The subject of this paper is stochastic acceleration by plasma turbulence, a process akin to the original model proposed by Fermi. We review the relative merits of different acceleration models, in particular the so called first order Fermi acceleration by shocks and second order Fermi by stochastic processes, and point out that plasma waves or turbulence play an important role in all mechanisms of acceleration. Thus, stochastic acceleration by turbulence is active in most situations. We also show that it is the most efficient mechanism of acceleration of relatively cool non relativistic thermal background plasma particles. In addition, it can preferentially accelerate electrons relative to protons as is needed in many astrophysical radiating sources, where usually there are no indications of presence of shocks. We also point out that a hybrid acceleration mechanism consisting of initial acceleration by turbulence of background particles followed by a second stage acceleration by a shock has many attractive features. It is demonstrated that the above scenarios can account for many signatures of the accelerated electrons, protons and other ions, in particular $^3$He and $^4$He, seen directly as Solar Energetic Particles and through the radiation they produce in solar flares.
A new particle acceleration process in a developing Alfvén turbulence in the course of successive parametric instabilities of a relativistic pair plasma is investigated by utilyzing one-dimensional electromagnetic full particle code. Coherent wave-particle interactions result in efficient particle acceleration leading to a power-law like energy distribution function. In the simulation high energy particles having large relativistic masses are preferentially accelerated as the turbulence spectrum evolves in time. Main acceleration mechanism is simultaneous relativistic resonance between a parti…
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…
Magnetohydrodynamic (MHD) turbulence is an important agent of energetic particle acceleration. Focusing on the compressible properties of magnetic turbulence, we adopt test particle method to study the particle acceleration from Alfvén, slow and fast modes in four turbulence regimes that may appear in a realistic astrophysical environment. Our studies show that (1) the second-order Fermi mechanism drives the acceleration of particles in the cascade processes of three modes by particle-turbulence interactions, regardless of whether the shock wave appears; (2) not only can the power spectra of m…
We explore constraints imposed by shear-driven instabilities on the acceleration of energetic particles in relativistic shearing flows. We show that shearing layers in large-scale AGN jets are likely to encompass a sizeable fraction ($\geq 0.1$) of the jet radius, requiring seed injection of GeV electrons for efficient acceleration. While the diffusion process may depend on pre-developed turbulence if injection occurs at higher energies, electron acceleration to PeV and proton acceleration to EeV energies appears possible within the constraints imposed by jet stability.
We use analytic estimates and numerical simulations of test particles interacting with magnetohydrodynamic (MHD) turbulence to show that subsonic MHD turbulence produces efficient second-order Fermi acceleration of relativistic particles. This acceleration is not well-described by standard quasi-linear theory but is a consequence of resonance broadening of wave-particle interactions in MHD turbulence. We provide momentum diffusion coefficients that can be used for astrophysical and heliospheric applications and discuss the implications of our results for accretion flows onto black holes. In pa…
Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show h…
Astrophysical reconnection takes place in a turbulent medium. The turbulence in most cases is pre-existing, not caused by the reconnection itself. The model of magnetic reconnection in Lazarian & Vishniac (1999) predicts that in the presence of turbulence the reconnection becomes fast, i.e. it is independent of resistivity, but dependent on the level of turbulence. Magnetic reconnection injects energy into plasmas through a turbulent outflow from the reconnection region and this outflow can enhance the level of turbulence creating bursts of reconnection. Magnetic reconnection in the presence o…
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…
We discuss the physics of stochastic particle acceleration in relativistic magnetohydrodynamic (MHD) turbulence, combining numerical simulations of test-particle acceleration in synthetic wave turbulence spectra with detailed analytical estimates. In particular, we study particle acceleration in wavelike isotropic fast mode turbulence, in Alfvén and slow Goldreich-Sridhar type wave turbulence (properly accounting for anisotropy effects), including resonance broadening due to wave decay and pitch-angle randomization. At high particle rigidities, the contributions of those three modes to acceler…
We consider particle acceleration by large-scale incompressible turbulence with a lengthscale larger than the particle mean free path. We derive an ensemble-averaged transport equation of energetic charged particles from an extended transport equation which contains the shear acceleration. The ensemble-averaged transport equation describes particle acceleration by incompressible turbulence (turbulent shear acceleration). We find that for Kolmogorov turbulence, the turbulent shear acceleration becomes important in small scale. Moreover, by Monte Carlo simulations, we confirm that the ensemble-a…
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）
Due to its ubiquitous presence, turbulence is often invoked to explain the origin of nonthermal particles in astrophysical sources of high-energy emission. With particle-in-cell simulations, we study decaying turbulence in magnetically-dominated (or equivalently, "relativistic") pair plasmas. We find that the generation of a power-law particle energy spectrum is a generic by-product of relativistic turbulence. The power-law slope is harder for higher magnetizations and stronger turbulence levels. In large systems, the slope attains an asymptotic, system-size-independent value, while the high-e…
Fast particles are accelerated in astrophysical environments by a variety of processes. Acceleration in reconnection sites has attracted the attention of researchers recently. In this letter we analyze the energy distribution evolution of test particles injected in three dimensional (3D) magnetohydrodynamic (MHD) simulations of different magnetic reconnection configurations. When considering a single Sweet-Parker topology, the particles accelerate predominantly through a first-order Fermi process, as predicted in previous work (de Gouveia Dal Pino & Lazarian, 2005) and demonstrated numerically…
Most theoretical investigations of particle acceleration during solar flares cannot be applied to observations for detailed study of the time evolution. We propose a phenomenological model for turbulence evolution and stochastic particle acceleration that links observations to the energy release and particle acceleration through two coefficients characterizing particle interactions with turbulent electromagnetic fields. In the linear regime the particle distribution does not affect the turbulence energy cascade. It is shown that electron acceleration critically depends on the intensity of smal…
The spectral shape of the prompt emissions of gamma-ray bursts (GRBs) is typically expressed by the Band function: smooth joining of two power-law functions for high-energy and low-energy regions. To reveal the origin of the Band function, we revisit the stochastic acceleration model, in which electrons are accelerated via scattering with turbulent waves in the GRB outflow. The balance between the acceleration and synchrotron cooling yields a narrow energy-distribution similar to the Maxwellian distribution. The synchrotron spectrum becomes consistent with the observed hard photon index for th…
Nonthermal acceleration of particles in magnetohydrodynamic (MHD) turbulence plays a central role in a wide variety of astrophysical sites. This physics is addressed here in the context of a strong turbulence, composed of coherent structures rather than waves, beyond the realm of quasilinear theory. The present description tracks the momentum of the particle through a sequence of frames in which the electric field vanishes, in the spirit of the original Fermi scenario. It connects the sources of energy gain (or loss) to the gradients of the velocity of the magnetic field lines, in particular t…
I discuss three mutually-supportive notions or assumptions regarding jets and accretion. The first is magnetocentrifugal acceleration (MCA), the overwhelmingly favored mechanism for the production of jets in most steady accreting systems. The second is the zero-torque inner boundary condition. The third is that effective viscous dissipation is like real dissipation, leading directly to heating. All three assumptions fit nicely together in a manner that is simple, persuasive, and mutually-consistent. All, I argue, are incorrect. For concreteness I focus on protostars. Magnetohydrodynamic (MHD) …
Turbulence, magnetic reconnection, and shocks can be present in explosively unstable plasmas, forming a new electromagnetic environment, which we call here turbulent reconnection, and where spontaneous formation of current sheets takes place. We will show that the heating and the acceleration of particles is the result of the synergy of stochastic (second order Fermi) and systematic (first order Fermi) acceleration inside fully developed turbulence. The solar atmosphere is magnetically coupled to a turbulent driver (the convection zone), therefore the appearance of turbulent reconnection in th…
Fast magnetic reconnection may occur in different astrophysical sources, producing flare-like emission and particle acceleration. Currently, this process is being studied as an efficient mechanism to accelerate particles via a first-order Fermi process. In this work we analyse the acceleration rate and the energy distribution of test particles injected in three-dimensional magnetohydrodynamical (MHD) domains with large-scale current sheets where reconnection is made fast by the presence of turbulence. We study the dependence of the particle acceleration time with the relevant parameters of the…
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…
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…
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…
We investigate acceleration and propagation processes of high-energy particles inside hot accretion flows. The magnetorotational instability (MRI) creates turbulence inside accretion flows, which triggers magnetic reconnection and may produce non-thermal particles. They can be further accelerated stochastically by the turbulence. To probe the properties of such relativistic particles, we perform magnetohydrodynamic simulations to obtain the turbulent fields generated by the MRI, and calculate orbits of the high-energy particles using snapshot data of the MRI turbulence. We find that the partic…
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…
Electrons emitting non-thermal photons in blazars are possibly accelerated by turbulences developed in jets. In this paper, we consider the case so-called hard-sphere scattering as an interaction model between turbulences and electrons, in which the acceleration timescale is independent of the electron energy. We numerically simulate broad-band emission from blazar jets with a one-zone time-dependent code, taking into account the turbulence acceleration. Our model reproduces various blazar spectra with simple assumptions, such as constant particle injection rate, constant diffusion coefficient…
About 1/3 of X-ray-luminous clusters show smooth, Mpc-scale radio emission, known as giant radio haloes. One promising model for radio haloes is Fermi-II acceleration of seed relativistic electrons by compressible turbulence. The origin of these seed electrons has never been fully explored. Here, we integrate the Fokker-Planck equation of the cosmic ray (CR) electron and proton distributions when post-processing cosmological simulations of cluster formation, and confront them with radio surface brightness and spectral data of Coma. For standard assumptions, structure formation shocks lead to a…
In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a non-thermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter $σ\gg 1$) quickly evolves into a state with ultra-relativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent $α$ in the power-law particle energy distribution function, $f(γ)dγ\…
Nature's most powerful high-energy sources are capable of accelerating particles to high energy and radiate it away on extremely short timescales, even shorter than the light crossing time of the system. It is yet unclear what physical processes can produce such an efficient acceleration, despite the copious radiative losses. By means of radiative particle-in-cell simulations, we show that magnetically dominated turbulence in pair plasmas subject to strong synchrotron cooling generates a nonthermal particle spectrum with a hard power-law range (slope $p \sim 1$) within a few eddy turnover time…
We investigate stochastic particle acceleration in accretion flows. It is believed that the magnetorotational instability (MRI) generates turbulence inside accretion flows and that cosmic rays (CRs) are accelerated by the turbulence. We calculate equations of motion for CRs in the turbulent fields generated by MRI with the shearing box approximation without back reaction to the field. The results show that the CRs randomly gain or lose their energies through the interaction with the turbulent fields. The CRs diffuse in the configuration space anisotropically: The diffusion coefficient in direc…
We introduce a non-resonant acceleration mechanism arising from the second adiabatic invariant in magnetic turbulence and apply it to study the prompt emission spectra of gamma-ray bursts (GRBs). The mechanism contains both the first- and second-order Fermi acceleration, originating from the interacting turbulent reconnection and dynamo processes. It leads to a hard electron energy distribution up to a cutoff energy at the balance between the acceleration and synchrotron cooling. The sufficient acceleration rate ensures a rapid hardening of any initial energy distribution to a power-law distri…
In the next years the FERMI gamma ray telescope and the Cherenkov telescopes will put very stringent constraints to models of gamma ray emission from galaxy clusters providing crucial information on relativistic particles in the inter-galactic-medium. We derive the broad band non-thermal spectrum of galaxy clusters in the context of general calculations in which relativistic particles (protons and secondary electrons due to proton-proton collisions) interact with MHD turbulence generated in the cluster volume during cluster mergers, and discuss the importance of future gamma ray observations.
We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin--Helmholtz, Rayleigh--Taylor, or Richtmyer--Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is differen…
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…
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, …
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…
Turbulent high-energy astrophysical systems often feature asymmetric energy injection: for instance, Alfven waves propagating from an accretion disk into its corona. Such systems are "imbalanced": the energy fluxes parallel and anti-parallel to the large-scale magnetic field are unequal. In the past, numerical studies of imbalanced turbulence have focused on the magnetohydrodynamic regime. In the present study, we investigate externally-driven imbalanced turbulence in a collisionless, ultrarelativistically hot, magnetized pair plasma using three-dimensional particle-in-cell (PIC) simulations. …
Stochastic acceleration of nonthermal electrons is investigated in the context of hard photon spectra of blazars. It is well known that this acceleration mechanism can produce a hard electron spectrum of $m \equiv \partial \ln n_{\rm e}(γ)/\partial \ln γ= 2$ with the high-energy cutoff, called an ultrarelativistic Maxwellian-like distribution, where $n_{\rm e}(γ)$ is an electron energy spectrum. We revisit the formation of this characteristic spectrum, considering a particular situation where the electrons are accelerated through gyroresonant interaction with magnetohydrodynamic wave turbulenc…
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 …
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 apply collisionless particle-in-cell simulations of relativistic pair plasmas to explore whether driven turbulence is a viable high-energy astrophysical particle accelerator. We characterize nonthermal particle distributions for varying system sizes up to $L/2πρ_{e0} = 163$, where $L/2π$ is the driving scale and $ρ_{e0}$ is the initial characteristic Larmor radius. We show that turbulent particle acceleration produces power-law energy distributions that, when compared at a fixed number of large-scale dynamical times, slowly steepen with increasing system size. We demonstrate, however, that …
Hot accretion flows contain collisionless plasmas that are believed to be capable of accelerating particles to very high energies, as a result of turbulence generated by the magnetorotational instability (MRI). We conduct unstratified shearing-box simulations of the MRI turbulence in ideal magnetohydrodynamic (MHD), and inject energetic (relativistic) test particles in simulation snapshots to conduct a detailed investigation on particle diffusion and stochastic acceleration. We consider different amount of net vertical magnetic flux to achieve different disk magnetizations levels at saturated …
We study the physics of electron acceleration at collisionless shocks that move through a plasma containing large-scale magnetic fluctuations. We numerically integrate the trajectories of a large number of electrons, which are treated as test particles moving in the time dependent electric and magnetic fields determined from 2-D hybrid simulations (kinetic ions, fluid electron). The large-scale magnetic fluctuations effect the electrons in a number of ways and lead to efficient and rapid energization at the shock front. Since the electrons mainly follow along magnetic lines of force, the large…
We find that hydromagnetic flux tubes in back-flows in the lobes of radio galaxies offer a suitable environment for the acceleration of cosmic rays (CR) to ultra-high energies. We show that CR can reach the Hillas (1984) energy even if the magnetised turbulence in the flux tube is not sufficiently strong for Bohm diffusion to apply. First-order Fermi acceleration by successive weak shocks in a hydromagnetic flux tube is shown to be equivalent to second-order Fermi acceleration by strong turbulence.
We investigate the acceleration of charged particles (both electrons and protons) at collisionless shocks predicted to exist in the vicinity of solar flares. The existence of standing termination shocks has been examined by flare models and numerical simulations e.g., Shibata,Forbes. We study electron energization by numerically integrating the equations of motion of a large number of test-particle electrons in the time-dependent two-dimensional electric and magnetic fields generated from hybrid simulations (kinetic ions and fluid electron) using parameters typical of the solar flare plasma en…
We use the Matryoshka run to study the time dependent statistics of structure-formation driven turbulence in the intracluster medium of a 10$^{15}M_\odot$ galaxy cluster. We investigate the turbulent cascade in the inner Mpc for both compressional and incompressible velocity components. The flow maintains approximate conditions of fully developed turbulence, with departures thereof settling in about an eddy-turnover-time. Turbulent velocity dispersion remains above $700$ km s$^{-1}$ even at low mass accretion rate, with the fraction of compressional energy between 10% and 40%. Normalisation an…
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 …
A new analytic solution for 2nd-order Fermi acceleration is presented. In particular, we consider time-dependent rates for stochastic acceleration, diffusive and convective escape as well as adiabatic losses. The power law index q of the turbulence spectrum is unconstrained and can therefore account for Kolmogorov (q = 5/3) and Kraichnan (q = 3/2) turbulence, Bohm diffusion (q = 1) as well as the hard-sphere approximation (q = 2). This considerably improves beyond solutions known to date and will prove a useful tool for more realistic modelling of 2nd-order Fermi acceleration in a variety of a…
