Physics of relativistic collisionless shocks: The scattering-center frame

Electron Heating in High Mach Number Collisionless Shocks

The energy partition in high Mach number collisionless shock waves is central to a wide range of high-energy astrophysical environments. We present a new theoretical model for electron heating that accounts for the energy exchange between electrons and ions at the shock. The fundamental mechanism relies on the difference in inertia between electrons and ions, resulting in differential scattering of the particles off a decelerating magnetically dominated microturbulence across the shock transition. We show that the self-consistent interplay between the resulting ambipolar-type electric field and diffusive transport of electrons leads to efficient heating in the magnetic field produced by the Weibel instability in the high Mach number regime and is consistent with fully kinetic simulations.

High-energy acceleration phenomena in extreme-radiation-plasma interactions

We simulate, using a particle-in-cell code, the chain of acceleration processes at work during the Compton-based interaction of a dilute electron-ion plasma with an extreme-intensity, incoherent γ-ray flux with a photon density several orders of magnitude above the particle density. The plasma electrons are initially accelerated in the radiative flux direction through Compton scattering. In turn, the charge-separation field from the induced current drives forward the plasma ions to near-relativistic speed and accelerates backwards the nonscattered electrons to energies easily exceeding those of the driving photons. The dynamics of those energized electrons is determined by the interplay of electrostatic acceleration, bulk plasma motion, inverse Compton scattering and deflections off the mobile magnetic fluctuations generated by a Weibel-type instability. The latter Fermi-like effect notably gives rise to a forward-directed suprathermal electron tail. We provide simple analytical descriptions for most of those phenomena and examine numerically their sensitivity to the parameters of the problem.

Saturation of the asymmetric current filamentation instability under conditions relevant to relativistic shock precursors

The current filamentation instability, which generically arises in the counterstreaming of plasma flows, is known for its ability to convert the free energy associated with anisotropic momentum distributions into kinetic-scale magnetic fields. The saturation of this instability has been extensively studied in symmetric configurations where the interpenetrating plasmas share the same properties (velocity, density, temperature). In many physical settings, however, the most common configuration is that of asymmetric plasma flows. For instance, the precursor of relativistic collisionless shock waves involves a hot, dilute beam of accelerated particles reflected at the shock front and a cold, dense inflowing background plasma. To determine the appropriate criterion for saturation in this case, we have performed large-scale two-dimensional particle-in-cell simulations of counterstreaming electron-positron pair and electron-ion plasmas. We show that, in interpenetrating pair plasmas, the relevant criterion is that of magnetic trapping as applied to the component (beam or plasma) that carries the larger inertia of the two; namely, the instability growth suddenly slows down once the quiver frequency of those particles equals or exceeds the instability growth rate. We present theoretical approximations for the saturation level. These findings remain valid for electron-ion plasmas provided that electrons and ions are close to equipartition in the plasma flow of larger inertia. Our results can be directly applied to the physics of relativistic, weakly magnetized shock waves, but they can also be generalized to other cases of study.

Physics and Phenomenology of Weakly Magnetized, Relativistic Astrophysical Shock Waves

Weakly magnetized, relativistic collisionless shock waves are not only the natural offsprings of relativistic jets in high-energy astrophysical sources, they are also associated with some of the most outstanding displays of energy dissipation through particle acceleration and radiation. Perhaps their most peculiar and exciting feature is that the magnetized turbulence that sustains the acceleration process, and (possibly) the secondary radiation itself, is self-excited by the accelerated particles themselves, so that the phenomenology of these shock waves hinges strongly on the microphysics of the shock. In this review, we draw a status report of this microphysics, benchmarking analytical arguments with particle-in-cell simulations, and extract consequences of direct interest to the phenomenology, regarding, in particular, the so-called microphysical parameters used in phenomenological studies.

Physics of relativistic collisionless shocks. II. Dynamics of the background plasma

In this second paper of a series, we discuss the dynamics of a plasma entering the precursor of an unmagnetized, relativistic collisionless pair shock. We discuss how this background plasma is decelerated and heated through its interaction with a microturbulence that results from the growth of a current filamentation instability in the shock precursor. We make use, in particular, of the reference frame R_{w} in which the turbulence is mostly magnetic. This frame moves at relativistic velocities towards the shock front at rest, decelerating gradually from the far to the near precursor. In a first part, we construct a fluid model to derive the deceleration law of the background plasma expected from the scattering of suprathermal particles off the microturbulence. This law leads to the relationship γ_{p}∼ξ_{b}^{-1/2} between the background plasma Lorentz factor γ_{p} and the normalized pressure of the beam ξ_{b}; it is found to match nicely the spatial profiles observed in large-scale 2D3V particle-in-cell simulations. In a second part, we model the dynamics of the background plasma at the kinetic level, incorporating the inertial effects associated with the deceleration of R_{w} into a Vlasov-Fokker-Planck equation for pitch-angle diffusion. We show how the effective gravity in R_{w} drives the background plasma particles through friction on the microturbulence, leading to efficient plasma heating. Finally, we compare a Monte Carlo simulation of our model with dedicated PIC simulations and conclude that it can satisfactorily reproduce both the heating and the deceleration of the background plasma in the shock precursor, thereby providing a successful one-dimensional description of the shock transition at the microscopic level.

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)≈γ_{p}ε_{B}^{-1}(p/γ_{∞}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_{∞} its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.

Physics of Weibel-Mediated Relativistic Collisionless Shocks

We develop a comprehensive theoretical model of relativistic collisionless pair shocks mediated by the current filamentation instability. We notably characterize the noninertial frame in which this instability is of a mostly magnetic nature, and describe at a microscopic level the deceleration and heating of the incoming background plasma through its collisionless interaction with the electromagnetic turbulence. Our model compares well to large-scale 2D3V particle-in-cell simulations, and provides an important touchstone for the phenomenology of such plasma systems.