In situ observations of energetic particles at the Earth's bow-shock that are attainable by the satellite missions have long created the opinion that electrons are most efficiently accelerated in a quasi-perpendicular shock geometry. However, shocks that are deemed to be responsible for the production of cosmic ray electrons and their radiation from sources such as supernova remnants are much more powerful and larger than the Earth's bow-shock. Their remote observations and in situ measurements at Saturn's bow shock, suggest that electrons are accelerated very efficiently in the quasi-parallel shocks as well. In this paper we investigate the possibility that protons that are accelerated to high energies create sufficient wave turbulence, which is necessary for the electron preheating and subsequent injection into the diffusive shock acceleration in a quasi-parallel shock geometry. An additional test-particle-electron population, which is meant to be a low-density addition to the electron core-distribution on which the hybrid simulation operates, is introduced. We investigate how these electrons are energized by the hybrid electromagnetic field. The reduced spatial dimensionality allowed us to dramatically increase the number of macro-ions per numerical cell and achieve the converged results for the velocity distributions of test electrons. We discuss the electron preheating mechanisms, which can make a significant part of thermal electrons accessible to the ion-driven waves observed in hybrid simulations. We find that the precursor wave field supplied by ions has a considerable potential to preheat the electrons before they are shocked at the subshock.
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.
Many high-energy astrophysical systems contain magnetized collisionless plasmas with relativistic particles, in which turbulence can be driven by an arbitrary mixture of solenoidal and compressive motions. For example, turbulence in hot accretion flows may be driven solenoidally by the magnetorotational instability or compressively by spiral shock waves. It is important to understand the role of the driving mechanism on kinetic turbulence and the associated particle energization. In this work, we compare particle-in-cell simulations of solenoidally driven turbulence with similar simulations of…
Examining energization of kinetic plasmas in phase space is a growing topic of interest, owing to the wealth of data in phase space compared to traditional bulk energization diagnostics. Via the field-particle correlation (FPC) technique and using multiple means of numerically integrating the plasma kinetic equation, we have studied the energization of ions in phase space within oblique collisionless shocks. The perspective afforded to us with this analysis in phase space allows us to characterize distinct populations of energized ions. In particular, we focus on ions which reflect multiple ti…
Electron and ion energization (i.e., heating and nonthermal acceleration) is a fundamental, but poorly understood, outcome of plasma turbulence. In this work, we present new results on this topic from particle-in-cell simulations of driven turbulence in collisionless, relativistic electron-ion plasma. We focus on temperatures such that ions (protons) are sub-relativistic and electrons are ultra-relativistic, a regime relevant for high-energy astrophysical systems such as hot accretion flows onto black holes. We find that ions tend to be preferentially heated, gaining up to an order of magnitud…
Highly energetic, relativistic electrons are commonly present in many astrophysical systems, from solar flares to the intra-cluster medium, as indicated by observed electromagnetic radiation. However, open questions remain about the mechanisms responsible for their acceleration, and possible re-acceleration. Ubiquitous plasma turbulence is one of the possible universal mechanisms. We study the energization of transrelativistic electrons in turbulence using hybrid particle-in-cell, which provide a realistic model of Alfvénic turbulence from MHD to sub-ion scales, and test particle simulations f…
Collisionless, magnetized turbulence offers a promising framework for the generation of non-thermal high-energy particles in various astrophysical sites. Yet, the detailed mechanism that governs particle acceleration has remained subject to debate. By means of 2D and 3D PIC, as well as 3D (incompressible) magnetohydrodynamic (MHD) simulations, we test here a recent model of non-resonant particle acceleration in strongly magnetized turbulence~\cite{2021PhRvD.104f3020L}, which ascribes the energization of particles to their continuous interaction with the random velocity flow of the turbulence, …
Earth's magnetotail is an excellent laboratory to study the interplay of reconnection and turbulence in determining electron energization. The process of formation of a power law tail during turbulent reconnection is a documented fact still in need of a comprehensive explanation. We conduct a massively parallel particle in cell 3D simulation and use enhanced statistical resolution of the high energy range of the particle velocities to study how reconnection creates the conditions for the tail to be formed. The process is not direct acceleration by the coherent, laminar, reconnection-generated …
We perform particle-in-cell simulations of perpendicular nonrelativistic collisionless shocks to study electron heating and pre-acceleration for parameters that permit extrapolation to the conditions at young supernova remnants. Our high-resolution large-scale numerical experiments sample a representative portion of the shock surface and demonstrate that the efficiency of electron injection is strongly modulated with the phase of the shock reformation. For plasmas with low and moderate temperature (plasma beta $β_{\rm p}=5\cdot 10^{-4}$ and $β_{\rm p}=0.5$), we explore the nonlinear shock stru…
Turbulence is often invoked to explain the origin of nonthermal particles in space and astrophysical plasmas. By means of 3D fully kinetic particle-in-cell simulations, we demonstrate that turbulence in low-$β$ plasmas ($β$ is the ratio of plasma pressure to magnetic pressure) accelerates ions and electrons into a nonthermal energy distribution with a power-law energy range. The ion spectrum is harder than the electron one, and both distributions get steeper for higher $β$. We show that the energization of electrons is accompanied by a significant energy-dependent pitch-angle anisotropy, with …
We discuss the phenomenon of energization of relativistic charged particles in three-dimensional (3D) incompressible MHD turbulence and the diffusive properties of the motion of the same particles. We show that the random electric field induced by turbulent plasma motion leads test particles moving in a simulated box to be accelerated in a stochastic way, a second-order Fermi process. A small fraction of these particles happen to be trapped in large-scale structures, most likely formed due to the interaction of islands in the turbulence. Such particles get accelerated exponentially, provided t…
This work provides a concrete implementation of E. Fermi's model of particle acceleration in magnetohydrodynamic (MHD) turbulence, connecting the rate of energization to the gradients of the velocity of magnetic field lines, which it characterizes within a multifractal picture of turbulence intermittency. It then derives a transport equation in momentum space for the distribution function. This description is shown to be substantiated by a large-scale numerical simulation of strong MHD turbulence. The present, general framework can be used to model particle acceleration in a variety of environ…
Particle acceleration and heating at mildly relativistic magnetized shocks in electron-ion plasma are investigated with unprecedentedly high-resolution two-dimensional particle-in-cell simulations that include ion-scale shock rippling. Electrons are super-adiabatically heated at the shock, and most of the energy transfer from protons to electrons takes place at or downstream of the shock. We are the first to demonstrate that shock rippling is crucial for the energization of electrons at the shock. They remain well below equipartition with the protons. The downstream electron spectra are approx…
Electron acceleration associated with various plasma kinetic instabilities in a nonrelativistic, very-high-Alfvén Mach-number ($M_A \sim 45$) shock is revealed by means of a two-dimensional fully kinetic PIC simulation. Electromagnetic (ion Weibel) and electrostatic (ion-acoustic and Buneman) instabilities are strongly activated at the same time in different regions of the two-dimensional shock structure. Relativistic electrons are quickly produced predominantly by the shock surfing mechanism with the Buneman instability at the leading edge of the foot. The energy spectrum has a high-energy ta…
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.
The important characteristic of turbulent reconnection is that it combines large scale magnetic disturbances $(δB/B \sim 1)$ with randomly distributed Unstable Current Sheets (UCSs). Many well known non linear MHD structures (strong turbulence, current sheet(s), shock(s)) lead asymptotically to the state of turbulent reconnection. We analyze in this article, for the first time, the energization of electrons and ions in a {\bf large scale} environment that {\bf combines} large amplitude disturbances propagating with sub-Alfvénic speed with UCSs. The magnetic disturbances interact stochastically…
Electron injection at high Mach-number nonrelativistic perpendicular shocks is studied here for parameters that are applicable to young SNR shocks. Using high-resolution large-scale two-dimensional fully kinetic particle-in-cell (PIC) simulations and tracing individual particles we in detail analyze the shock surfing acceleration (SSA) of electrons at the leading edge of the shock foot. The central question is to what degree the process can be captured in 2D3V simulations. We find that the energy gain in SSA always arises from the electrostatic field of a Buneman wave. Electron energization is…
Particle Acceleration in Magnetized Shear-Driven Turbulence
University of Michigan（密歇根大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Princeton University（普林斯顿大学）；University of Chicago（芝加哥大学）；University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
The interaction of collisionless shocks with fully developed plasma turbulence is numerically investigated. Hybrid kinetic simulations, where a turbulent jet is slammed against an oblique shock, are employed to address the role of upstream turbulence on plasma transport. A novel technique, using coarse-graining of the Vlasov equation, is proposed, showing that the transport properties strongly depend on upstream turbulence strength, with turbulent structures-modulated patterns. These results might be relevant for the understanding of acceleration and heating processes in space plasmas.
The collision of two plasma clouds at a speed that exceeds the ion acoustic speed can result in the formation of shocks. This phenomenon is observed not only in astrophysical scenarios such as the propagation of supernova remnant (SNR) blast shells into the interstellar medium, but also in laboratory-based laser-plasma experiments. These experiments and supporting simulations are thus seen as an attractive platform for the small-scale reproduction and study of astrophysical shocks in the laboratory. We model two plasma clouds, which consist of electrons and ions, with a 2D PIC simulation. The …
The Weibel/filamentation instability is known to play a key role in the physics of weakly magnetized collisionless shock waves. From the point of view of high energy astrophysics, this instability also plays a crucial role because its development in the shock precursor populates the downstream with a small-scale magneto-static turbulence which shapes the acceleration and radiative processes of suprathermal particles. The present work discusses the physics of the dissipation of this Weibel-generated turbulence downstream of relativistic collisionless shock waves. It calculates explicitly the fi…
The topic of this review paper is on the influence of solar wind turbulence on shock propagation and its consequence on the acceleration and transport of energetic particles at shocks. As the interplanetary shocks sweep through the turbulent solar wind, the shock surfaces fluctuate and ripple in a range of different scales. We discuss particle acceleration at rippled shocks in the presence of ambient solar-wind turbulence. This strongly affects particle acceleration and transport of energetic particles (both ions and electrons) at shock fronts. In particular, we point out that the effects of u…
In order for diffusive shock acceleration (DSA) to accelerate particles to high energies, the energetic particles must be able to interact with magnetic turbulence over a broad wavelength range. The weakly anisotropic distribution of accelerated particles, i.e., cosmic rays (CRs), is believed capable of producing this turbulence in a symbiotic relationship where the magnetic turbulence required to accelerate the CRs is created by the accelerated CRs themselves. In efficient DSA, this wave-particle interaction can be strongly nonlinear where CRs modify the plasma flow and the specific mechanism…
We explore electron pre-acceleration at high Mach-number nonrelativistic perpendicular shocks at, e.g., young supernova remnants, which are a prerequisite of further acceleration to very high energies via diffusive shock acceleration. Using fully kinetic particle-in-cell simulations of shocks and electron dynamics in them, we investigate the influence of shock-surfing acceleration at the shock foot on the nonthermal population of electrons downstream of the shock. The shock-surfing acceleration is followed by further energization at the shock ramp where the Weibel instability spawns a type of …
The late afterglow of gamma-ray burst is believed to be due to progressive deceleration of the forward shock wave driven by the gamma-ray burst ejecta propagating in the interstellar medium. We study the dynamic effect of interstellar turbulence on shock wave propagation. It is shown that the shock wave decelerates more quickly than previously assumed without the turbulence. As an observational consequence, an earlier jet break will appear in the light curve of the forward shock wave. The scatter of the jet-corrected energy release for gamma-ray burst, inferred from the jet-break, may be partl…
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…
Galactic cosmic rays are believed to be mostly accelerated at supernova shocks. However, the interstellar magnetic field is too weak to efficiently accelerate galactic cosmic rays up to the highest energies, i.e. $10^{15}$ eV. A stronger magnetic field in the pre-shock region could provide the efficiency required. Bell's cosmic-ray nonresonant streaming instability has been claimed to be responsible for the amplification of precursor magnetic fields. However, an alternative mechanism has been proposed in which the cosmic-ray pressure gradient forms the shock precursor and drives turbulence, am…
Supernova Remnants (SNRs) shocks are believed to accelerate charged particles and to generate strong turbulence in the post-shock flow. From high-energy observations in the past decade, a magnetic field at SNR shocks largely exceeding the shock-compressed interstellar field has been inferred. We outline how such a field amplification results from a small-scale dynamo process downstream of the shock, providing an explicit expression for the turbulence back-reaction to the fluid whirling. The spatial scale of the $X-$ray rims and the short time-variability can be obtained by using reasonable par…
It is shown that ions can be accelerated to MeV energy range in the direction perpendicular to the magnetic field by the ExB mechanism of electrostatic waves. The acceleration occurs in discrete steps of duration being a small fraction the gyroperiod and can explain observations of ion energization to 10 keV at quasi-perpendicular shocks and to 100-1000 keV at quasi-parallel shocks. A general expression is provided for the maximum energy of ions accelerated in shocks of arbitrary configuration. The waves involved in the acceleration are related to three cross-field current-driven instabilities…
Particle acceleration in collisionless plasma systems is a central question in astroplasma and astroparticle physics. The structure of the acceleration regions, electron-ion energy equilibration, preacceleration of particles at shocks to permit further energization by diffusive shock acceleration, require knowledge of the distribution function of particles besides the structure and dynamic of electromagnetic fields, and hence a kinetic description is desirable. Particle-in-cell simulations offer an appropriate, if computationally expensive method of essentially conducting numerical experiments…
Shock waves play an important role in turbulent astrophysical media by compressing the gas and dissipating the turbulent energy into the thermal energy. We here study shocks in magnetohydrodynamic turbulence using high-resolution simulations. Turbulent Mach numbers of $\mathcal{M}_\text{turb}=0.5-7$ and initial magnetic fields of plasma beta $β_0=0.1 - 10$ are considered, targeting turbulences in interstellar and intracluster media. Specifically, we present the statistics of fast and slow shocks, such as the distribution of shock Mach numbers ($M_\text{s}$) and the energy dissipation at shocks…
Diffusive shock acceleration is considered as the main mechanism for particle energization in supernova remnants, as well as in other classes of sources. The existence of some remnants that show a bilateral morphology in the X-rays and gamma rays suggests that this process occurs with an efficiency that depends upon the inclination angle between the shock normal and the large scale magnetic field in which the shock propagates. This interpretation is additionally supported by recent particle-in-cell simulations that show how ions are not injected if the shock is more oblique than $\sim 45^{o}$.…
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…
Successful phenomenological models of pulsar wind nebulae assume efficient dissipation of the Poynting flux of the magnetized electron-positron wind as well as efficient acceleration of the pairs in the vicinity of the termination shock, but how this is realized is not yet well understood. The present paper suggests that the corrugation of the termination shock, at the onset of non-linearity, may lead towards the desired phenomenology. Non-linear corrugation of the termination shock would convert a fraction of order unity of the incoming ordered magnetic field into downstream turbulence, slowi…
Using test particle simulations we study electron acceleration at collisionless shocks with a two-component model turbulent magnetic field with slab component including dissipation range. We investigate the importance of shock normal angle $θ_{Bn}$, magnetic turbulence level $\left(b/B_0\right)^2$, and shock thickness on the acceleration efficiency of electrons. It is shown that at perpendicular shocks the electron acceleration efficiency is enhanced with the decreasing of $\left(b/B_0\right)^2$, and at $\left(b/B_0\right)^2=0.01$ the acceleration becomes significant due to strong drift electr…
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale model, the full range of part…
The shock waves produce relativistic particles via the diffusive shock acceleration (DSA) mechanism. Among various circumstances, fast acceleration has been expected for perpendicular shocks. We investigate the acceleration time and the energy spectrum of particles accelerated at a perpendicular shock. In our model, the upstream perpendicular magnetic field has no fluctuation, and the downstream region is highly turbulent. Then, the particle motion is the gyration in the upstream region and Bohm-like diffusion downstream. Under this situation, we derive an analytical form of the acceleration t…
How electrons get accelerated to relativistic energies in a high-Mach-number quasi-perpendicular shock is presented by means of ab initio particle-in-cell simulations in three dimensions. We found that coherent electrostatic Buneman waves and ion-Weibel magnetic turbulence coexist in a strong-shock structure whereby particles gain energy during shock-surfing and subsequent stochastic drift accelerations. Energetic electrons that initially experienced the surfing acceleration undergo pitch-angle diffusion by interacting with magnetic turbulence and continuous acceleration during confinement in …
Small-scale fluctuating magnetic fields of order $n$G are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel three-dimensional magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The…
Relativistic astrophysical phenomena such as gamma-ray bursts (GRBs) and active galactic nuclei often require long-lived strong magnetic field. Here, we report on three-dimensional special-relativistic magnetohydrodynamic (MHD) simulations to explore the amplification and decay of macroscopic turbulence dynamo excited by the so-called Richtmyer-Meshkov instability (RMI; a Rayleigh-Taylor type instability). This instability is an inevitable outcome of interactions between shock and ambient density fluctuations. We find that the magnetic energy grows exponentially in a few eddy turnover times, a…
The analytical theory of diffusive cosmic ray acceleration at parallel stationary shock waves with magnetostatic turbulence is generalized to arbitrary shock speeds $V_s=β_1c$, including in particular relativistic speeds. This is achieved by applying the diffusion approximation to the relevant Fokker-Planck particle transport equation formulated in the mixed comoving coordinate system. In this coordinate system the particle's momentum coordinates $p$ and $μ=p_{\parallel }/p$ are taken in the rest frame of the streaming plasma, whereas the time and space coordinates are taken in the observer's …
We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in…
We explore the shock acceleration model for giant radio relics, in which relativistic electrons are accelerated via diffusive shock acceleration (DSA) by merger-driven shocks in the outskirts of galaxy clusters. In addition to DSA, turbulent acceleration by compressive MHD mode downstream of the shock is included as well as energy losses of postshock electrons by Coulomb scattering, synchrotron emission, and inverse Compton scattering off the cosmic background radiation. Considering that only a small fraction of merging clusters host radio relics, we favor the reacceleration scenario in which …
Diffusive shock acceleration (DSA) at relativistic shocks is widely thought to be an important acceleration mechanism in various astrophysical jet sources, including radio-loud active galactic nuclei such as blazars. Such acceleration can produce the non-thermal particles that emit the broadband continuum radiation that is detected from extragalactic jets. An important recent development for blazar science is the ability of Fermi-LAT spectroscopy to pin down the shape of the distribution of the underlying non-thermal particle population. This paper highlights how multi-wavelength spectra spann…
Statistics of the magnetic field disturbances in the supernova remnants (SNRs) can be accessed using the second-order correlation function of the synchrotron intensities. Here we measure the magnetic energy spectra in supernova remnant Cassiopeia-A by two-point correlation of the synchrotron intensities, using a recently developed unbiased method. The measured magnetic energy spectra in the vicinity of supernova remnant shocks are found to be 2/3 power law over the decade of range scales, showing the developed trans-Alfvenic magnetohydrodynamic turbulence. Our results are globally consistent w…
We model strong forward shocks in young supernova remnants with efficient particle acceleration where a nonresonant instability driven by the cosmic ray current amplifies magnetic turbulence in the shock precursor. Particle injection, magnetic field amplification (MFA) and the nonlinear feedback of particles and fields on the bulk flow are derived consistently. The shock structure depends critically on the efficiency of turbulence cascading. If cascading is suppressed, MFA is strong, the shock precursor is stratified, and the turbulence spectrum contains several discrete peaks. These peaks, as…
Cosmic-ray acceleration at non-relativistic shocks relies on scattering by turbulence that the cosmic rays drive upstream of the shock. We explore the rate of energy transfer from cosmic rays to non-resonant Bell modes and the spectral softening it implies. Accounting for the finite time available for turbulence driving at supernova-remnant shocks yields a smaller spectral impact than found earlier with steady-state considerations. Generally, for diffusion scaling with the Bohm rate by a factor $η$, the change in spectral index is at most $η$ divided by the Alfvénic Mach number of the thermal …
