G. Pelletier

Particle transport and heating in the microturbulent precursor of relativistic shocks

Collisionless relativistic shocks have been the focus of intense theoretical and numerical investigations in recent years. The acceleration of particles, the generation of electromagnetic microturbulence and the building up of a shock front are three interrelated essential ingredients of a relativistic collisionless shock wave. In this paper we investigate two issues of importance in this context: (1) the transport of suprathermal particles in the excited microturbulence upstream of the shock and its consequences regarding particle acceleration; (2) the preheating of incoming background electrons as they cross the shock precursor and experience relativistic oscillations in the microturbulent electric fields. We place emphasis on the importance of the motion of the electromagnetic disturbances relatively to the background plasma and to the shock front. This investigation is carried out for the two major instabilities involved in the precursor of relativistic shocks, the filamentation instability and the oblique two stream instability. Finally, we use our results to discuss the maximal acceleration at the external shock of a gamma-ray burst; we find in particular a maximal synchrotron photon energy of the order of a few GeV.

Particle transport in intense small-scale magnetic turbulence with a mean field

Various astrophysical studies have motivated the investigation of the transport of high energy particles in magnetic turbulence, either in the source or en route to the observation sites. For strong turbulence and large rigidity, the pitch-angle scattering rate is governed by a simple law involving a mean free path that increases proportionally to the square of the particle energy. In this paper, we show that perpendicular diffusion deviates from this behavior in the presence of a mean field. We propose an exact theoretical derivation of the diffusion coefficients and show that a mean field significantly changes the transverse diffusion even in the presence of a stronger turbulent field. In particular, the transverse diffusion coefficient is shown to reach a finite value at large rigidity instead of increasing proportionally to the square of the particle energy. Our theoretical derivation is corroborated by a dedicated Monte Carlo simulation. We briefly discuss several possible applications in astrophysics.

Current-driven filamentation upstream of magnetized relativistic collisionless shocks

The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron relativistic shocks and we argue that this instability shapes the micro-physics at moderate magnetization levels and/or large Lorentz factors. This instability is seeded by the electric current carried by the accelerated particles in the shock precursor as they gyrate around the background magnetic field. The compensation current induced in the background plasma leads to an unstable configuration, with the appearance of charge neutral filaments carrying a current of the same polarity, oriented along the perpendicular current. This ``current-driven filamentation instability grows faster than any other instability studied so far upstream of relativistic shocks, with a growth rate comparable to the plasma frequency. Furthermore, the compensation of the current is associated with a slow-down of the ambient plasma as it penetrates the shock precursor (as viewed in the shock rest frame). This slow-down of the plasma implies that the ``current driven filamentation instability can grow for any value of the shock Lorentz factor, provided the magnetization sigma <~ 10^{-2}. We argue that this instability explains the results of recent particle-in-cell simulations in the mildly magnetized regime.

A fast current-driven instability in relativistic collisionless shocks

We report here on a fast current-driven instability at relativistic collisionless shocks, triggered by the perpendicular current carried by the supra-thermal particles as they gyrate around the background magnetic field in the shock precursor. We show that this instability grows faster than any other instability studied so far in this context, and we argue that it is likely to shape the physics of the shock and of particle acceleration in a broad parameter range.

Langmuir turbulence as a critical phenomenon. Part 1. Destruction of the statistical equilibrium of an interacting-modes ensemble

This paper is the first part of a work concerning a statistical theory of Langmuir turbulence in which the destabilization of an ensemble of plasmons by self- modulation is considered as a critical phenomenon. The first part is devoted to a discussion of the existence of a statistical equilibrium for the ensemble of modes. A transition curve, which separates equilibrium from non-equilibrium, is found. Several properties of the plasma, when the self-modulation instability is saturated, are derived in the neighbourhood of the critical Langmuir energy density W c . In particular, the Langmuir energy spectrum is found to be proportional to k d-3 , the correlation length is found to diverge as uW–W c u– half , and the anomalous conductivity at the plasma frequency is found to diverge as uW – W c u- 1 .

Fluctuation spectrum in turbulent plasma

A nonlinear fluctuation—dissipation theorem is derived for a turbulent plasma. The method of dressed test particles is generalized to a nonlinearly stable plasma; the turbulent state is described by the Dupree—Weinstock formalism. A comparison with the Cook—Taylor theory is discussed.

Towards Understanding the Physics of Collisionless Relativistic Shocks

Relativistic astrophysical collisionless shocks represent outstanding dissipation agents of the huge power of relativistic outflows produced by accreting black holes, core collapsed supernovae and other objects into multi-messenger radiation (cosmic rays, neutrinos, electromagnetic radiation). This article provides a theoretical discussion of the fundamental physical ingredients of these extreme phenomena. In the context of weakly magnetized shocks, in particular, it is shown how the filamentation type instabilities, which develop in the precursor of pair dominated or electron-ion shocks, provide the seeds for the scattering of high energy particles as well as the agent which preheats and slows down the incoming precursor plasma. This analytical discussion is completed with a mesoscopic, non-linear model of particle acceleration in relativistic shocks based on Monte Carlo techniques. This Monte Carlo model uses a semi-phenomenological description of particle scattering which allows it to calculate the back-reaction of accelerated particles on the shock structure on length and momentum scales which are currently beyond the range of microscopic particle-in-cell (PIC) simulations.

Analysis of the Dupree-Weinstock theory of turbulent plasma in a magnetic field

The Dupree-Weinstock model which describes the plasma turbulence is analysed with an applied strong magnetic field. The conservation of energy and the validity of the weak coupling assumption are investigated. The theory is applied to the particular case of an ion acoustic turbulence.

Relativistic outflows from compact objects and generation of Astroparticles

High Energy Astrophysics relates to the environment of compact objects that manifest themselves through the generation of non-thermal radiation from radio band up to very high energy gamma rays, cosmic ray generation up to the Ultra High Energy range (a few 1020eV ), very high energy neutrinos (as recorded now by Icecube observatory); in the future, we can expect the detection of Gravitational Waves produced by the formation of compact objects. There are two major physical processes that underline that manifestation, first the formation of relativistic jets, especially in the vicinity of Black Holes, second the formation of relativistic shocks that dissipate their energy with the production of electromagnetic turbulence and astroparticles. These two major processes are paradoxical in the sense that they do not rely on common physical sense and require some inquiry involving non trivial mechanism of General Relativity or non trivial mechanism of collisionless micro-physics. These two processes will be briefly presented with an update of their status.