Two dimensional modeling of collisionless shocks has been of tremendous importance in understanding the physics of the non-linear evolution, momentum transfer and particle acceleration, but current computer capacities have now reached a point where three dimensional modeling is becoming feasible. We present the first three dimensional model of a fully developed and relaxed relativistic ion-electron shock, and analyze and compare it to similar 2D models. Quantitative and qualitative differences are found with respect to the two-dimensional models. The shock jump conditions are of course different, because of the extra degree of freedom, but in addition it is found that strong parallel electric fields develop at the shock interface, the level of magnetic field energy is lower, and the non-thermal particle distribution is shallower with a powerlaw index of ~2.2.
In this paper, we study shock structures of collisionless shocks in partially ionized plasmas by means of two-dimensional hybrid simulations, where the shock is a perpendicular shock with shock velocity Vsh ~ 40 Va ~ 1333 km/s and the upstream ionization fraction is 0.5. We find that large density fluctuations and large magnetic fields fluctuations are generated both in the upstream and downstream regions. In addition, we find that the velocity distribution of downstream hydrogen atoms has three components. Observed shock structures suggest that diffusive shock acceleration can operate at perp…
Perpendicular collisionless shocks propagating into partially ionized plasmas are investigated by two-dimensional hybrid particle simulations. It is shown that some neutral particles leak into the upstream region from the downstream region, the leaking neutral particles become pickup ions in the upstream region and modify the shock structure, the pickup ions are preferentially accelerated, and plasma instabilities are excited by the pickup ions in the upstream and downstream regions.
Recent studies about collisionless shocks in partially ionized plasmas showed that some of neutral particles leak into the shock upstream region from the downstream region. In this paper, we perform a linear analysis and show that acoustic waves are unstable in the neutral precursor region. The acoustic instability amplifies fluctuations of magnetic field and density in the upstream region. The fluctuations are indispensable for the diffusive shock acceleration and could be important for the downstream turbulence.
The formation of non-relativistic collisionless shocks in laboratory with ultrahigh intensity lasers is studied via \emph{ab initio} multi-dimensional particle-in-cell simulations. The microphysics behind shock formation and dissipation, and the detailed shock structure are analyzed, illustrating that the Weibel instability plays a crucial role in the generation of strong subequipartition magnetic fields that isotropize the incoming flow and lead to the formation of a collisionless shock, similarly to what occurs in astrophysical scenarios. The possibility of generating such collisionless shoc…
Collisionless shocks occur in various fields of physics. In the context of space and astrophysics they have been investigated for many decades. However, a thorough understanding of shock formation and particle acceleration is still missing. Collisionless shocks can be distinguished into electromagnetic and electrostatic shocks. Electromagnetic shocks are of importance mainly in astrophysical environments and they are mediated by the Weibel or filamentation instability. In such shocks, charged particles gain energy by diffusive shock acceleration. Electrostatic shocks are characterized by a str…
Relativistic particle acceleration in collisionless shocks of supernova remnants is accompanied by magnetic field amplification from cosmic ray (CR) driven plasma instabilities. Bell's fast CR-current instability is predicted to produce turbulence with a non-zero mean electric field in the shock precursor. We present a Monte Carlo model of Fermi shock acceleration explicitly taking into account an effective mean upstream electric field. Our model is nonlinear and includes the backreaction effects of efficient Fermi acceleration on the shock structure.
The interactions between a relativistic magnetized collisionless shock and dense clumps have been expected to play a crucial role on the magnetic field amplification and cosmic-ray acceleration. We investigate this process by two-dimensional Particle-In-Cell (PIC) simulations for the first time, where the clump size is much larger than the gyroradius of downstream particles. We also perform relativistic magnetohydrodynamic (MHD) simulations for the same condition to see the kinetic effects. We find that particles escape from the shocked clump along magnetic field lines in the PIC simulations, …
We analyze the main features of radiation-mediated shocks at arbitrary shock velocities, both non-relativistic and relativistic. We describe two mechanisms, which may lead to formation of a sharp viscous subshock within otherwise smooth velocity profile at the shock front, even if the radiation pressure in the upstream is overwhelmingly large. These mechanisms are specific to sub-relativistic and relativistic radiation-mediated shocks and set high-velocity shocks apart from their non-relativistic counterparts, which do not develop a subshock if the radiation pressure is high enough. We briefly…
In this review we discuss some observational aspects and theoretical models of astrophysical collisionless shocks in partly ionized plasma with the presence of non-thermal components. A specific feature of fast strong collisionless shocks is their ability to accelerate energetic particles that can modify the shock upstream flow and form the shock precursors. We discuss the effects of energetic particle acceleration and associated magnetic field amplification and decay in the extended shock precursors on the line and continuum multi-wavelength emission spectra of the shocks. Both Balmer-type an…
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.
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 PIC simulations, and provides an important touchstone for the phenomenology of such plasma systems.
Collisionless shocks in plasmas play an important role in space physics (Earth's bow shock) and astrophysics (supernova remnants, relativistic jets, gamma-ray bursts, high energy cosmic rays). While the formation of a fluid shock through the steepening of a large amplitude sound wave has been understood for long, there is currently no detailed picture of the mechanism responsible for the formation of a collisionless shock. We unravel the physical mechanism at work and show that an electromagnetic Weibel shock always forms when two relativistic collisionless, initially unmagnetized, plasma shel…
We discuss the mechanism of electron energization in the upstream region of relativistic e/i shock. By using particle-in-cell simulations, we demonstrate the electrons interacting with enhanced electric and magnetic fields of the magnetic vortices (MVs) can gain a significant amount of energy during interaction. MVs are self generated in the upstream region of relativistic electron-ion shock.
Electron acceleration in collisionless shocks with arbitrary magnetic field orientations is discussed. It is shown that the injection of thermal electrons into diffusive shock acceleration process is achieved by an electron beam with a loss-cone in velocity space that is reflected back upstream from the shock through shock drift acceleration mechanism. The electron beam is able to excite whistler waves which can scatter the energetic electrons themselves when the Alfven Mach number of the shock is sufficiently high. A critical Mach number for the electron injection is obtained as a function of…
We present a particle-in-cell simulation of the generation of a collisionless turbulent shock in a dense plasma driven by an ultra-high-intensity laser pulse. From the linear analysis, we highlight the crucial role of the laser-heated and return-current electrons in triggering a strong Weibel-like instability, giving rise to a magnetic turbulence able to isotropize the target ions.
Supernova remnants (SNRs), the products of stellar explosions, are powerful astrophysical laboratories, which allow us to study the physics of collisionless shocks, thanks to their bright electromagnetic emission. Blast wave shocks generated by supernovae (SNe) provide us with an observational window to study extreme conditions, characterized by high Mach (and Alfvenic Mach) numbers, together with powerful nonthermal processes. In collisionless shocks, temperature equilibration between different species may not be reached at the shock front. In this framework, different particle species might …
We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the traject…
We report on the temporally and spatially resolved detection of the precursory stages that lead to the formation of an unmagnetized, supercritical collision-less shock in a laser-driven laboratory experiment. The measured evolution of the electrostatic potential associated with the shock unveils the transition from a current free double layer into a symmetric shock structure, stabilized by ion reflection at the shock front. Supported by a matching Particle-In-Cell simulation and theoretical considerations, we suggest that this process is analogeous to ion reflection at supercritical collisionl…
Most of the plasma microphysics which shapes the acceleration process of particles at collisionless shock waves takes place in the cosmic-ray precursor, through the interaction of accelerated particles with the unshocked plasma. Detecting directly or indirectly the synchrotron radiation of accelerated particles in this precursor would open a new window on the microphysics of acceleration and of collisionless shock waves. We provide analytical estimates of the spectrum and of the polarization fraction of the synchrotron precursor for both relativistic and non-relativistic collisionless shock fr…
We study diffusive shock acceleration (DSA) of electrons in non-relativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell (PIC) simulations. By exploring the parameter space of sonic and Alfvénic Mach numbers we find that high Mach number quasi-perpendicular shocks can efficiently accelerate electrons to power-law downstream spectra with slopes consistent with DSA prediction. Electrons are reflected by magnetic mirroring at the shock and drive non-resonant waves in the upstream. Reflected electrons are trapped between the shock front and upstream waves and …
Laser-driven collisonless electrostatic shock formation and the subsequent ion acceleration have been studied in near critical density plasmas. Particle-in-cell simulations show that both the speed of laser-driven collisionless electrostatic shock and the energies of shock-accelerated ions can be greatly enhanced due to fast laser propagation in near critical density plasmas. However, a response time longer than tens of laser wave cycles is required before the shock formation in a near critical density plasma, in contrast to the quick shock formation in a highly overdense target. More importan…
The electron beam Weibel instability in the electrostatic collisionless shock is studied via particle in cell simulation. When the non-relativistic incoming plasmas collide with cold dilute plasmas, an electrostatic shock forms near the interface. Following that, a filamentary out-of-plane magnetic field is formed as a result of the Weibel instability. It is demonstrated that the anisotropy of incoming hot electrons is insufficient to trigger the Weibel instability. And the Weibel instability is excited by cold electrons in dilute plasmas. After being accelerated to relativistic velocities by …
Intense laser-plasma interactions are an essential tool for the laboratory study of ion acceleration at a collisionless shock. With two-dimensional particle-in-cell calculations of a multicomponent plasma we observe two electrostatic collisionless shocks at two distinct longitudinal positions when driven with a linearly-polarized laser at normalized laser vector potential a0 that exceeds 10. Moreover, these shocks, associated with protons and carbon ions, show a power-law dependence on a0 and accelerate ions to different velocities in an expanding upstream with higher flux than in a single-com…
We describe numerical simulations, using the particle-in-cell (PIC) and hybrid-PIC code Lsp [T. P. Hughes et al., Phys. Rev. ST Accel. Beams 2, 110401 (1999)], of the head-on merging of two laboratory supersonic plasma jets. The goals of these experiments are to form and study astrophysically relevant collisionless shocks in the laboratory. Using the plasma jet initial conditions (density ~ 10^14-10^16 cm^(-3), temperature ~ few eV, and propagation speed ~ 20-100 km/s), large-scale simulations of jet propagation demonstrate that interactions between the two jets are essentially collisionless a…
Long-lived >100 MeV emission has been a common feature of most Fermi-LAT detected gamma-ray bursts (GRBs), e.g., detected up to ~10^3s in long GRBs 080916C and 090902B and ~10^2s in short GRB 090510. This emission is consistent with being produced by synchrotron emission of electrons accelerated to high energy by the relativistic collisionless shock propagating into the weakly magnetized medium. Here we show that this high-energy afterglow emission constrains the preshock magnetic field to satisfy 1(n/1cc)^{9/8} mG<B<10^2(n/1cc)^{3/8}mG, where n is the preshock density, more stringent than the…
A novel collisionless shock jump condition is suggested by modeling the entropy production at the shock transition region. We also calculate downstream developments of the atomic ionization balance and the ion temperature relaxation in supernova remnants (SNRs). The injection process and subsequent acceleration of cosmic-rays (CRs) in the SNR shocks are closely related to the formation process of the collisionless shocks. The formation of the shock is caused by wave-particle interactions. Since the wave-particle interactions result in energy exchanges between electromagnetic fields and charged…
When two plasmas collide, their interaction can be mediated by collisionless plasma instabilities or binary collisions between particles of each shell. By comparing the maximum growth rate of the collisionless instabilities with the collision frequency between particles of the shells, we determine the critical density separating the collisionless formation from the collisional formation of the resulting shock waves. This critical density is also the density beyond which the shock downstream is field free, as plasma instabilities do not have time to develop electromagnetic patterns. We further …
We used unprecedentedly large 2D and 3D hybrid (kinetic ions - fluid electrons) simulations of non-relativistic collisionless strong shocks in order to investigate the effects of self-consistently accelerated ions on the overall shock dynamics. The current driven by suprathermal particles streaming ahead of the shock excites modes transverse to the background magnetic field. The Lorentz force induced by these self-amplified fields tends to excavate tubular, underdense, magnetic-field-depleted cavities that are advected with the fluid and perturb the shock surface, triggering downstream turbule…
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 inten…
Although collisionless shocks are ubiquitous in astrophysics, certain key aspects of them are not well understood. In particular, the process known as collisionless electron heating, whereby electrons are rapidly energized at the shock front, is one of the main open issues in shock physics. Here we present the first clear evidence for efficient collisionless electron heating at the reverse shock of Tycho's supernova remnant (SNR), revealed by Fe-K diagnostics using high-quality X-ray data obtained by the Suzaku satellite. We detect K-beta (3p->1s) fluorescence emission from low-ionization Fe e…
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, prov…
The so-called internal shock model aims to explain the light-curves and spectra produced by non-thermal processes originated in the flow of blazars and gamma-ray bursts. A long standing question is whether the tenuous collisionless shocks, driven inside a relativistic flow, are efficient enough to explain the amount of energy observed as compared with the expected kinetic power of the outflow. In this work we study the dynamic efficiency of conversion of kinetic-to- thermal/magnetic energy of internal shocks in relativistic magnetized outflows. We find that the collision between shells with a …
Astrophysical shocks at all scales, from those in the heliosphere up to the cosmological shock waves, are typically "collisionless", because the thickness of their jump region is much shorter than the collisional mean free path. Across these jumps, electrons, protons, and ions are expected to be heated at different temperatures. Supernova remnants (SNRs) are ideal targets to study collisionless processes because of their bright post-shock emission and fast shocks. Although optical observations of Balmer-dominated shocks in young SNRs showed that the post-shock proton temperature is higher than…
Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic PIC simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analy…
The results of hybrid simulation of low-beta supercritical quasi-parallel shocks in high metallicity plasma are presented. The structure of upstream and downstream turbulence is addressed and velocities of the corresponding scattering centers are derived. It is shown that independently of their chemical composition the shocks experience self-reformation process. However, the period of self-reformation as well as the wave spectrum is greatly affected by the presence of substantial admixture of weakly charged heavy ions. Also the downstream magnetic field amplification is stronger for the high m…
The properties of collisionless shocks are frequently assessed in the magnetohydrodynamics (MHD) model. Yet, in a collisionless plasma, an ambient magnetic field can sustain a stable anisotropy in the upstream or the downstream, resulting in a departure from the MHD predicted behavior. We present a model allowing to derive the downstream anisotropy, hence the shock density jump, in terms of the upstream quantities. For simplicity, the case of a parallel shock in pair plasma is considered. Contrary to previous works where the upstream was assumed isotropic, here the upstream anisotropy $A=T_\pe…
Using large-scale fully-kinetic two-dimensional particle-in-cell simulations, we investigate the effects of shock rippling on electron acceleration at low-Mach-number shocks propagating in high-$β$ plasmas, in application to merger shocks in galaxy clusters. We find that the electron acceleration rate increases considerably when the rippling modes appear. The main acceleration mechanism is stochastic shock-drift acceleration, in which electrons are confined at the shock by pitch-angle scattering off turbulence and gain energy from the motional electric field. The presence of multi-scale magnet…
We extract synthetic photon spectra from first-principles particle-in-cell simulations of relativistic shocks propagating in unmagnetized pair plasmas. The two basic ingredients for the radiation, namely accelerated particles and magnetic fields, are produced self-consistently as part of the shock evolution. We use the method of Hededal & Nordlund (2005) and compute the photon spectrum via Fourier transform of the electric far-field from a large number of particles, sampled directly from the simulation. We find that the spectrum from relativistic collisionless shocks is entirely consistent wit…
A full particle simulation study is carried out on a perpendicular collisionless shock with a relatively low Alfven Mach number (M_A=5). In the present study, we have performed a two-dimensional (2D) electromagnetic full particle simulation with a "shock-rest-frame model". The simulation domain is taken to be larger than the ion inertial length in order to include full kinetics of both electrons and ions. The present simulation result has confirmed the transition of shock structures from the cyclic self-reformation to the quasi-stationary shock front. During the transition, electrons and ions …
Context. The diffusive shock acceleration mechanism has been widely accepted as the acceleration mechanism for galactic cosmic rays. While self-consistent hybrid simulations have shown how power-law spectra are produced, detailed information on the interplay of diffusive particle motion and the turbulent electromagnetic fields responsible for repeated shock crossings are still elusive. Aims. The framework of test-particle theory is applied to investigate the effect of diffusive shock acceleration by inspecting the obtained cosmic-ray energy spectra. The resulting energy spectra can be obtained…
We investigate shock structure and particle acceleration in relativistic magnetized collisionless pair shocks by means of 2.5D and 3D particle-in-cell simulations. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. We find that only magnetic inclinations corresponding to "subluminal" shocks, where relativistic particles following the magnetic field can escape ahead of the shock, lead to particle acceleration. The downstream spectrum in such shocks consists of a relativistic Maxwellian and a high-energy power-law tail with exponential cutoff. For…
While the front of a fluid shock is a few mean-free-paths thick, the front of a collisionless shock can be orders of magnitude thinner. By bridging between a collisional and a collisionless formalism, we assess the transition between these two regimes. We consider non-relativistic, un-magnetized, planar shocks in electron/ion plasmas. In addition, our treatment of the collisionless regime is restricted to high Mach number electrostatic shocks. We find that the transition can be parameterized by the upstream plasma parameter $Λ$ which measures the coupling of the upstream medium. For $Λ\lesssim…
Collisionless shocks are loosely defined as shocks where the transition between pre-and post-shock states happens on a length scale much shorter than the collisional mean free path. In the absence of collision to enforce thermal equilibrium post-shock, electrons and ions need not have the same temperatures. While the acceleration of electrons for injection into shock acceleration processes to produce cosmic rays has received considerable attention, the related problem of the shock heating of quasi-thermal electrons has been relatively neglected. In this paper we review that state of our knowle…
Within the context of Magnetohydrodynamics (MHD), the properties of a parallel shock do not depend on the field strength, as the field and the fluid are disconnected for such a geometry. However, in the collisionless case, the field can sustain a stable anisotropy in the downstream, triggering a departure from the expected MHD behavior. In a recent work [A. Bret and R. Narayan, J. Plasma Phys. \textbf{84}, 905840604 (2018)], a theoretical model was presented allowing to derive the density ratio of a non-relativistic parallel collisionless shock in an electron/positron plasma, as a function of …
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 backgr…
Ion temperature anisotropy is a common feature for (quasi-)perpendicular collisionless shocks. By using two-dimensional full particle simulations, it is shown, that the ion temperature component perpendicular to the shock magnetic field at the shock foot region is proportional to the square of the Alfven Mach number divided by the plasma beta. This result is also explained by a simple analytical argument, in which the reflected ions get energy from upstream plasma flow. By comparing our analytic and numerical results, it is also confirmed that the fraction of the reflected ions hardly depends …
Collisionless shocks, that is shocks mediated by electromagnetic processes, are customary in space physics and in astrophysics. They are to be found in a great variety of objects and environments: magnetospheric and heliospheric shocks, supernova remnants, pulsar winds and their nebulæ, active galactic nuclei, gamma-ray bursts and clusters of galaxies shock waves. Collisionless shock microphysics enters at different stages of shock formation, shock dynamics and particle energization and/or acceleration. It turns out that the shock phenomenon is a multi-scale non-linear problem in time and spac…
A study of collisionless external shocks in gamma-ray bursts is presented. The shock structure, electromagnetic fields, and process of electron acceleration are assessed by performing a self-consistent 3D particle-in-cell (PIC) simulation. In accordance with hydrodynamic shock systems, the shock consists of a reverse shock (RS) and forward shock (FS) separated by a contact discontinuity (CD). The development and structure are controlled by the ion Weibel instability. The ion filaments are sources of strong transverse electromagnetic fields at both sides of the double shock structure over a len…
A full particle simulation study is carried out for studying microinstabilities generated at the shock front of perpendicular collisionless shocks. The structure and dynamics of shock waves are determined by Alfven Mach number and plasma beta, while microinstabilities are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the plasma-to-cyclotron frequency. Thus, growth rates of microinstabilities are changed by the ion-to-electron mass ratio, even with the same Mach number and plasma beta. The present two-dimensional simulations show that the electron cy…
