fields, we show how these configurations are capable of sustaining both toroidal and poloidal current densities. As a result, we suggest the possible existence of a ki- netic dynamo effect, which can generate a stationary toroidal magnetic field in the disc even without any net radial accretion flow. The results presented may have important implications for equilibrium solutions and stability analysis of accretion disc dynamics. In this paper basic issues concerned with the origin and the structure of magnetic fields in accretion disc (AD) plasmas are discussed, with particular reference to the dynamo phenomenon which leads to the self-generation of the magnetic field appearing in these systems. More precisely, we address the problem of the generation of both the poloidal and toroidal components of the AD magnetic field as a consequence of plasma currents produced purely by collisionless and quasi-stationary kinetic mechanisms. Experimental observations and theoretical models based on fluid MHD descriptions suggest that accretion discs should be characterized by coherent and slowly time-varying magnetic fields with both poloidal and toroidal components (see for example Frank et al., 2002 and Szuszkiewicz & Miller, 2001). An interesting development within this context has been the work by Coppi (2005) and Coppi & Rousseau (2006), who showed that stationary magnetic configurations in AD plasmas, for both low and high magnetic en- ergy densities, can exhibit complex magnetic structures characterized locally by plasma rings with closed nested magnetic surfaces. However, even the most sophisticated fluid models are still not able to give a satisfactory explanation for all of the complexity of the phenomena arising in these systems. In particular, the precise origin of these mag- netic structures and their interaction with the disc plasmas remains unclear. This is especially true for what concerns the toroidal magnetic field. Usually it is thought that such fields are the result of non-stationary processes associated with some ongoing in- stabilities in the plasma (possibly the same ones responsible for the accretion), but the

A characteristic feature of fluid theories concerns the difficulty of uniquely defining consistent closure conditions for the fluid equations. In fact it is well known that fluid theories cannot generally provide a closed system of equations for the fluid fields. This feature is typical of collisionless plasmas where, in contrast to collisional plasmas, asymptotic closure conditions do not follow as a consequence of an H-theorem This issue is of particular relevance in astrophysics where fluid approaches are usually adopted. On the other hand, it is well known that the determination of the closure conditions is in principle achievable in the context of kinetic theory. In the case of multi-species thermal magnetoplasmas this requires the determination of the species tensor pressure and of the corresponding heat fluxes. In this paper we investigate this problem in the framework of the Vlasov-Maxwell description for collisionless axisymmetric magnetoplasmas arising in astrophysics, with particular reference to accretion discs around compact objects (like black holes and neutron stars). The dynamics of collisionless plasmas in these environments is determined by the simultaneous presence of gravitational and magnetic fields, where the latter may be both externally produced and self-generated by the plasma currents. Our starting point here is the construction of a solution for the stationary distribution function describing slowly-varying gyrokinetic equilibria. The treatment is applicable to non-relativistic axisymmetric systems characterized by temperature anisotropy and differential rotation flows. It is shown that the kinetic formalism allows one to solve the closure problem and to consistently compute the relevant fluid fields with the inclusion of finite Larmor-radius effects. The main features of the theory and relevant applications are discussed.

Phase-space Lagrangian dynamics in ideal fluids (i.e, continua) is usually related to the so-called {\it ideal tracer particles}. The latter, which can in principle be permitted to have arbitrary initial velocities, are understood as particles of infinitesimal size which do not produce significant perturbations of the fluid and do not interact among themselves. An unsolved theoretical problem is the correct definition of their dynamics in ideal fluids. The issue is relevant in order to exhibit the connection between fluid dynamics and the classical dynamical system, underlying a prescribed fluid system, which uniquely generates its time-evolution. \ The goal of this paper is to show that the tracer-particle dynamics can be {\it exactly} established for an arbitrary incompressible fluid uniquely based on the construction of an inverse kinetic theory (IKT) (Tessarotto \textit{et al.}, 2000-2008). As an example, the case of an incompressible Newtonian thermofluid is here considered., submitted to Physica A

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., Accepted version for Physics of Plasmas