A comprehensive review is given of the various processes proposed for accelerating particles by shocks to high energies. These energies are limited by several bounds: the non-relativistic nature of the heliospheric collisionless shocks to which this review restricts, the finite size of these shocks, the finite width of the downstream region, and to the nature of turbulence. In general, collisionless shocks in the heliosphere cannot accelerate particles to very high energies. As a fundamental problem of the acceleration mechanism the injection of see particles is identified. Some mecchanisms for production of seed particles are invoked. Acceleration of electrons begins to uncover its nature. The following problems are covered in this chapter: 1. Introduction -- first and second order Fermi acceleration, 2. Accelerating ions when they are already fast, diffusive acceleration, convection diffusion equation, Lee's self-consistent quasilinear shock acceleration model, 3. Observations, 4. The injection problem, ion surfing, test particle simulations, self-consistent shock acceleration simulations, downstream leakage, trapped particle acceleration, 5. Accelerating electrons, Sonnerup-Wu mechanism, Hoshino's electron shock surfing on quasi-perpendicular shocks, quasiparallel shock surfing.
The problem of collisionless shocks is posed as the problem of understanding how in a completely collisionless streaming high-temperature plasma shocks can develop at all, forming discontinuous transition layers of thickness much less than any collisional mean free path length. The history of shock research is briefly reviewed. It is expressed that collisionless shocks as a realistic possibility of a state of matter have been realized not earlier than roughly half a centruy ago. The basic properties of collisionless shocks are noted in preparing the theory of collisionless shocks and a classif…
A direct numerical simulation of a strong relativistic collisionless shock propagating into an unmagnetized medium has been performed in two spatial dimensions. It is found that: (i) collisionless shock exists, (ii) particle acceleration is insignificant, (iii) the shock does not generate ``quasi-static'' magnetic fields, contrary to recent claims by other authors. All our results agree with a simple plasma-physical model of collisionless shocks. On the other hand, astrophysical evidence indicates that shocks do accelerate charged particles, and GRB phenomenology indicates that shocks do gener…
We discuss 3D simulations of relativistic collisionless shocks in electron-positron pair plasmas using the particle-in-cell (PIC) method. The shock structure is mainly controlled by the shock's magnetization ("sigma" parameter). We demonstrate how the structure of the shock varies as a function of sigma for perpendicular shocks. At low magnetizations the shock is mediated mainly by the Weibel instability which generates transient magnetic fields that can exceed the initial field. At larger magnetizations the shock is dominated by magnetic reflections. We demonstrate where the transition occurs…
The theory and simulations of quasi-perpendicular and strictly perpendicular collisionless shocks are reviewed. The text is structured into the following sections and subsections: 1. Setting the frame, where the quasi-perpendicular shock problem is formulated, reflected particle dynamics is described in theoretical terms, foot formation and foot ion acceleration discussed, and the shock potential explained. 2. Shock structure, 3. Ion dynamics, describing its role in shock reformation and the various ion-excited instabilities. 4. Electron dynamics, describing electron instabilities in the foot;…
We suggest that coherent radiation may occur in relativistic collisionless shocks via two-stream Weibel instabilities. The coherence amplifies the radiation power by many orders [$\sim 10^{12}$ in Gamma-Ray Bursts (GRBs)] and particles cool very fast before being randomized. We imply (1) GRBs accompany strong infrared emission, (2) protons efficiently transfer energy to electrons and (3) prompt GRBs might be the upscattered coherent radiation.
We show that the Weibel-mediated collisionless shocks are driven at non-relativistic propagation speed (0.1c < V < 0.45c) in unmagnetized electron-ion plasmas by performing two-dimensional particle-in-cell simulations. It is shown that the profiles of the number density and the mean velocity in the vicinity of the shock transition region, which are normalized by the respective upstream values, are almost independent of the upstream bulk velocity, i.e., the shock velocity. In particular, the width of the shock transition region is ~100 ion inertial length independent of the shock velocity. For …
Using a so-called hemispherical model we derive a general transport equation for cosmic ray and thermal particles scattered in pitch angle by magnetic inhomogeneities in a moving collisionless plasma. The weak scattering through 90 degrees results in isotropic particle distributions in each hemisphere. The consideration is not limited by small anisotropies and by the condition that particle velocities are higher than characteristic flow velocity differences. For high velocities and small anisotropies the standard cosmic ray transport equation is recovered. We apply the equations derived for in…
We present numerical results from plasma particle simulations of collisionless shocks and ultra-relativistic counter-streaming plasmas. We demonstrate how the field-particle interactions lead to particle acceleration behind the shock-front. Further, we demonstrate how ultra relativistic counter-streaming plasmas create large scale patchy magnetic field structures and that these field structures propagate down-stream of the shock front. These results may help explain the origin of the magnetic fields and accelerated electrons responsible for afterglow synchrotron radiation from gamma ray bursts…
A two-dimensional (2D) shock-rest-frame model for particle simulations is developed. Then full kinetic dynamics of a perpendicular collisionless shock is examined by means of a 2D full particle simulation. We found that in the 2D simulation there are fewer nonthermal electrons due to surfing acceleration which was seen in the previous 1D simulations of a high Mach number perpendicular shock in a low-beta and weakly magnetized plasma. This is because the particle motion along the ambient magnetic field disturbs the formation of coherent electrostatic solitary structures which is necessary for e…
We summarize latest PIC simulation results on the radiation from Poynting jets and strongly magnetized collisionless shocks when a Poynting jet runs into cold ambient medium. We find that in all cases the radiative power output is much below that predicted by synchrotron radiation and the critical frequency is also much lower than the synchrotron critical frequency. We discuss the implications for the interpretation of GRB prompt emission data.
1. Introduction, 2. The (quasi-parallel) foreshock; Ion foreshock, Ion foreshock boundary region; Diffuse ions;Low-frequency upstream waves; Ion beam waves; The expected wave modes; Observations; Diffuse ion waves; Electron foreshock; Electron beams; Langmuir waves; stability of the electron beam; Electron foreshock boundary waves; Nature of electron foreshock waves; Radiation; Observations; Interpretation; 3. Quasi-parallel shock reformation; Low-Mach number quasi-parallel shocks; Turbulent reformation; Observations; Simulations of quasi-parallel shock reformation; Hybrid simulations in 1D; H…
Particle acceleration in collisionless shocks is believed to be responsible for the production of cosmic-rays over a wide range of energies, from few GeV to >10^{20}eV, as well as for the non-thermal emission of radiation from a wide variety of high energy astrophysical sources. A theory of collisionless shocks based on first principles does not, however, exist. Observations of gamma-ray burst (GRB) "afterglows" provide a unique opportunity for diagnosing the physics of relativistic collisionless shocks. Most GRBs are believed to be associated with explosions of massive stars. Their "afterglow…
It is shown that collisionless shock waves can be driven in unmagnetized electron-positron plasmas by performing a two-dimensional particle-in-cell simulation. At the shock transition region, strong magnetic fields are generated by a Weibel-like instability. The generated magnetic fields are strong enough to deflect the incoming particles from upstream of the shock at a large angle and provide an effective dissipation mechanism for the shock. The structure of the collisionless shock propagates at an almost constant speed. There is no linear wave corresponding to the shock wave and therefore th…
Collisionless shocks play a role in many astrophysical phenomena, from coronal mass ejections (CMEs) in the heliosphere to supernova remnants. Their role in heating and accelerating particles is well accepted yet the exact mechanism for ion heating is not well understood. Two systems, CMEs and supernova remnants, were examined to determine the heating of heavy ions as they pass through collisionless shocks thus providing a seed population for cosmic ray acceleration processes. Three parameters are examined, the plasma beta, the Mach number of the shock and the magnetic angle of the shock. CMEs…
The radiation from afterglows of gamma-ray bursts is generated in the collisionless plasma shock interface between a relativistic outflow and a quiescent circum-burst medium. The two main ingredients responsible for the radiation are high-energy, non-thermal electrons and a strong magnetic field. In this Letter we present, for the first time, synthetic spectra extracted directly from first principles particle-in-cell simulations of relativist collisionless plasma shocks. The spectra are generated by a numerical Fourier transformation of the electrical far-field from each of a large number of p…
Tsiklauri et al. recently published a theoretical model of electron acceleration by Alfvén waves in a nonuniform collisionless plasmas. We compare their work with a series of results published earlier by an another team, of which Tsiklauri et al. were probably unaware. We show that these two series of works, apparently conducted independently, lead to the same conclusions. This reinforces the theoretical consistency of the model.
A full particle simulation study is carried out on the electron acceleration at a collisionless, relatively low Alfven Mach number (M_A=5), perpendicular shock. Recent self-consistent hybrid shock simulations have demonstrated that the shock front of perpendicular shocks has a dynamic rippled character along the shock surface of low-Mach-number perpendicular shocks. In this paper, the effect of the rippling of perpendicular shocks on the electron acceleration is examined by means of large-scale (ion-scale) two-dimensional full particle simulations. It has been shown that a large-amplitude elec…
This paper develops the basic sets of equations which lead to the conservation laws describing collisionless plasma shock waves. We discuss the evolution of shock waves by wave steepening, derive the Rankine-Hugoniot conditions for magnetogasdynamic shocks, discuss various analytical models of shock formation, and discuss the basic instabilities which may become important in collisionless shock physics. We then present a survey of the theory of anomalous resistivity in the quasilinear limit and beyond and discuss mechanisms of shock particle reflection as far as they have been investigated in …
The identification of pre-acceleration mechanisms for cosmic ray ions in supernova remnant shocks is an important problem in astrophysics. Recent particle-in-cell (PIC) shock simulations have shown that inclusion of the full electron kinetics yields non-time-stationary solutions, in contrast to previous hybrid (kinetic ions, fluid electrons) simulations. Here, by running a PIC code at high phase space resolution, ion acceleration mechanisms associated with the time dependence of a supercritical collisionless perpendicular shock are examined. In particular the components of $\int \mathbf{F} \cd…
Relativistic collisionless shocks in electron-ion plasma are thought to occur in the afterglow phase of Gamma-Ray Bursts (GRBs), and in other environments where relativistic flows interact with the interstellar medium. A particular regime of shocks in an unmagnetized plasma has generated much interest for GRB applications. In this paper we present ab-initio particle-in-cell simulations of unmagnetized relativistic electron-ion shocks. Using long-term 2.5-dimensional simulations with ion-electron mass ratios from 16 to 1000 we resolve the shock formation and reach a steady-state shock structure…
We analytically study diffusive particle acceleration in relativistic, collisionless shocks. We find a simple relation between the spectral index s and the anisotropy of the momentum distribution along the shock front. Based on this relation, we obtain s = (3beta_u - 2beta_u*beta_d^2 + beta_d^3) / (beta_u - beta_d) for isotropic diffusion, where beta_u (beta_d) is the upstream (downstream) fluid velocity normalized to the speed of light. This result is in agreement with previous numerical determinations of s for all (beta_u,beta_d), and yields s=38/9 in the ultra-relativistic limit. The spectr…
Electron acceleration mechanism at high Mach number collisionless shocks propagating in a weakly magnetized medium is investigated by a self-consistent two-dimensional particle-in-cell simulation. Simulation results show that strong electrostatic waves are excited via the electron-ion electrostatic two-stream instability at the leading edge of the shock transition region as in the case of earlier one-dimensional simulations. We observe strong electron acceleration that is associated with the turbulent electrostatic waves in the shock transition region. The electron energy spectrum in the shock…
Collisionless shocks are commonly argued to be the sites of cosmic ray (CR) acceleration. We study the influence of CRs on weakly magnetized relativistic collisionless shocks and apply our results to external shocks in gamma-ray burst (GRB) afterglows. The common view is that the transverse Weibel instability (TWI) generates a small-scale magnetic field that facilitates collisional coupling and thermalization in the shock transition. The TWI field is expected to decay rapidly, over a finite number of proton plasma skin depths from the transition. However, the synchrotron emission in GRB afterg…
The outflows from gamma ray bursts, active galactic nuclei and relativistic jets in general interact with the surrounding media through collisionless shocks. With three dimensional relativistic particle-in-cell simulations we investigate such shocks. The results from these experiments show that small--scale magnetic filaments with strengths of up to percents of equipartition are generated and that electrons are accelerated to power law distributions N(E)~E^{-p} in the vicinity of the filaments through a new acceleration mechanism. The acceleration is locally confined, instantaneous and differs…
It is argued and demonstrated by particle-in-cell simulations that the synchrotron maser instability could develop at the front of a relativistic, magnetized shock. The instability generates strong low-frequency electromagnetic waves propagating both upstream and downstream of the shock. Upstream of the shock, these waves make electrons lag behind ions so that a longitudinal electric field arises and the electrons are accelerated up to the ion kinetic energy. Then thermalization at the shock front results in a plasma with equal temperatures of electrons and ions. Downstream of the shock, the a…
We present results from three-dimensional particle simulations of collisionless shocks with relativistic counter-streaming ion-electron plasmas. Particles are followed over many skin depths downstream of the shock. Open boundaries allow the experiments to be continued for several particle crossing times. The experiments confirm the generation of strong magnetic and electric fields by a Weibel-like kinetic streaming instability, and demonstrate that the electromagnetic fields propagate far downstream of the shock. The magnetic fields are predominantly transversal, and are associated with mergin…
Using a three dimensional relativistic particle-in-cell code we have performed numerical experiments of plasma shells colliding at relativistic velocities. Such scenarios are found in many astrophysical objects e.g. the relativistic outflow from gamma ray bursts, active galactic nuclei jets and supernova remnants. We show how a Weibel-like two-stream instability is capable of generating small-scale magnetic filaments with strength up to percents of equipartition. Such field topology is ideal for the generation of jitter radiation as opposed to synchrotron radiation. We also explain how the fie…
Gamma ray bursts are among the most energetic events in the known universe. A highly relativistic fireball is ejected. In most cases the burst itself is followed by an afterglow, emitted under deceleration as the fireball plunges through the circum-stellar media. To interpret the observations of the afterglow emission, two physical aspects need to be understood: 1) The origin and nature of the magnetic field in the fireball and 2) the particle velocity distribution function behind the shock. Both are necessary in existing afterglow models to account for what is believed to be synchrotron radia…
The kinetic theory of collisionless electrostatic shocks resulting from the collision of plasma slabs with different temperatures and densities is presented. The theoretical results are confirmed by self-consistent particle-in-cell simulations, revealing the formation and stable propagation of electrostatic shocks with very high Mach numbers ($M \gg 10$), well above the predictions of the classical theories for electrostatic shocks.
It is generally accepted that magnetic fields generated in the nonlinear development of the transverse Weibel instability provide effective collisionality in unmagnetized collisionless shocks. Recently, extensive two and three dimensional simulations improved our understanding of the growth and saturation of the instability in colliding plasma shells. However, the steady-state structure of the shock wave transition layers remains poorly understood. We use basic physical considerations and order-of-magnitude arguments to study the steady state structure in relativistic unmagnetized collisionles…
Charged plasma particles form an anisotropic counter-streaming distribution at the front of a shock. In the near- and ultra-relativistic regimes, Weibel (or two-stream) instability produces near-equipartition, chaotic, small-scale magnetic fields. The fields introduce effective collisions and "thermalize" the plasma particles via pitch-angle scattering. The properties of jitter radiation emitted by accelerated electrons from these small-scale fields are markedly different from synchrotron spectra. Here we theoretical summary and the results of recent numerical 3D PIC plasma kinetic simulations…
Particle-In-Cell (kinetic) simulations of shear Alfvén wave interaction with one dimensional, across the uniform magnetic field, density inhomogeneity (phase mixing) in collisionless plasma were performed for the first time. As a result a new electron acceleration mechanism is discovered. Progressive distortion of Alfvén wave front, due to the differences in local Alfvén speed, generates nearly parallel to the magnetic field electrostatic fields, which accelerate electrons via Landau damping. Surprisingly, amplitude decay law in the inhomogeneous regions, in the kinetic regime, is the same as …
We study the long term evolution of magnetic fields generated by an initially unmagnetized collisionless relativistic $e^+e^-$ shock. Our 2D particle-in-cell numerical simulations show that downstream of such a Weibel-mediated shock, particle distributions are approximately isotropic, relativistic Maxwellians, and the magnetic turbulence is highly intermittent spatially, nonpropagating, and decaying. Using linear kinetic theory, we find a simple analytic form for these damping rates. Our theory predicts that overall magnetic energy decays like $(ω_p t)^{-q}$ with $q \sim 1$, which compares fav…
The radiation from afterglows of gamma-ray bursts (GRB) is generated in collisionless plasma shocks. The two main ingredients behind the radiation are high-energy, non-thermal electrons and a strong magnetic field. I argue that in order to make the right conclusions about gamma-ray burst and afterglow parameters from observations, it is crucial to have a firm understanding of the microphysics of collisionless shock. I present the results of self-consistent, three-dimensional particle-in-cell computational simulations of the collision of weakly magnetized plasma shells: The experiments show how…
The analysis of Balmer-dominated optical spectra from non-radiative (adiabatic) SNRs has shown that the ratio of the electron to proton temperature temperature at the blast wave is close to unity at v_s <= 400 km/s, but declines sharply down to the minimum value of (m_e/m_p) dictated by the jump conditions at shock speeds exceeding 2000 km/s. We propose a physical model for the heating of electrons and ions in non-cosmic ray dominated, strong shocks (v_s > 400 km/s) wherein the electrons are heated by lower hybrid waves immediately ahead of the shock front. These waves arise naturally from the…
Models for the synchrotron emission of gamma-ray burst afterglows suggest that the magnetic field is generated in the shock wave that forms as relativistic ejecta plow through the circum-burst medium. Transverse Weibel instability efficiently generates magnetic fields near equipartition with the post-shock energy density. The detailed saturated state of the instability, as seen in particle-in-cell simulations, consists of magnetically self-pinched current filaments. The filaments are parallel to the direction of propagation of the shock and are about a plasma skin depth in radius, forming a qu…
Understanding the heating of electrons to quasi-thermal energies at collisionless shocks has broad implications for plasma astrophysics. It directly impacts the interpretation of X-ray spectra from shocks, is important for understanding how energy is partitioned between the thermal and cosmic ray populations, and provides insight into the structure of the shock itself. In Ghavamian, Laming & Rakowski (2007) we presented observational evidence for an inverse square relation between the electron-to-proton temperature ratio and the shock speed at the outer blast waves of supernova remnants in par…
The full kinetic dynamics of a perpendicular collisionless shock is studied by means of a one-dimensional electromagnetic full particle simulation. The present simulation domain is taken in the shock rest frame in contrast to the previous full particle simulations of shocks. Preliminary results show that the downstream state falls into a unique cyclic reformation state for a given set of upstream parameters through the self-consistent kinetic processes.
We study relativistic unmagnetized collisionless shocks using unprecedentedly large particle-in-cell simulations of two-dimensional pair plasma. High energy particles accelerated by the shock are found to drive magnetic field evolution on a timescale >10^4 plasma times. Progressively stronger magnetic fields are generated on larger scales in a growing region around the shock. Shock-generated magnetic fields and accelerated particles carry >1% and >10% of the downstream energy flux, respectively. Our results suggest limits on the magnetization of relativistic astrophysical flows.
A simplified model of particle transport at a quasiparallel one-dimensional collisionless shock is suggested. In this model the MHD-turbulence behind the shock is dominated by a circularly polarized, large amplitude Alfvén wave originated upstream from the turbulence excited by particles leaking from the downstream medium. It is argued that such a wave having significantly increased its magnetic field during the transmission through the shock interface can effectively trap thermal ions, regulating their leakage upstream. Together with a background turbulence this wave also plays a fundamental …
We discuss electron acceleration and heating during collisionless magnetic reconnection by using the results of implicit kinetic simulations of Harris current sheets. We consider and compare electron dynamics in plasmas with different βvalues and perform simulations up to the physical mass ratio. We analyze the typical trajectory of electrons passing through the reconnection region, we study the electron velocity, focusing on the out-of-plane velocity, and we discuss the electron heating along the in-plane and out-of-plane directions.
