arXiv subjects

Guy Pelletier

Publications and source records attributed to Guy Pelletier.

At least 19 recordsLinked to original sources

arXiv2019

Physics of relativistic collisionless shocks: III The suprathermal particles

In this third paper of a series, we discuss the physics of the population of accelerated particles in the precursor of an unmagnetized, relativistic collisionless pair shock. In particular, we provide a theoretical estimate of their scattering length $l_{scatt}(p)$ in the self-generated electromagnetic turbulence, as well as an estimate of their distribution function. We obtain $l_{scatt}(p) \simeq (γ_p /ε_B)(p/γ_{\infty} mc)^2 (c/ω_p)$, with p the particle momentum in the rest frame of the shock front, $ε_B$ the strength parameter of the microturbulence, $γ_p$ the Lorentz factor of the background plasma relative to the shock front and $γ_{\infty}$ its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.

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arXiv2017

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.

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arXiv2014

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.

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arXiv2014

Collisionless Relativistic Shocks:current driven turbulence and particle acceleration

The physics of collisionless relativistic shocks with a moderate magnetization is presented. Micro-physics is relevant to explain the most energetic radiative phenomena of Nature, namely that of the termination shock of Gamma Ray Bursts. A transition towards Fermi process occurs for decreasing magnetization around a critical value which turns out to be the condition for the scattering to break the mean field inhibition. Scattering is produced by magnetic micro-turbulence driven by the current carried by returning particles, which had not been considered till now, but turns out to be more intense than Weibel's one around the transition. The current is also responsible for a buffer effect on the motion of the incoming flow, on which the threshold for the onset of turbulence depends.

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arXiv2012

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.

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arXiv2012

Particle acceleration in relativistic outflows

In this review we confront the current theoretical understanding of particle acceleration at relativistic outflows with recent observational results on various source classes thought to involve such outflows, e.g. gamma-ray bursts, active galactic nuclei, and pulsar wind nebulae. We highlight the possible contributions of these sources to ultra-high-energy cosmic rays.

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arXiv2011

Particle acceleration at relativistic shock waves

Relativistic sources, e.g. gamma-ray bursts, pulsar wind nebulae and powerful active galactic nuclei produce relativistic outflows that lead to the formation of collisionless shock waves, where particle acceleration is thought to take place. Our understanding of relativistic shock acceleration has improved in the past decade, thanks to the combination of analytical studies and high level numerical simulations. In ultra-relativistic shocks, particle acceleration is made difficult by the generically transverse magnetic field and large advection speed of the shocked plasma. Fast growing microturbulence is thus needed to make the Fermi process operative. It is thought, and numerical simulations support that view, that the penetration of supra-thermal particles in the shock precursor generates a magnetic turbulence which in turn produces the scattering process needed for particle acceleration through the Fermi mechanism. Through the comparison of the growth timescale of the microinstabilities in the shock precursor and the precursor crossing timescale, it is possible to delimit in terms of magnetization and shock Lorentz factor the region in which micro-turbulence may be excited, hence whether and how Fermi acceleration is triggered. These findings are summarized here and astrophysical consequences are drawn.

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arXiv2011

Gamma-ray bursts afterglows in magnetized stellar winds

Recent analytical and numerical work argue that successful relativistic Fermi acceleration requires a weak magnetization of the unshocked plasma, all the more so at high Lorentz factors. The present paper tests this conclusion by computing the afterglow of a gamma-ray burst outflow propagating in a magnetized stellar wind using "ab initio" principles regarding the microphysics of relativistic Fermi acceleration. It is shown that in magnetized environments, one expects a drop-out in the X-ray band on sub-day scales as the synchrotron emission of the shock heated electrons exits the frequency band. At later times, Fermi acceleration becomes operative when the blast Lorentz factor drops below a certain critical value, leading to the recovery of the standard afterglow light curve. Interestingly, the observed drop-out bears resemblance with the fast decay found in gamma-ray bursts early X-ray afterglows.

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arXiv2011

Dispersion and thermal effects on electromagnetic instabilities in the precursor of relativistic shocks

Fermi acceleration can develop efficiently at relativistic collisionless shock waves provided the upstream (unshocked) plasma is weakly magnetized. At low magnetization, the large size of the shock precursor indeed provides enough time for electromagnetic micro-instabilities to grow and such micro-instabilities generate small scale turbulence that in turn provides the scattering required. The present paper extends our previous analysis on the development of these micro-instabilities to account for the finite angular dispersion of the beam of reflected and accelerated particles and to account for the expected heating of the upstream electrons in the shock precursor. We show that the oblique two stream instability may operate down to values of the shock Lorentz factor gamma_{sh}~10 as long as the electrons of the upstream plasma remain cold, while the filamentation instability is strongly inhibited in this limit; however, as electrons get heated to relativistic temperatures, the situation becomes opposite and the two stream instability becomes inhibited while the filamentation mode becomes efficient, even at moderate values of the shock Lorentz factor. The peak wavelength of these instabilities migrates from the inertial electron scale towards the proton inertial scale as the background electrons get progressively heated during the crossing of the shock precursor. We also discuss the role of current driven instabilities upstream of the shock. In particular, we show that the returning/accelerated particles give rise to a transverse current through their rotation in the background magnetic field. We find that the compensating current in the background plasma can lead to a Buneman instability which provides an efficient source of electron heating. [Abridged]

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arXiv2009

On electromagnetic instabilities at ultra-relativistic shock waves

(Abridged) This paper addresses the issue of magnetic field generation in a relativistic shock precursor through micro-instabilities. The level of magnetization of the upstream plasma turns out to be a crucial parameter, notably because the length scale of the shock precursor is limited by the Larmor rotation of the accelerated particles in the background magnetic field and by the speed of the shock wave. We discuss in detail and calculate the growth rates of the following beam plasma instabilities seeded by the accelerated and reflected particle populations: for an unmagnetized shock, the Weibel and filamentation instabilities, as well as the Cerenkov resonant longitudinal and oblique modes; for a magnetized shock, the Weibel instability and the resonant Cerenkov instabilities with the longitudinal electrostatic modes, as well as the Alfven, Whisler and extraordinary modes. All these instabilities are generated upstream, then they are transmitted downstream. The modes excited by Cerenkov resonant instabilities take on particular importance with respect to the magnetisation of the downstream medium since, being plasma eigenmodes, they have a longer lifetime than the Weibel modes. We discuss the main limitation of the wave growth associated with the length of the precursor and the magnetisation of the upstream medium for both oblique and parallel shock waves. We also characterize the proper conditions to obtain Fermi acceleration. We recover some results of most recent particle-in-cell simulations and conclude with some applications to astrophysical cases of interest, pulsar winds and gamma-ray burst external shock waves in particular. (Abridged)

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arXiv2008

On Fermi acceleration and MHD-instabilities at ultra-relativistic magnetized shock waves

Fermi acceleration can take place at ultra-relativistic shock waves if the upstream or downstream magnetic field has been remodeled so that most of the magnetic power lies on short spatial scales. The relevant conditions under which Fermi acceleration become efficient in the presence of both a coherent and a short scale turbulent magnetic field are addressed. Within the MHD approximation, this paper then studies the amplification of a pre-existing magnetic field through the streaming of cosmic rays upstream of a relativistic shock wave. The magnetic field is assumed to be perpendicular in the shock front frame, as generally expected in the limit of large shock Lorentz factor. In the MHD regime, compressive instabilities seeded by the net cosmic-ray charge in the shock precursor (as seen in the shock front frame) develop on the shortest spatial scales but saturate at a moderate level deltaB/B ~ 1, which is not sufficient for Fermi acceleration. As we argue, it is possible that other instabilities outside the MHD range provide enough amplification to allow successful Fermi acceleration.

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arXiv2008

Fermi Acceleration at relativistic Shocks

After a successful development of theoretical and numerical works on Fermi acceleration at relativistic shocks, some difficulties recently raised with the scattering issue, a crucial aspect of the process. Most pioneering works were developed assuming the scattering off magnetic fluctuations as given. Even in that case, when a mean field is considered, its orientation is mostly perpendicular to the shock normal in the front frame, and this tends to quench the scattering process. Solving this difficulty leads to address the issue of the generation of very intense magnetic fluctuations at short wave lengths. The relativistic motion of the shock front let the cosmic rays to visit upstream during a very short time only, making this generation of magnetic fluctuations very challenging. Anyway there is some hope to solve the problem. Thanks to a recent work by Spitkovsky (2008) \cite{AS}, we know that the process works without any mean field and now we have to investigate up to which intensity the mean field can be amplified for allowing Fermi process with appropriate fast instabilities. In this presentation, the collisionless shock structure in relativistic regime is sketched, the scattering issue is presented, and the instabilities that can provide the expected magnetic field amplification are presented as well. Although there exists observational evidence that particles are accelerated in relativistic flows and are distributed according to a power law suggesting a Fermi process, the drastic conditions for Fermi process to work are not always clearly fulfilled.

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arXiv2008

3-d resistive MHD simulations of magnetic reconnection and the tearing mode instability in current sheets

Magnetic reconnection plays a critical role in many astrophysical processes where high energy emission is observed, e.g. particle acceleration, relativistic accretion powered outflows, pulsar winds and probably in dissipation of Poynting flux in GRBs. The magnetic field acts as a reservoir of energy and can dissipate its energy to thermal and kinetic energy via the tearing mode instability. We have performed 3d nonlinear MHD simulations of the tearing mode instability in a current sheet. Results from a temporal stability analysis in both the linear regime and weakly nonlinear (Rutherford) regime are compared to the numerical simulations. We observe magnetic island formation, island merging and oscillation once the instability has saturated. The growth in the linear regime is exponential in agreement with linear theory. In the second, Rutherford regime the island width grows linearly with time. We find that thermal energy produced in the current sheet strongly dominates the kinetic energy. Finally preliminary analysis indicates a P(k) 4.8 power law for the power spectral density which suggests that the tearing mode vortices play a role in setting up an energy cascade.

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arXiv2006

On the efficiency of Fermi acceleration at relativistic shocks

It is shown that Fermi acceleration at an ultra-relativistic shock wave cannot operate on a particle for more than 1 1/2 Fermi cycle (i.e., u -> d -> u -> d) if the particle Larmor radius is much smaller than the coherence length of the magnetic field on both sides of the shock, as is usually assumed. This conclusion is shown to be in excellent agreement with recent numerical simulations. We thus argue that efficient Fermi acceleration at ultra-relativistic shock waves requires significant non-linear processing of the far upstream magnetic field with strong amplification of the small scale magnetic power. The streaming or transverse Weibel instabilities are likely to play a key role in this respect.

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arXiv2006

Turbulence and particle acceleration in collisionless supernovae remnant shocks: I-Anisotropic spectra solutions

This paper investigates the nature of the MHD turbulence excited by the streaming of accelerated cosmic rays in a shock wave precursor. The two recognised regimes (non-resonant and resonant) of the streaming instability are taken into account. We show that the non-resonant instability is very efficient and saturates through a balance between its growth and non-linear transfer. The cosmic-ray resonant instability then takes over and is quenched by advection through the shock. The level of turbulence is determined by the non-resonant regime if the shock velocity $V_{\rm sh}$ is larger than a few times $ξ_{\rm CR} c$, where $ξ_{\rm CR}$ is the ratio of the cosmic-ray pressure to the shock kinetic energy. The instability determines the dependence of the spectrum with respect to $k_\parallel$ (wavenumbers along the shock normal). The transverse cascade of Alfvén waves simultaneously determines the dependence in $k_{\perp}$. We also study the redistribution of turbulent energy between forward and backward waves, which occurs through the interaction of two Alfvén and one slow magneto-sonic wave. Eventually the spectra at the longest wavelengths are found almost proportional to $k_{\parallel}^{-1}$. Downstream, anisotropy is further enhanced through the compression at shock crossing.

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arXiv2006

Turbulence and particle acceleration in collisionless supernovae remnant shocks: II- Cosmic-ray transport

Supernovae remnant shock waves could be at the origin of cosmic rays up to energies in excess of the knee ($E\simeq3\cdot 10^{15} $eV) if the magnetic field is efficiently amplified by the streaming of accelerated particles in the shock precursor. This paper follows up on a previous paper \citep{pell05} which derived the properties of the MHD turbulence so generated, in particular its anisotropic character, its amplitude and its spectrum. In the present paper, we calculate the diffusion coefficients, also accounting for compression through the shock, and show that the predicted three-dimensional turbulence spectrum $k_\perp S_{3\rm d}(k_\parallel,k_\perp)\propto k_\parallel^{-1}k_\perp^{-α}$ (with $k_\parallel$ and $k_\perp$ the wavenumber components along and perpendicular to the shock normal) generally leads to Bohm diffusion in the parallel direction. However, if the anisotropy is constrained by a relation of the form $k_\parallel \propto k_\perp^{2/3}$, which arises when the turbulent energy cascade occurs at a constant rate independent of scale, then the diffusion coefficient loses its Bohm scaling and scales as in isotropic Kolmogorov turbulence. We show that these diffusion coefficients allow to account for X-ray observations of supernova remnants. This paper also calculates the modification of the Fermi cycle due to the energy lost by cosmic rays in generating upstream turbulence and the concomittant steepening of the energy spectrum. Finally we confirm that cosmic rays can produced an amplified turbulence in young SNr during their free expansion phase such that the maximal energy is close to the knee and the spectral index is close to 2.3 in the warm phase of the interstellar medium

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arXiv2004

High Energy Emission and Cosmic Rays from Gamma-Ray Bursts

The paper is devoted to the analysis of particle acceleration in Gamma-Ray Bursts and its radiative consequences. Therefore we get on one hand constraints on the physics and on the other hand possible signatures of particle acceleration that could be recorded by the new gamma ray instruments. We have previously shown that UHECRs can be generated in GRBs even with conservative assumptions on the magnetic field and the scattering capability of its perturbations, provided that a suitable relativistic Fermi process is at work during the so-called "internal shock" phase. We extend here the analysis of the consequences of these assumptions to the whole prompt emission of both electrons and protons. Indeed, assuming that the magnetic field decays in $1/r^2$ and that the scattering time of particles is longer than the Bohm's assumption, in particular with a rule derived from Kolmogorov scaling, we show with no other parameter adaptation that the intensity of the subequipartition magnetic field, that: i) UHECRs can be generated with a sufficient flux within the GZK-sphere to account for the CR-spectrum at the ankle. ii) The peak energy of the gamma spectrum around 100 keV, namely the so-called $E_{peak}$, is conveniently explained. iii) A thermal component below the $E_{peak}$ is often unavoidable. iv) The cosmic rays could radiate gamma rays around 67 MeV (in the co-moving frame, which implies $\simeq 20$ GeV for the observer) due to $π^0$-decay and a low energy neutrino emission (around 0.2 GeV) associated to neutron decay and also neutrinos of energy between 5 and 150 GeV from muon decay. v) The UHECRs radiate high energy gamma rays between a few tens of MeV and 10 GeV (taking the pair creation process into account) due to their synchrotron emission with a sufficient flux to be observable.

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arXiv2001

Transport of Cosmic Rays in Chaotic Magnetic Fields

The transport of charged particles in disorganised magnetic fields is an important issue which concerns the propagation of cosmic rays of all energies in a variety of astrophysical environments, such as the interplanetary, interstellar and even extra-galactic media, as well as the efficiency of Fermi acceleration processes. We have performed detailed numerical experiments using Monte-Carlo simulations of particle propagation in stochastic magnetic fields in order to measure the parallel and transverse spatial diffusion coefficients and the pitch angle scattering time as a function of rigidity and strength of the turbulent magnetic component. We confirm the extrapolation to high turbulence levels of the scaling predicted by the quasi-linear approximation for the scattering frequency and parallel diffusion coefficient at low rigidity. We show that the widely used Bohm diffusion coefficient does not provide a satisfactory approximation to diffusion even in the extreme case where the mean field vanishes. We find that diffusion also takes place for particles with Larmor radii larger than the coherence length of the turbulence. We argue that transverse diffusion is much more effective than predicted by the quasi-linear approximation, and appears compatible with chaotic magnetic diffusion of the field lines. We provide numerical estimates of the Kolmogorov length and magnetic line diffusion coefficient as a function of the level of turbulence. Finally we comment on applications of our results to astrophysical turbulence and the acceleration of high energy cosmic rays in supernovae remnants, in super-bubbles, and in jets and hot spots of powerful radio-galaxies.

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