天体物理中的高能电子加速机制

Using particle-in-cell simulations of magnetic reconnection (MR), we investigate how the changing magnetic guide field strength impacts the evolution of electron Kelvin–Helmholtz instability (EKHI) and the associated Fermi electron acceleration proposed by H. Che & G. P. Zank. Through this investigation, an Alfvénic-like Fermi electron acceleration mechanism is discovered for strong guide field MR Bg/B0 > 2.5, where Bg is the magnetic guide field. The electrons are accelerated by the intensive electric potential produced through δUi×B , where the ion velocity fluctuations δUi propagate parallel to the direction of the Alfvén-like waves. Differing from the two-stage second-order Fermi acceleration produced by the stochastic electric field of EKHI, the Alfvén-like wave mechanism is a much more efficient one-stage process that produces a much harder power-law electron energy spectrum, with an index ∼2, than that of the EKHI, with an index ∼4.

Magnetic reconnection accelerates electrons in both space and lab plasmas. The source of energy for this acceleration is the reconnecting magnetic field component. For fully ion-coupled reconnection in a one-dimensional current sheet, the efficiency and mechanism for electron acceleration are a strong function of the strength of the “guide” magnetic field directed perpendicular to the plane of reconnection. When the guide field is strong, the mechanism for electron acceleration is the parallel electric field, and it becomes less efficient with increasing guide field. We present data from studies of electron acceleration in the PHAse Space MApping (PHASMA) experiment, which induces reconnection between two electron-scale magnetic flux ropes. Our measurements show decreasing electron acceleration as the guide field is increased from 5 to 25 times the reconnecting field strength, with the input magnetic energy associated with the reconnecting component held constant. Electron acceleration is inferred from retarding field energy analyzer measurements, which complement measurements from a Thomson scattering diagnostic. The observed energies are consistent with the energy gain expected from acceleration via the parallel electric field, whereas estimates for expected energy gains from the Fermi acceleration fall well short of the observed values. Magnetic measurements show that the current sheet's thickness increases when the guide field is increased from 10 to 25. A thicker current sheet is believed to weaken the parallel electric field, consistent with the observed diminishment in electron acceleration.

The Magnetospheric Multiscale mission has identified regions of magnetic reconnection surrounded by strong turbulence associated with particle acceleration in the Earth’s magnetotail. In these turbulent reconnection regions, ion and electron distributions have substantially elevated temperatures and display nonthermal tails indicating acceleration to over ∼100 times their initial thermal energies. We investigate electron energization and acceleration using 3D test-particle simulations based on the measured magnetic and electric fields in a representative magnetic reconnection geometry. We explore stochastic, Fermi, betatron, Speiser, and turbulence-boosted Speiser-like energization and acceleration. We find that stochastic energization and Speiser-like motion (Speiser orbits and turbulence-boosted Speiser-like orbits) dominate energization and acceleration at high turbulence levels and make the largest contribution to the nonthermal tail. Electron energization comes mostly from second-order impulses from electric fields with frequencies above the ion cyclotron frequency. Perpendicular electric fields contribute to the majority of the energization (∼75%). However, the exiting electron fluxes show the reverse; most (∼62%) of the electron energy flux exits as parallel energy. Trapping in the low magnetic field near the magnetic reconnection current sheet plays an important role by increasing dwell time in the turbulence, which enhances stochastic and Speiser-like processes. One of our primary conclusions is that magnetic reconnection and turbulence appear to combine as an efficient accelerator; the turbulent acceleration near a magnetic reconnection current sheet favors high-energy electrons, generating the energetic tail. Given its widespread presence in space and astrophysical plasmas, turbulent magnetic reconnection should be considered an important source of accelerated electrons.

Particle acceleration during magnetic reconnection is a key process in space physics and astrophysics, yet the direct role of induced electric fields in fully time-dependent three-dimensional (3D) topologies remains poorly quantified. In true 3D reconnection, incorporating full temporal evolution into analytical theory is exceptionally challenging, and in existing 3D simulations, the role of the time-varying induced electric field is not easily isolated, since it is inherently entangled with other contributions. Moreover, no systematic study has compared particle acceleration across the primary 3D topologies, non-null, spine, and fan, including A-type, B-type, and X-type null geometries, within a unified, time-dependent framework. Here, we develop the first analytical, time-dependent models for these configurations, with the background magnetic field decaying as B(t) ∝ exp(−kt), allowing the decay rate k to serve as an independent control parameter for temporal dynamics. By systematically comparing electron energy spectra, representative trajectories, and field distributions, we establish a clear hierarchy of acceleration efficiency among topologies and identify the physical mechanisms that govern these differences. We further reveal a quadratic scaling of mean energy gain with k, ΔW ∝ k2, a signature that emerges when the global induced electric field becomes the dominant driver of acceleration. Collectively, these findings reveal how magnetic geometry and the global field decay rate jointly control acceleration efficiency and its scaling, which might also provide a predictive physical basis for interpreting particle energization in extreme astrophysical events.

To investigate how magnetic reconnection (MR) accelerates electrons to a power-law energy spectrum in solar flares, we explore the scaling of a kinetic model proposed by Che & Zank (CZ) and compare it to observations. Focusing on thin current sheet MR particle-in-cell (PIC) simulations, we analyze the impact of domain size on the evolution of the electron Kelvin–Helmholtz instability (EKHI). We find that the duration of the growth stage of the EKHI ( tG∼Ωe−1 ) is short and remains nearly unchanged because the electron gyrofrequency Ω e is independent of domain size. The quasi-steady stage of the EKHI (t MR) dominates the electron acceleration process and scales linearly with the size of the simulations as L/v A0, where v A0 is the Alfvén speed. We use the analytical results obtained by CZ to calculate the continuous temporal evolution of the electron energy spectra from PIC simulations and linearly scale them to solar flare observational scales. For the first time, an electron acceleration model predicts the sharp two-stage transition observed in typical soft–hard–harder electron energy spectra, implying that the electron acceleration model must be efficient with an acceleration timescale that is a small fraction of the duration of solar flares. Our results suggest that we can use PIC MR simulations to investigate the observational electron energy spectral evolution of solar flares if the ratio t MR/t G is sufficiently small, i.e., ≲10%.

We performed 3D Particle-In-Cell simulations to study electron acceleration in the electron dissipation region of asymmetrical electron magnetic reconnection driven by ultra-intensity lasers, which is similar to the Earth’s magnetosphere reconnection process. Within the electron dissipation region, electrons exhibit a nonthermal distribution, and as the asymmetry increases, the power-law spectrum becomes steeper. Remarkably, the electron spectrum closely resembles a delta distribution, arising from the intense acceleration imparted by the reconnection electric field near the X-line. Both parallel electric field acceleration and the Betatron acceleration mechanism play pivotal roles in this reconnection process. Furthermore, as the magnetic reconnection asymmetry intensifies, the parallel electric acceleration mechanism becomes stronger near the X-point region, whereas the Betatron acceleration mechanism wanes, primarily concentrated in the outflow region.

We perform a 2.5-dimensional particle-in-cell simulation of a quasi-parallel shock, using parameters for the Earth’s bow shock, to examine electron acceleration and heating due to magnetic reconnection. The shock transition region evolves from the ion-coupled reconnection dominant stage to the electron-only reconnection dominant stage, as time elapses. The electron temperature enhances locally in each reconnection site, and ion-scale magnetic islands generated by ion-coupled reconnection show the most significant enhancement of the electron temperature. The electron energy spectrum shows a power law, with a power-law index around 6. We perform electron trajectory tracing to understand how they are energized. Some electrons interact with multiple electron-only reconnection sties, and Fermi acceleration occurs during multiple reflections. Electrons trapped in ion-scale magnetic islands can be accelerated in another mechanism. Islands move in the shock transition region, and electrons can obtain larger energy from the in-plane electric field than the electric potential in those islands. These newly found energization mechanisms in magnetic islands in the shock can accelerate electrons to energies larger than the achievable energies by the conventional energization due to the parallel electric field and shock drift acceleration. This study based on the selected particle analysis indicates that the maximum energy in the nonthermal electrons is achieved through acceleration in ion-scale islands, and electron-only reconnection accounts for no more than half of the maximum energy, as the lifetime of sub-ion-scale islands produced by electron-only reconnection is several times shorter than that of ion-scale islands.

Magnetic reconnection driven by a capacitor coil target is an innovative way to investigate low-β magnetic reconnection in the laboratory, where β is the ratio of particle thermal pressure to magnetic pressure. Low-β magnetic reconnection frequently occurs in the Earth’s magnetosphere, where the plasma is characterized by β ≲ 0.01. In this paper, we analyze electron acceleration during magnetic reconnection and its effects on the electron energy spectrum via particle-in-cell simulations informed by parameters obtained from experiments. We note that magnetic reconnection starts when the current sheet is down to about three electron inertial lengths. From a quantitative comparison of the different mechanisms underlying the electron acceleration in low-β reconnection driven by coil targets, we find that the electron acceleration is dominated by the betatron mechanism, whereas the parallel electric field plays a cooling role and Fermi acceleration is negligible. The accelerated electrons produce a hardened power-law spectrum with a high-energy bump. We find that injecting electrons into the current sheet is likely to be essential for further acceleration. In addition, we perform simulations for both a double-coil co-directional magnetic field and a single-coil one to eliminate the possibility of direct acceleration of electrons beyond thermal energies by the coil current. The squeeze between the two coil currents can only accelerate electrons inefficiently before reconnection. The simulation results provide insights to guide future experimental improvements in low-β magnetic reconnection driven by capacitor coil targets.

The first self-consistent simulations of electron acceleration during magnetic reconnection in a macroscale system are presented. Consistent with solar flare observations, the spectra of energetic electrons take the form of power laws that extend more than two decades in energy. The drive mechanism for these nonthermal electrons is Fermi reflection in growing and merging magnetic flux ropes. A strong guide field suppresses the production of nonthermal electrons by weakening the Fermi drive mechanism. For a weak guide field the total energy content of nonthermal electrons dominates that of the hot thermal electrons even though their number density remains small. Our results are benchmarked with the hard x-ray, radio, and extreme ultraviolet observations of the X8.2-class solar flare on September 10, 2017.

The relaxation of field-line tension during magnetic reconnection gives rise to a universal Fermi acceleration process involving the curvature drift of particles. However, the efficiency of this mechanism is limited by the trapping of energetic particles within flux ropes. Using 3D fully kinetic simulations, we demonstrate that the flux-rope kink instability leads to strong field-line chaos in weak-guide-field regimes where the Fermi mechanism is most efficient, thus allowing particles to transport out of flux ropes and undergo further acceleration. As a consequence, both ions and electrons develop clear power-law energy spectra that contain a significant fraction of the released energy. The low-energy bounds are determined by the injection physics, while the high-energy cutoffs are limited only by the system size. These results have strong relevance to observations of nonthermal particle acceleration in space and astrophysics.

Particle acceleration and pitch-angle anisotropy resulting from magnetic reconnection are investigated in highly magnetized ion-electron plasmas. By means of fully kinetic particle-in-cell simulations, we demonstrate that magnetic reconnection generates anisotropic particle distributions fs∣cosα∣,ε , characterized by broken power laws in the particle energy spectrum f s (ε) ∝ ε −p and pitch angle 〈sin2α〉∝εm . The characteristics of these distributions are determined by the relative strengths of the magnetic field’s guide and reconnecting components (B g /B 0) and the plasma magnetization (σ 0). Below the injection break energy ε 0, ion and electron energy spectra are extremely hard (p < ≲ 1) for any B g /B 0 and σ 0 ≳ 1, while above ε 0 the spectral index steepens (p > ≳ 2), displaying high sensitivity to both B g /B 0 and σ 0. The pitch angle displays power-law ranges with negative slopes (m <) below and positive slopes (m >) above εminα , steepening with increasing B g /B 0 and σ 0. The ratio B g /B 0 regulates the redistribution of magnetic energy between ions (ΔE i ) and electrons (ΔE e ), with ΔE i ≫ ΔE e for B g /B 0 ≪ 1, ΔE i ∼ ΔE e for B g /B 0 ∼ 1, and ΔE i ≪ ΔE e for B g /B 0 ≫ 1, with ΔE i /ΔE e approaching unity when σ 0 ≫ 1. The anisotropic distribution of accelerated particles results in an optically thin synchrotron power spectrum F ν (ν) ∝ ν (2−2p+m)/(4+m) and a linear polarization degree Πlin = (p + 1)/(p + 7/3 + m/3) for a uniform magnetic field. Pitch-angle anisotropy also induces temperature anisotropy and eases synchrotron cooling, along with producing beamed radiation aligned with the magnetic field, which is potentially responsible for rapid frequency-dependent variability.

Anti‐dipolarization front (ADF), characterized by the sharp increase of the southward magnetic field (BZ,GSM < 0), is a magnetic structure with reconnected magnetic field enhancement in the magnetotail reconnection. It is considered to be an important region for energy conversion in the tailward reconnection jet. In this paper, we report an ADF event within the magnetotail reconnection diffusion region, which may comprise two ADFs and exhibit a significant enhancement of energetic electron flux. We analyze the corresponding electron acceleration mechanisms and find that the Fermi acceleration dominates the local electron energy gain, contributing to the production of energetic electrons. The magnetic mirror effect and large‐scale parallel electric potential may effectively trap the energetic electrons and facilitate Fermi acceleration. Our study provides important information for further understanding the mechanisms of energetic electron generation in space plasma.

Electron energisation by magnetic reconnection has historically been studied in the Lagrangian guiding-centre framework. Insights from such studies include that Fermi acceleration in magnetic islands can accelerate electrons to high energies. An alternative Eulerian fluid formulation of electron energisation was recently used to study electron energisation during magnetic reconnection in the absence of magnetic islands. Here, we use particle-in-cell simulations to compare the Eulerian and Lagrangian models of electron energisation in a set-up where reconnection leads to magnetic island formation. We find the largest energisation at the edges of magnetic islands. There, energisation related to the diamagnetic drift dominates in the Eulerian model, while the Fermi related term dominates in the Lagrangian model. The models predict significantly different energisation rates locally. A better agreement is found after integrating over the simulation domain. We show that strong magnetic curvature can break the magnetic moment conservation assumed by the Lagrangian model, leading to erroneous results. The Eulerian fluid model is a complete fluid description and accurately models bulk energisation. However, local measurements of its constituent energisation terms need not reflect locations where plasma is heated or accelerated. The Lagrangian guiding centre model can accurately describe the energisation of particles, but it cannot describe the evolution of the fluid energy. We conclude that while both models can be valid, they describe two fundamentally different quantities, and care should be taken when choosing which model to use.

High energy electron bunches from the laser-driven relativistic magnetic reconnection (MR) has been intensively studied. However, diagnostic methods for identifying such acceleration mechanism remain inadequate. This study utilizes 2.5-dimensional particle-in-cell simulations to explore a diagnostic approach based on electron polarization dynamics governed by the Thomas–Bargmann–Michel–Telegdi equation. The trajectories of electrons accelerated by the MR are confined in the current sheet, where the magnetic field is effectively annihilated. The resulting electron beam exhibits extremely low depolarization, distinguishing it from other accelerated populations and serving as a definitive signature of MR. This diagnostic approach enables more detailed investigations of MR—driven acceleration mechanisms in future studies.

Understanding plasma dynamics and nonthermal particle acceleration in 3D magnetic reconnection has been a long-standing challenge. In this paper, we explore these problems by performing large-scale fully kinetic simulations of multi-X-line plasmoid reconnection with various parameters in both the weak- and strong-guide-field regimes. In each regime, we have identified its unique 3D dynamics that lead to field-line chaos and efficient acceleration, and we have achieved nonthermal acceleration of both electrons and protons into power-law spectra. The spectral indices agree well with a simple Fermi acceleration theory that includes guide-field dependence. In the low-guide-field regime, the flux rope kink instability governs the 3D dynamics for efficient acceleration. The weak dependence of the spectra on the ion-to-electron mass ratio and β (≪1) implies that the particles are sufficiently magnetized for Fermi acceleration in our simulations. While both electrons and protons are injected at reconnection exhausts, protons are primarily injected by perpendicular electric fields through Fermi reflections and electrons are injected by a combination of perpendicular and parallel electric fields. The magnetic power spectra agree with in situ magnetotail observations, and the spectral index may reflect a reconnection-driven size distribution of plasmoids instead of the Goldreich–Sridhar vortex cascade. As the guide field becomes stronger, the oblique flux ropes of large sizes capture the main 3D dynamics for efficient acceleration. Intriguingly, the oblique flux ropes can also experience flux rope kink instability, to drive extra 3D dynamics. This work has broad implications for 3D reconnection dynamics and particle acceleration in heliophysics and astrophysics.

We report new theories and simulations for electron acceleration in magnetic islands generated by magnetic reconnection in the shock turbulence in a quasi-parallel shock, using a 2 and 1/2 dimensional particle-in-cell simulation. When an island is moving, unmagnetized electrons are accelerated by the Hall electric field pointing toward the island center. In a stationary island, some electrons are energized by “island betatron acceleration” due to the induction electric field when the island core magnetic field changes with time. In the simulation, almost all of the high-energy electrons in the shock transition region that show a power-law distribution are accelerated in ion-skin-depth-scale magnetic flux ropes, and about half of them are accelerated by the Hall electric field and island betatron acceleration. These mechanisms can produce a power-law electron distribution, and also inject electrons into the diffusive shock acceleration. The mechanisms are applicable to quasi-parallel shocks with high Alfvén Mach numbers (M A > 10), including planetary bow shocks and shocks in astrophysical objects such as supernova remnants.

Magnetic reconnection releases the magnetic energy through the contraction of multi-magnetic island leading to the electron acceleration as proposed by Drake et. al in 2006. However, how the released magnetic energy is converted into electron’s kinetic energy is still theoretically not well understood. We model in particular the kinetic process assuming the adiabatic contraction of magnetic island that induces electric field which is proportional to the vector potential of the magnetic island and approximate the magnetic island with an ellipse. Under this model, we show that the energy gain is achieved through the work of inductive electric field. We further show that the curvature drift which is along the inductive electric field dominates the energy gain. We compared our model with the magnetic island formed by tearing instability in a 2.5D particle-in-cell simulation of magnetic reconnection and found the results from the model consistent with that of the simulation.

Magnetic reconnection is a fundamental process known to play a crucial role in electron acceleration and heating, however, the mechanism of electron energization during reconnection is still not fully understood. This study introduces a novel electron acceleration mechanism in which electrons can be accelerated by secondary reconnection in the separatrix region. The secondary reconnection occurs in a thin current sheet resulted from the shear of the out‐of‐plane Hall magnetic fields of the primary magnetopause reconnection. It results in the intense electron energy fluxes toward the primary X‐line. This mechanism will likely be an important piece in the puzzle of particle acceleration by reconnection.

Electrons are accelerated to high, nonthermal energies during explosive energy-release events in space, such as magnetic reconnection. However, the properties and acceleration mechanisms of relativistic electrons directly associated with the reconnection X-line are not well understood. This study utilizes Magnetospheric Multiscale (MMS) measurements to analyze the flux and spectral features of subrelativistic to relativistic (∼80–560 keV) electrons during a magnetic reconnection event in Earth’s magnetotail. This event provided a unique opportunity to measure the electrons directly energized by the X-line as MMS stayed in the separatrix layer, where the magnetic field directly connects to the X-line, for approximately half of the observation period. Our analysis revealed that the fluxes of relativistic electrons were clearly enhanced within the separatrix layer, and the highest flux was directed away from the X-line, which suggested that these electrons originated directly from the X-line. Spectral analysis showed that these relativistic electrons deviated from the main plasma sheet population and exhibited an “ankle” feature similar to that observed in galactic cosmic rays. The contribution of “ankle” electrons to the total electron energy density increased from 0.1% to 1% in the separatrix layer though the spectral slopes did not exhibit clear variations. Further analysis indicated that while these relativistic electrons originated from the X-line, they experienced a nonnegligible degree of scattering during transport. These findings provide clear evidence that magnetic reconnection in Earth’s magnetotail can efficiently energize relativistic electrons directly at the X-line, providing new insights into the complex processes governing electron dynamics during magnetic reconnection.

In this work, we investigated the magnetic annihilation and reconnection and the resulted hot electron acceleration driven by double-beam intense laser pulses in two-layer near critical density (NCD) plasma target. The results are obtained by performing two-dimensional (2D) particle-in-cell (PIC) simulations. It is found that a quasi-mono-energetic peak can be formed in the energy spectrum of electrons accelerated by the process of magnetic field annihilation (MA) at cutoff energy. Electron spectra feature depends on the length of the second low-density layer. This suggests that the process of relativistic magnetic annihilation may be controlled in experiments by target design.

Magnetic reconnection can effectively convert magnetic energy into plasma energy, and accelerate electrons. In this article, the electrons with energies up to 150 keV are observed in the separatrix region and near the electron diffusion region (EDR) detected by the Magnetospheric Multiscale mission in the magnetotail. Combined with the electron pitch‐angle distribution, the electrons in these two regions have a striking behavior: the low‐energy electrons (<∼10 keV) move mainly toward the X‐line, while the energetic electrons (69–139 keV) move mainly away from the X‐line. In the EDR, the energy of electrons can reach up to 10 keV and there is a notable enhancement in the flux of electrons in the direction perpendicular to the magnetic field, which implies the presence of acceleration processes occurring in the EDR, leading to the energization of electrons. Furthermore, the energy spectrum of non‐thermal electron with energies above 6 keV shows a power law distribution in this event, suggesting the occurrence of multiple acceleration processes rather than a single energization mechanism. These findings underscore the EDR's role as a crucial region for electron acceleration during magnetic reconnection. The study provides essential clues about the mechanisms driving electron acceleration, contributing to our understanding of space weather phenomena and the broader dynamics of plasma physics in space environments.

No abstract available

We extend the sub-grid model of Nurisso et al. (2023) to include particle acceleration and to predict the resulting energy spectra produced by magnetic reconnection events in large-scale relativistic magnetohydrodynamic (RMHD) simulations. Our method is consistently calibrated on particle-in-cell results and employs a particle-tracking approach that builds upon Vaidya et al. (2018). In this framework, the non-thermal spectral distribution of each macro-particle—representing an electron cloud—is updated by solving the relativistic cosmic-ray transport equation using the local fluid conditions. The proposed model predicts the slope and the maximum energy of the macro particle spectral distribution from the sampled values of plasma β and σ (magnetization) parameters, and it estimates the amount of magnetic energy feeding the non-thermal population including the contribution given by the guide field. A convolution method similar to the one proposed by Mukherjee et al. (2021) is employed in order to account for multiple acceleration episodes. The method has been implemented in the new GPU-ready version of the pluto code. We demonstrate its validity to predict particle spectra for a stationary current sheet. Furthermore, an application to a 3D unstable plasma column, where multiple current sheets are formed as by-product of the current-driven instability, is presented. Our results indicate an early-time cumulative power law with spectral index p ∼ 2.7 which evolves in a broken power-law at later stages (with a high energy tail slope p ∼ 4). Lastly, we demonstrate the capability of the module to predict the non-thermal emission intensity, polarization angle and degree of the system for two line of sights.

Magnetic reconnection is a fundamental energy conversion process occurred when two oppositely directed magnetic field lines break and reconnect, in which the stored magnetic energy is converted into plasma kinetic and thermal energy. This paper aims to examine the favorable conditions for electron heating and acceleration during reconnection. Two reconnection events observed by Cluster spacecraft in the magnetotail were studied, in which a magnetic X-line was encountered. Preliminary results show that (1) thin plasma sheet has a strong current density as expected, (2) electrons are mainly accelerated along the field-aligned direction, and (3) energetic electron fluxes are enhanced for thin plasma sheet. More reconnection events and other reconnection properties (e.g., reconnection electric field and the normal electric field) will be analyzed for a statistical study.

Coalescence of magnetic flux ropes (MFRs) is suggested as a crucial mechanism for electron acceleration in various astrophysical plasma systems. However, how electrons are being accelerated/heated via MFR coalescence is not fully understood. In this paper, we quantitatively analyze electron heating and acceleration during the coalescence of three MFRs at Earth's magnetopause using in‐situ Magnetospheric Multiscale (MMS) observations. We find that suprathermal electrons are enhanced in the coalescing MFRs than those in the ambient magnetosheath and non‐coalescing MFRs. Both first‐order Fermi and E|| acceleration were responsible for this electron acceleration, while the overall effect of betatron process cooled the electrons. The most intense Fermi acceleration was observed in the trailing part of the middle MFR, while E|| acceleration occurred primarily at the reconnection sites between the coalescing MFRs. For non‐coalescing MFRs, the dominant mechanism for energizing electrons is the E|| acceleration. Our results further consolidate the important role of MFR coalescence in electron heating/acceleration in space plasma.

Solar flares are explosive releases of magnetic energy stored in the solar corona, driven by magnetic reconnection. These events accelerate electrons, generating hard X-ray emissions, and often display quasi-periodic pulsations (QPPs) across the energy spectra. However, the energy transfer process remains poorly constrained, with competing theories proposing different acceleration mechanisms. We investigate electron acceleration and transport in a flaring coronal loop by solving a time-dependent Fokker–Planck equation. Our model incorporates transient turbulent acceleration, simulating the effects of impulsive energy input to emulate the dynamics of time-dependent reconnection processes. We compute the density-weighted electron flux, a diagnostic directly comparable to observed X-ray emissions, across the energy and spatial domains from the corona to the chromosphere. We investigate different time-dependent functional forms of the turbulent acceleration, finding that the functional form of the acceleration source maintains its signature across energy bands (1–100 keV) with a response time that is energy dependent (with higher-energy bands displaying longer response times). In addition, we find that (a) for a square pulse the switch on and off response time is different; (b) for a sinusoidal input the periodicity is preserved; and (c) for a damped sinusoidal the decay rate increases with density and higher-energy bands lose energy faster. This work presents a novel methodology for analyzing electron acceleration and transport in flares driven by time-dependent sources.

Density inhomogeneities are ubiquitous in space and astrophysical plasmas, particularly at magnetic reconnection sites, shock fronts, and within compressible turbulence. The gradients associated with these inhomogeneous plasma regions serve as free energy sources that can drive plasma instabilities, including the lower-hybrid drift instability (LHDI). Notably, lower-hybrid waves are frequently observed in magnetized space plasma environments, such as Earth's magnetotail and magnetopause. Previous studies have primarily focused on modeling particle acceleration via LHDI in these regions using a quasilinear approach. This study expands the investigation of LHDI to a broader range of environments, spanning weakly to strongly magnetized media, including interplanetary, interstellar, intergalactic, and intracluster plasmas. To explore the applicability of LHDI in various astrophysical settings, we employ two key parameters: (1) plasma magnetization, characterized by the plasma beta parameter, and (2) the spectral slope of suprathermal electrons following a power-law distribution. Using a quasilinear model, we determine the critical values of plasma beta and spectral slope that enable efficient electron acceleration via LHDI by comparing the rate of growth of instability and the damping rate of the resulting fluctuations. We further analyze the time evolution of the electron distribution function to confirm these critical conditions. Our results indicate that electron acceleration is generally most efficient in low-beta plasmas (1). Finally, we discuss the astrophysical implications of our findings, highlighting the role of LHDI in electron acceleration across diverse plasma environments.

We study electron energization in turbulence-generated current sheets in the shock transition region by means of fully kinetic collisionless plasma simulations and theory. Using parameters in the Earth’s bow shock, we perform a two-dimensional particle-in-cell simulation of a quasi-parallel shock. In shock turbulence, many current sheets are produced, including those exhibiting magnetic reconnection and those that are not reconnecting. The electron temperature is enhanced in nonreconnecting current sheets as well as in reconnecting current sheets and magnetic islands. Performing electron trajectory tracing analysis, we find that energetic electrons are produced in nonreconnecting thinning current sheets. The motional electric field during the thinning process of a current sheet energizes both magnetized and unmagnetized electrons. We analytically show that the energization rate for unmagnetized electrons is slightly less than that of adiabatic energization for magnetized electrons, but unmagnetized electrons can be effectively trapped in magnetic field structures formed in thinning current sheets and continue to be energized. These nonreconnecting current sheets produce energetic electrons whose energies are comparable to the energetic electrons produced in magnetic islands, and they can reach the injection energy for diffusive shock acceleration, which is an acceleration mechanism for producing cosmic rays. The number of electrons that are energized in nonreconnecting current sheets is about a quarter of that in reconnection regions. The energization mechanism can be applicable to various space and astrophysical environments, including planetary bow shocks and supernova remnant shocks.

No abstract available

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 electric field. Rather, reconnection causes turbulent outflows where energy exchange is dominated by a highly non-Gaussian distribution of fluctuations. Electron energization is diffuse throughout the entire reconnection outflow, but it is heightened by regions of intensified magnetic field such as dipolarization fronts traveling toward Earth.

Secondary flux ropes are suggested to play important roles in energy dissipation and particle acceleration during magnetic reconnection. However, their generation mechanism is not fully understood. In this Letter, we present the first direct evidence that a secondary flux rope was generated due to the evolution of an electron vortex, which was driven by the electron Kelvin-Helmholtz instability in an ion diffusion region as observed by the Magnetospheric Multiscale mission. The subion scale (less than the ion inertial length) flux rope was embedded within the electron vortex, which contained a secondary electron diffusion region at the trailing edge of the flux rope. We propose that intense electron shear flow produced by reconnection generated the electron Kelvin-Helmholtz vortex, which induced a secondary reconnection in the exhaust of the primary X line and then led to the formation of the flux rope. This result strongly suggests that secondary electron Kelvin-Helmholtz instability is important for reconnection dynamics.

Observations of galaxy clusters show radio emission extended over almost the system scale, necessitating mechanisms for particle acceleration. Previous models for acceleration, such as diffusive shock acceleration and that due to turbulence, can fall short in terms of efficiency. In this Letter, we propose the possibility of acceleration via magnetic reconnection. In particular, we invoke the plasmoid instability, which has been previously applied to understand particle energization in high-energy systems. Turbulence in galaxy clusters leads to fluctuation dynamos that are known to generate magnetic field structures consisting of sharp reversals. These form natural sites of reconnection. We perform particle-in-cell simulations of the plasmoid instability in collisionless and nonrelativistic plasmas. We show that the resulting electron energy spectra have power-law indices that are consistent with those inferred from observations. Our estimates show that the acceleration timescales are much smaller than the lifetime of the reconnecting magnetic structures indicating the feasibility of our model. The synchrotron radio luminosity estimate is about 1041 erg s−1, agreeing with observations. Finally, we find that the maximum achievable Lorentz factor can go up to 105 indicating that acceleration due to magnetic reconnection is a promising avenue for understanding the origin of nonthermal emission in galaxy clusters.

We investigate electron heating by magnetic-field-aligned electric fields (E_{∥}) during antiparallel magnetic reconnection in the Earth's magnetotail. Using a statistical sample of 140 reconnection outflows, we infer the acceleration potential associated with E_{∥} from the shape of the electron velocity distribution functions. We show that heating by E_{∥} in the reconnection outflow can reach up to 10 times the inflow electron temperature. We demonstrate that the magnitude of the acceleration potential scales with the inflow Alfvén and electron thermal speeds to maintain quasineutrality in the reconnection region. Our results suggest that, as the inflow plasma parameter β_{e∞} increases, E_{∥} becomes increasingly important to the ion-to-electron energy partition associated with magnetic reconnection.

Magnetic reconnection is often invoked as a source of high-energy particles, and in relativistic astrophysical systems it is regarded as a prime candidate for powering fast and bright flares. We present a novel analytical model—supported and benchmarked with large-scale three-dimensional kinetic particle-in-cell simulations in electron–positron plasmas—that elucidates the physics governing the generation of power-law energy spectra in relativistic reconnection. Particles with Lorentz factor γ ≳ 3σ (here, σ is the magnetization) gain most of their energy in the inflow region, while meandering between the two sides of the reconnection layer. Their acceleration time is tacc∼γηrec−1ωc−1≃20γωc−1 , where η rec ≃ 0.06 is the inflow speed in units of the speed of light and ω c = eB 0/mc is the gyrofrequency in the upstream magnetic field. They leave the region of active energization after t esc, when they get captured by one of the outflowing flux ropes of reconnected plasma. We directly measure t esc in our simulations and find that t esc ∼ t acc for σ ≳ few. This leads to a universal (i.e., σ-independent) power-law spectrum dNfree/dγ∝γ−1 for the particles undergoing active acceleration, and dN/dγ∝γ−2 for the overall particle population. Our results help to shed light on the ubiquitous presence of power-law particle and photon spectra in astrophysical nonthermal sources.

No abstract available

A concise review is given on the past two decades’ results from laboratory experiments on collisionless magnetic reconnection in direct relation with space measurements, especially by the Magnetospheric Multiscale (MMS) mission. Highlights include spatial structures of electromagnetic fields in ion and electron diffusion regions as a function of upstream symmetry and guide field strength, energy conversion and partitioning from magnetic field to ions and electrons including particle acceleration, electrostatic and electromagnetic kinetic plasma waves with various wavelengths, and plasmoid-mediated multiscale reconnection. Combined with the progress in theoretical, numerical, and observational studies, the physics foundation of fast reconnection in collisionless plasmas has been largely established, at least within the parameter ranges and spatial scales that were studied. Immediate and long-term future opportunities based on multiscale experiments and space missions supported by exascale computation are discussed, including dissipation by kinetic plasma waves, particle heating and acceleration, and multiscale physics across fluid and kinetic scales.

The possibility of studying nonthermal electron energization in laser-driven plasma experiments of magnetic reconnection is studied using two- and three-dimensional particle-in-cell simulations. It is demonstrated that nonthermal electrons with energies more than an order of magnitude larger than the initial thermal energy can be produced in plasma conditions currently accessible in the laboratory. Electrons are accelerated by the reconnection electric field, being injected at varied distances from the X points, and in some cases trapped in plasmoids, before escaping the finite-sized system. Trapped electrons can be further energized by the electric field arising from the motion of the plasmoid. This acceleration gives rise to a nonthermal electron component that resembles a power-law spectrum, containing up to ∼8% of the initial energy of the interacting electrons and ∼24% of the initial magnetic energy. Estimates of the maximum electron energy and of the plasma conditions required to observe suprathermal electron acceleration are provided, paving the way for a new platform for the experimental study of particle acceleration induced by reconnection.

We use the Magnetospheric Multiscale mission (MMS) to study electron acceleration at Earth's quasi‐perpendicular bow shock to address the long‐standing electron injection problem. The observations are compared to the predictions of the stochastic shock drift acceleration (SSDA) theory. Recent studies based on SSDA predict electron distribution being a power law with a cutoff energy that scales with upstream parameters. This scaling law has been successfully tested for a single Earth's bow shock crossing by MMS. Here we extend this study and test the prediction of the scaling law for seven MMS Earth's bow shock crossings with different upstream parameters. A goodness‐of‐fit test shows good agreement between observations and SSDA theoretical predictions, thus supporting SSDA as one of the most promising candidates for solving the electron injection problem.

We use the Magnetospheric Multiscale (MMS) mission to present a case study of electron acceleration at Earth's bow shock due to an interaction with a solar wind magnetic depression. The magnetic depression is identified as a reconnecting current sheet and is observed both at the bow shock, using MMS, and upstream of the shock at the Lagrange point 1 using the ACE, WIND, and DSCOVR spacecraft. The interaction with the current sheet and drop in magnetic field magnitude enables electrons to be accelerated from thermal energies (10–20 eV) up to suprathermal energies (1–5 keV) in a process producing a power‐law with a spectral index p=−2.3 $p=-2.3$ close to that predicted by first order Fermi acceleration (p=−2) $(p=-2)$ . The observations are compared to a numerical model of Fermi acceleration considering two approaching magnetic mirrors and pitch angle scattering by whistler waves, and good agreement is shown. Thus, we add another piece to resolving the long‐standing electron injection problem.

Shock waves, the interface of supersonic and subsonic plasma flows, are the primary region for charged particle acceleration in multiple space plasma systems, including Earth’s bow shock, which is readily accessible for in-situ measurements. Spacecraft frequently observe relativistic electron populations within this region, characterized by energy levels surpassing those of solar wind electrons by a factor of 10,000 or more. However, mechanisms of such strong acceleration remain elusive. Here we use observations of electrons with energies up to 200 kiloelectron volts and a data-constrained model to reproduce the observed power-law electron spectrum and demonstrate that the acceleration by more than 4 orders of magnitude is a compound process including a complex, multi-step interaction between more commonly known mechanisms and resonant scattering by several distinct plasma wave modes. The proposed model of electron acceleration addresses a decades-long issue of the generation of energetic (and relativistic) electrons at planetary plasma shocks. This work may further guide numerical simulations of even more effective electron acceleration in astrophysical shocks. Mechanisms responsible for the electron acceleration to near relativistic energies in Earth’s foreshock remains elusive. Here, the authors show that the combination of resonant scattering by distinct wave modes with known acceleration mechanisms explains the formation of observed electron fluxes up to and above 200 keV.

Recent observations and simulations indicate that solar flares undergo extremely complex 3D evolution, making 3D particle transport models essential for understanding electron acceleration and interpreting flare emissions. In this study, we investigate this problem by solving Parker’s transport equation with 3D MHD simulations of solar flares. By examining energy conversion in the 3D system, we evaluate the roles of different acceleration mechanisms, including reconnection current sheet (CS), termination shock (TS), and supra-arcade downflows (SADs). We find that large-amplitude turbulent fluctuations are generated and sustained in the 3D system. The model results demonstrate that a significant number of electrons are accelerated to hundreds of keV and even a few MeV, forming power-law energy spectra. These energetic particles are widely distributed, with concentrations at the TS and in the flare looptop region, consistent with results derived from recent hard X-ray (HXR) and microwave (MW) observations. By selectively turning particle acceleration on or off in specific regions, we find that the CS and SADs effectively accelerate electrons to several hundred keV, while the TS enables further acceleration to MeV. However, no single mechanism can independently account for the significant number of energetic electrons observed. Instead, the mechanisms work synergistically to produce a large population of accelerated electrons. Our model provides spatially and temporally resolved electron distributions in the whole flare region and at the flare footpoints, enabling synthetic HXR and MW emission modeling for comparison with observations. These results offer important insights into electron acceleration and transport in 3D solar flare regions.

The origin of energetic charged particles in universe remains an unresolved issue. Astronomical observations combined with simulations have provided insights into particle acceleration mechanisms, including magnetic reconnection acceleration, shock acceleration, and stochastic acceleration. Recent experiments have also confirmed that electrons can be accelerated through processes such as magnetic reconnection and collisionless shock formation. However, laboratory identifying stochastic acceleration as a feasible mechanism is still a challenge, particularly in the creation of collision-free turbulent plasmas. Here, we present experimental results demonstrating kinetic turbulence with a typical spectrum k−2.9 originating from Weibel instability. Energetic electrons exhibiting a power-law distribution are clearly observed. Simulations further reveal that thermal electrons undergo stochastic acceleration through collisions with multiple magnetic islands-like structures within the turbulent region. This study sheds light on a critical transition period during supernova explosion, where kinetic turbulences originating from Weibel instability emerge prior to collisionless shock formation. Our results suggest that electrons undergo stochastic acceleration during this transition phase. The origin of energetic charged particles in universe remains an unresolved issue, while one of the promising mechanism contributions is stochastic acceleration. Here the authors demonstrate electron stochastic acceleration of kinetic turbulence in a lab setting.

Plasma shock waves stand out as one of the most promising sites of efficient particle acceleration in extragalactic jets. In electron-ion plasma shocks, electrons can be heated up to large Lorentz factors, making them an attractive scenario to explain the high minimum electron Lorentz factors regularly needed to describe the emission of BL Lac type objects. Still, the (relativistic) thermal electron component is commonly neglected when modelling the observations, although it holds key information on the shock properties. Considering a shock acceleration scenario, we modelled the broadband emission of the archetypal high synchrotron peaked blazar Markarian 421; we employed particle distributions that included a thermal (relativistic) Maxwellian component at low energies followed by a non-thermal power law, as motivated by particle-in-cell simulations. The observations, in particular in the optical/UV and MeV-GeV bands, efficiently restricted the non-thermal emission from the Maxwellian electrons, which we used to derive constraints on the basic properties, such as the fraction ε_e of the total shock energy stored in the non-thermal electrons. The best-fit model yields a non-thermal electron power law with an index of ∼ 2.4, close to predictions from shock acceleration. Successful fits are obtained when the ratio between the Lorentz factor at which the non-thermal distribution begins (γ_̊m nth) and the dimensionless electron temperature (þeta) satisfies γ_ ̊m nth /þeta łesssim 8. Since γ_ ̊m nth /þeta controls ε_e, the latter limit implies that at least ε_e ≈ 10% of the shock energy is transferred to the non-thermal electrons. These results are almost insensitive to the shock velocity γ_̊m sh, but radio observations indicate γ_ ̊m sh ≳ 5 since for lower shock velocities the fluxes in the millimetre band are overproduced by the Maxwellian electrons. Therefore, if shocks drive the particle energisation, our findings indicate that they operate in the mildly to fully relativistic regime with efficient electron acceleration. This paper lays the ground for future works, in which we will use plasma simulations to investigate if, and under which conditions, the findings presented here can be reproduced.

We study diffusive shock acceleration (DSA) of protons and electrons at nonrelativistic, high Mach number, quasiparallel, collisionless shocks by means of self-consistent 1D particle-in-cell simulations. For the first time, both species are found to develop power-law distributions with the universal spectral index -4 in momentum space, in agreement with the prediction of DSA. We find that scattering of both protons and electrons is mediated by right-handed circularly polarized waves excited by the current of energetic protons via nonresonant hybrid (Bell) instability. Protons are injected into DSA after a few gyrocycles of shock drift acceleration (SDA), while electrons are first preheated via SDA, then energized via a hybrid acceleration process that involves both SDA and Fermi-like acceleration mediated by Bell waves, before eventual injection into DSA. Using the simulations we can measure the electron-proton ratio in accelerated particles, which is of paramount importance for explaining the cosmic ray fluxes measured on Earth and the multiwavelength emission of astrophysical objects such as supernova remnants, radio supernovae, and galaxy clusters. We find the normalization of the electron power law is ≲10^{-2} of the protons for strong nonrelativistic shocks.

The detail of the particle acceleration at trans-relativistic shocks is still under debate. We propose a way to probe the particle acceleration at trans-relativistic shocks with observations of gamma-ray burst (GRB) afterglows. In the afterglow phase, the shock wave launched in a GRB is gradually decelerated from the relativistic to non-relativistic regimes by sweeping up the ambient interstellar matter. If the electron power-law index depends on the shock Lorentz factor, it is reflected to the evolution of the afterglow spectrum. We theoretically study the time evolution of the electron power-law index imprinted in GRB afterglow spectra. We introduce a particle acceleration model by a trans-relativistic shock into the standard GRB afterglow model and apply the formulation to structured jet models that are consistent with GRB 170817A, which is the counterpart of the gravitational-wave signal GW170817 from a binary neutron star merger. As a result, we find that it is possible to observe the transition of the electron acceleration from the relativistic phase to the non-relativistic phase in the evolution of the afterglow spectrum, if GRBs similar to GRB 170817A take place in a dense environment at 200 Mpc. The detection number of short GRBs will increase in the era of the multi-messenger astronomy including gravitational waves. Thus, we expect that future GRBs can give a constraint on particle acceleration models as proposed in our study.

Gamma-ray observations of the Crab Nebula by two different space telescopes challenge particle acceleration theory. The well-known Crab Nebula is at the center of the SN1054 supernova remnant. It consists of a rotationally powered pulsar interacting with a surrounding nebula through a relativistic particle wind. The emissions originating from the pulsar and nebula have been considered to be essentially stable. Here, we report the detection of strong gamma-ray (100 mega–electron volts to 10 giga–electron volts) flares observed by the AGILE satellite in September 2010 and October 2007. In both cases, the total gamma-ray flux increased by a factor of three compared with the non-flaring flux. The flare luminosity and short time scale favor an origin near the pulsar, and we discuss Chandra Observatory x-ray and Hubble Space Telescope optical follow-up observations of the nebula. Our observations challenge standard models of nebular emission and require power-law acceleration by shock-driven plasma wave turbulence within an approximately 1-day time scale.

Using a semianalytic model of nonlinear diffusive shock acceleration, we model the total spectrum of cosmic ray (CR) electrons accelerated by supernova remnants (SNRs). Because electrons experience synchrotron losses in the amplified magnetic fields characteristic of SNRs, they exhibit substantially steeper spectra than protons. In particular, we find that the difference between the electron and proton spectral index (power law slope) ranges from 0.1 to 0.4. Our findings must be reckoned with theories of Galactic CR transport, which often assume that electrons and protons are injected with the same slope, and may especially have implications for the observed "positron excess".

No abstract available

Finding the injection threshold for diffusive shock acceleration (DSA) of electrons in collisionless shocks has been a longstanding unsolved problem. Using first-principles kinetic simulations, we identify the conditions for electron injection into DSA and quantify the evolution of the nonthermal tail in self-generated electromagnetic turbulence. By analyzing electron trajectories and their momentum gain during shock-recrossing cycles, we demonstrate that electrons start participating in DSA when their speed is large enough to overrun the shock. We develop a minimal model showing that speed-dependent injection reproduces nonthermal electron spectra observed in kinetic simulations. Our findings establish a new criterion for electron DSA, which has broad implications for the shock-powered nonthermal emission from space/astrophysical systems.

A theory for steady-state tempered superdiffusive shock acceleration of energetic particles at a plane perpendicular shock is presented that involves solving analytically a tempered fractional Parker transport equation for perpendicular transport in quasi-2D turbulence. The main predictions of the theory are as follows: (i) Tempered perpendicular superdiffusion (tempered Lévy flights) upstream reduces the effectiveness of classical perpendicular superdiffusion (standard Lévy flights) through a transition toward normal perpendicular diffusion when the particle transport distance upstream surpasses a critical spatial scale. Consequently, the accelerated particle distribution upstream decays spatially as a stretched exponential close to the shock that becomes a power law farther upstream under some conditions (superdiffusion), followed by an exponential rollover (transition to normal diffusion); (ii) Downstream, the accelerated particle distribution for tempered superdiffusion converges to a uniform distribution closer to the shock because of a stronger decay close to the shock compared to classical superdiffusion, and a shift of the peak in the distribution at the shock to just downstream of the shock occurs under some conditions; (iii) The accelerated power-law momentum spectrum at the shock is modulated upstream by the incoming solar wind flow to be a hardened power law instead of featuring an exponential rollover at lower particle momenta as for classical diffusive shock acceleration; and (iv) Tempered superdiffusive shock acceleration tends to be more efficient compared to standard superdiffusive shock acceleration.

In astrophysics, one significant challenge lies in understanding the acceleration of cosmic rays, which leads to the occurrence of a power law. In this article, momentum transport generated by the combined effects of pitch-angle diffusion and background flow velocity inhomogeneities is proposed to obtain a cosmic rays acceleration mechanism, starting from the well-known focused transport equation describing particle diffusion and acceleration. The inhomogeneities of background flow velocity are ubiquitous in the astrophysical environment. The equation for the isotropic part of the distribution function of charged energetic particles is derived, and its solution is obtained, demonstrating the form of momentum power laws of cosmic rays. In addition, if it is assumed that cosmic rays penetrate compressive MHD waves or turbulence, for quasi-steady states, the spectral index δ of the momentum power law spectrum of cosmic rays is found to be in the range [−5, −3], which includes the observed power law indices of galactic cosmic rays. The results obtained in this article demonstrate that the mechanism proposed in this article, along with shock acceleration, may also contribute to the acceleration of galactic cosmic rays. Furthermore, when momentum convection effect and higher-order momentum derivative terms are considered, the indices of power laws should be smaller than −5. This may explain the power laws of solar energetic particle events.

Spider pulsars are binary systems composed of a millisecond pulsar and a low-mass companion. Their X-ray emission, varying with orbital phase, originates from synchrotron radiation produced by high-energy electrons accelerated at the intrabinary shock. For fast-spinning pulsars in compact binary systems, the intrabinary shock emission occurs in the fast cooling regime. Using global two-dimensional particle-in-cell simulations, we investigate the effect of synchrotron losses on the shock structure and the resulting emission, assuming that the pulsar wind is stronger than the companion wind (so, the shock wraps around the companion), as expected in black widows. We find that the shock opening angle gets narrower for greater losses; the lightcurve shows a more prominent double-peaked signature (with two peaks just before and after the pulsar eclipse) for stronger cooling; below the cooling frequency, the synchrotron spectrum displays a hard power-law range, consistent with X-ray observations.

Suprathermal electrons are routinely observed in interplanetary space. At higher energies, there are in-situ evidences that shocks, both interplanetary shocks, often driven by fast coronal mass ejections, and terrestrial bow shocks, can accelerate electrons up to transrelativistic energies (∼MeVs). The acceleration mechanism responsible for these energetic electrons is still under debate. In this work, we study the effects of large-scale shock ripples on electron acceleration at a quasi-perpendicular shock in a 2D system. For tractability of the numerical simulation, we consider the scenario where the magnetic field line contains ripples, and the shock is assumed planar and piecewise. The propagation of gyrophase-averaged electrons is governed by the focused transport equation, where the effect of the turbulent magnetic field is modeled by the pitch-angle diffusion, described by the quasi-linear theory. A Monte Carlo simulation on the equivalent time-forward Itô stochastic differential equation is performed within a periodic box to obtain the phase-space distribution function of the accelerated electrons. Our model predicts power-law energy spectra with a cutoff at high-energy ends, whereas their spectral indices are softer than those predicted by the diffusive shock acceleration theory. We demonstrate that, with a suitable choice of pitch-angle diffusion strength, a small fraction of electrons can experience magnetic traps in multiple ripples along the shock surface, boosting their energies to ∼MeVs. Our results therefore provide a framework for a better understanding of relativistic electron events associated with shocks within the heliosphere.

We statistically investigate high-frequency whistler waves (with frequencies higher than ∼10% of the local electron cyclotron frequency) at Earth's bow shock using magnetospheric multi-scale (MMS) spacecraft observations. We focus specifically on the wave power within the shock transition layer, where we expect electron acceleration via stochastic shock drift acceleration (SSDA) to occur associated with efficient pitch-angle scattering by whistler waves. We find that the wave power is positively correlated with both the Alfvén Mach number in the normal incidence frame MA and in the de Hoffmann–Teller frame MA/cos θBn. The empirical relation with MA/cos θBn is compared with the theory of SSDA that predicts a threshold wave power proportional to (MA/cos θBn)−2. The result suggests that the wave power exceeds the theoretical threshold for MA/cos θBn≳30–60, beyond which efficient electron acceleration is expected. This aligns very well with previous statistical analysis of electron acceleration at Earth's bow shock [Oka et al., Geophys. Res. Lett. 33, 5–6 (2006)]. Therefore, we consider that this study provides further support for SSDA as the mechanism of electron acceleration at Earth's bow shock. At higher-Mach-number astrophysical shocks, SSDA will be able to inject electrons into the diffusive shock acceleration process for subsequent acceleration to cosmic-ray energies.

Energetic positrons have been observed in the interstellar medium, and high-energy positrons with relativistic energies up to approximately 1 TeV have been detected in Galactic cosmic rays. We conducted a study on the acceleration of particles, specifically positrons, in a nonrelativistic quasi-parallel collisionless shock induced by a plasma consisting of protons, electrons, and positrons. The positron-to-proton number density ratio in the plasma is 0.1. We focused on a representative shock with a sonic Mach number of 17.1 and an Alfvénic Mach number of 16.8 in the rest frame of the shock. To investigate the acceleration mechanisms of particles including positrons in the shock, we utilized 1D particle-in-cell simulations. It was found that all three species of particles in the shock can be accelerated and exhibit power-law spectra. At the shock front, a significant portion of incoming upstream particles are reflected and undergo significant energy increases, and these reflected particles can be efficiently injected into the process of diffusive shock acceleration (DSA). Moveover, the reflected positrons can be further accelerated by an electric field parallel to the magnetic field when they move along the magnetic field upstream of the shock. As a result, positrons can be preferentially accelerated to be injected in the DSA process compared to electrons.

Single electron-hole dynamics in a one-dimensional plasma composed of two species, electrons and protons, with reduced mass ratio, is investigated through numerical kinetic Vlasov–Maxwell simulations. The electron-hole's growth of phasetrophy and acceleration are systematically studied as a function of different plasma and electron-hole parameters such as electron drift velocity vd, initial hole velocity δvh, electric potential amplitude ϕ0, and gradients of the distribution functions fe,h′ and fi,h′. A first parameter scan shows two different regimes of positive exponential increase for the electron-holes growth-rate at both positive and negative gradient sides of the electron distribution function. Linear growth of an electron-hole is observed as a function of both ion and electron distribution functions. Moreover, two power laws are measured as a function of the electric potential amplitude in both low- and high-amplitude regimes. Finally, a qualitative agreement between measurements of phasetrophy growth-rate against an effective gradient is found, the latter considering variations and effects of the electron distribution function gradient over the electron-hole's width.

We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel nonrelativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speeds v sh ≈ 0.067–0.267c, Alfvén Mach numbers MA=5–40 , sonic Mach numbers Ms=5–160 , as well as the proton-to-electron mass ratios m i/m e = 16–1836. We find that high Alfvén Mach number shocks can channel a large fraction of their kinetic energy into nonthermal particles, self-sustaining magnetic turbulence and acceleration to larger and larger energies. The fraction of injected particles is ≲0.5% for electrons and ≈1% for protons, and the corresponding energy efficiencies are ≲2% and ≈10%, respectively. The extent of the nonthermal tail is sensitive to the Alfvén Mach number; when MA≲10 , the nonthermal electron distribution exhibits minimal growth beyond the average momentum of the downstream thermal protons, independently of the proton-to-electron mass ratio. Acceleration is slow for shocks with low sonic Mach numbers, yet nonthermal electrons still achieve momenta exceeding the downstream thermal proton momentum when the shock Alfvén Mach number is large enough. We provide simulation-based parameterizations of the transition from thermal to nonthermal distribution in the downstream (found at a momentum around pi,e/mivsh≈3mi,e/mi ), as well as the ratio of nonthermal electron to proton number density. The results are applicable to many different environments and are important for modeling shock-powered nonthermal radiation.

Two types of filamentary currents (FCs) were observed inside a magnetic flux rope at the magnetopause by the Magnetospheric Multiscale mission. The first FC is identified as an electron vortex, while the other is a reconnecting current sheet. Stochastic electric fields were generated within the FCs, resulting in electron acceleration up to a few keV, similar to recent simulations of electron acceleration inside vortex, which is a second‐order Fermi acceleration. Furthermore, two FCs propagated at different speeds, causing compression in the region between them. Energetic electrons up to 200 keV were detected in the compressed region and displayed a double power‐law spectrum. Observations suggest that the electrons were mainly accelerated by betatron mechanism in the compressed region. The formation, evolution, and interaction of FCs provide a novel mechanism for electron acceleration. These results clearly show the significance of electron‐scale dynamics within flux rope.

Short large-amplitude magnetic structures (SLAMS) are frequently detected during spacecraft crossings over Earth's bow shock. We investigate the existence of such structures at astrophysical shocks, where they could result from the steepening of cosmic-ray (CR) driven waves. Using kinetic particle-in-cell simulations, we study the growth of SLAMS and the appearance of associated transient shocks in the upstream region of parallel, nonrelativistic, high-Mach-number collisionless shocks. We find that high-energy CRs significantly enhance the transverse magnetic field within SLAMS, producing highly inclined field lines. As SLAMS are advected toward the shock, these field lines form an intermittent superluminal configuration that traps magnetized electrons at fast shocks. Due to their oscillatory nature, SLAMS are periodically separated by subluminal gaps with lower transverse magnetic field strength. In these regions, electrons diffuse and accelerate by bouncing between the shock and the approaching SLAMS' region through a mechanism that we call quasi-periodic shock acceleration (QSA). We analytically derive the distribution of electrons accelerated via QSA, f(p) ∼ p[−4.7,−5.7], which agrees well with the simulation spectra. We find that the electron power law remains steep until the end of our longest runs, providing a possible explanation for the steep electron spectra observed at least up to GeV energies in young and fast supernova remnants.

Pulsar wind nebulae (PWNe) are clouds of the magnetized relativistic electron/positron plasma supplied from the central pulsar. However, the number of radio-emitting particles inside a PWN is larger than the expectation from the study of pulsar magnetospheres and then their origin is still unclear. A stochastic acceleration of externally injected particles by a turbulence inside the PWN is proposed by our previous studies. In this paper, the previous stochastic acceleration model of the PWN broadband spectra is improved by taking into account the time evolution of the turbulent energy and then the total energy balance inside a PWN is maintained. The turbulent energy supplied from the central pulsar is wasted by the backreaction from the stochastic particle acceleration and the adiabatic cooling according the PWN expansion. The model is applied to the Crab Nebula and reproduce the current broadband emission spectrum, especially the flat radio spectrum although time evolution of the turbulent energy (diffusion coefficient) is a bit complicated compared with our previous studies, where we assumed an exponential behavior of the diffusion coefficient.

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-energy spectral cutoff increases linearly with system size; both the slope and the cutoff do not depend on the dimensionality of our domain. By following a large sample of particles, we show that particle injection happens at reconnecting current sheets; the injected particles are then further accelerated by stochastic interactions with turbulent fluctuations. Our results have important implications for the origin of nonthermal particles in high-energy astrophysical sources.

No abstract available

Gamma-ray data from Fermi Large Area Telescope reveal a bilobular structure extending up to ∼50° above and below the Galactic Center. It has been argued that the gamma rays arise from hadronic interactions of high-energy cosmic rays which are advected out by a strong wind, or from inverse-Compton scattering of relativistic electrons accelerated at plasma shocks present in the bubbles. We explore the alternative possibility that the relativistic electrons are undergoing stochastic 2nd-order Fermi acceleration by plasma wave turbulence through the entire volume of the bubbles. The observed gamma-ray spectral shape is then explained naturally by the resulting hard electron spectrum modulated by inverse-Compton energy losses. Rather than a constant volume emissivity as in other models, we predict a nearly constant surface brightness, and reproduce the observed sharp edges of the bubbles.

No abstract available

No abstract available

Transient electron dynamics near the interface of counterstreaming plasmas at the onset of a relativistic collisionless shock (RCS) is investigated using particle-in-cell simulations. We identify a slingshotlike injection process induced by the drifting electric field sustained by the flowing focus of backward-moving electrons, which is distinct from the well-known stochastic acceleration. The flowing focus signifies the plasma kinetic transition from a preturbulent laminar motion to a chaotic turbulence. We find a characteristic correlation between the electron dynamics in the slingshot acceleration and the photon emission features. In particular, the integrated radiation from the RCS exhibits a counterintuitive nonmonotonic dependence of the photon polarization degree on the photon energy, which originates from a polarization degradation of relatively high-energy photons emitted by the slingshot-injected electrons. Our results demonstrate the potential of photon polarization as an essential information source in exploring intricate transient dynamics in RCSs with relevance for Earth-based plasma and astrophysical scenarios.

The efficiency of particle acceleration at shock waves in relativistic, magnetized astrophysical outflows is a debated topic with far-reaching implications. Here, for the first time, we study the impact of turbulence in the pre-shock plasma. Our simulations demonstrate that, for a mildly relativistic, magnetized pair shock (Lorentz factor $\gamma_{\rm sh} \simeq 2.7$, magnetization level $\sigma \simeq 0.01$), strong turbulence can revive particle acceleration in a superluminal configuration that otherwise prohibits it. Depending on the initial plasma temperature and magnetization, stochastic-shock-drift or diffusive-type acceleration governs particle energization, producing powerlaw spectra $\mathrm{d}N/\mathrm{d}\gamma \propto \gamma^{-s}$ with $s \sim 2.5-3.5$. At larger magnetization levels, stochastic acceleration within the pre-shock turbulence becomes competitive and can even take over shock acceleration.

Cosmic ray acceleration in galaxy clusters is still an ongoing puzzle, with relativistic electrons forming radio relics at merger shocks and emitting synchrotron radiation. These shocks are also potential sources of ultra-high-energy cosmic rays, gamma rays, and neutrinos. Our recent work focuses on electron acceleration at low Mach number merger shocks in the hot intracluster medium which is characterized by high plasma beta. Using particle-in-cell (PIC) simulations, we previously showed that electrons are energized through the stochastic shock-drift acceleration process, which is facilitated by multi-scale turbulence, including ion-scale shock surface rippling. For the present work, we performed hybrid-kinetic simulations in a range of various quasi-perpendicular foreshock conditions, including plasma beta, magnetic obliquity, and the shock Mach number. We study the ion kinetic physics, which is responsible for the shock structure and wave turbulence, that in turn affects the particle acceleration processes. We cover the spatial and temporal scales, which allow the development of large-scale ion turbulence modes in the system. We applied a recently developed generalized fluid-particle hybrid numerical code that can combine fluid modeling for both electrons and ions with an arbitrary number of kinetic species. We limited this model to a standard hybrid simulation configuration with kinetic ions and fluid electrons. The model utilizes the exact form of the generalized Ohm's law, allowing for an arbitrary choice of mass and energy densities, as well as the charge-to-mass ratio of the kinetic species. We show that the properties of ion-driven multi-scale magnetic turbulence in merger shocks are in agreement with the ion structures observed in PIC simulations. In typical shocks with the sonic Mach number $M_s=3$, the magnetic structures and shock front density ripples grow and saturate at wavelengths reaching approximately four ion Larmor radii. Only shocks with $M_s 2.3$ develop ripples. At very weak shocks with $M_s 2.3$, weak turbulence is formed downstream of the shock. We observed a moderate dependence of the strength of magnetic field fluctuations on the quasi-perpendicular magnetic field obliquity. However, as the field obliquity decreases, the shock front ripples exhibit longer wavelengths. Finally, we note that the steady-state structure of $M_s=3$ shocks in high-beta plasmas shows evidence that there is little difference between 2D and 3D simulations. The turbulence near the shock front seems to be a 2D-like structure in 3D simulations.

No abstract available

The physics of particle acceleration in turbulent plasmas is a topic of broad interest, which is making rapid progress thanks to dedicated, large-scale numerical experiments. The first part of this paper presents an effective theory of stochastic Fermi acceleration, which subsumes all forms of nonresonant acceleration in ideal electric fields and is applicable in generic settings. It combines an exact equation connecting the energization rate to the statistics of the velocity field with a statistical model of particle transport through the structures (i.e., the regions of strong velocity gradients). In a second part, this formalism is applied to magnetohydrodynamic turbulence to obtain a comprehensive assessment of the scale-by-scale contributions to the advection and diffusion coefficients. Acceleration peaks on scales where particles can be trapped inside structures for an eddy turnaround time, or in intense structures associated with sharp bends of the magnetic field lines in large-amplitude turbulence (as reported earlier). These spatially inhomogeneous, rapid acceleration regimes pave the way for a rich phenomenology. We discuss the scalings obtained, their interpretation, and we show that the findings compare satisfactorily with existing numerical results.

No abstract available

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

We investigate the electron acceleration dynamics in spatially stochastic wave fields. For a bounded system, the spectra (frequency and wave number) of the stochastic wave fields are discrete so that they can form spatiotemporal “singular” structures once their phases are in synchronization. As a consequence, the electrons will experience significant scattering by these singular structures, which is an in-phase effect of an ensemble of non-resonant wave–particle interactions. In the presence of parallel symmetry breaking, it is found that the governing Fokker–Planck equation has a structure similar to that of the resonant wave–particle interaction but with a broader parameter regime in the velocity/energy space of the electron distribution function.

Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter this turbulence are typically accelerated according to the so-called second-order Fermi process. However, in most astrophysical environments there are additional competing processes, such as different kinds of first-order energy changes and particle escape, that affect the resulting momentum distribution of the particles. In this work we provide to our knowledge the first semianalytical solution of the isotropic steady-state momentum diffusion equation including continuous and catastrophic momentum changes that can be applied to any astrophysical system of interest that is under the influence of weak magnetic turbulence. Here, we adopt that the assigned magnetic turbulence is constrained to a finite range and the particle flux vanishes beyond these boundaries. Consequently, we show that the so-called pile-up bump—which has long been established for some special cases—is a universal feature of stochastic acceleration that emerges around the momentum χeq where acceleration and continuous loss are in equilibrium if the particle’s residence time in the system is sufficient at χeq. In general, the impact of continuous and catastrophic momentum changes plays a crucial role in the shape of the steady-state momentum distribution of the accelerated particles, where simplified unbroken power-law approximations are often not adequate.

Turbulent, relativistic nonthermal plasmas are ubiquitous in high-energy astrophysical systems, as inferred from broadband nonthermal emission spectra. The underlying turbulent nonthermal particle acceleration (NTPA) processes have traditionally been modelled with a Fokker-Planck (FP) diffusion-advection equation for the particle energy distribution. We test FP-type NTPA theories by performing and analysing particle-in-cell (PIC) simulations of turbulence in collisionless relativistic pair plasma. By tracking large numbers of particles in simulations with different initial magnetisation and system size, we first test and confirm the applicability of the FP framework. We then measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy γmc2, and compare their dependence to theoretical predictions. At high-energies, we robustly find D ∼ γ2 for all cases. Hence, we fit D = D0γ2 and find a scaling consistent with D0 ∼ σ3/2 at low instantaneous magnetisation σ(t), flattening to D0 ∼ σ at higher σ ∼ 1. We also find that the power-law index α(t) of the particle energy distribution converges exponentially in time. We build and test an analytic model connecting the FP coefficients and α(t), predicting A(γ) ∼ γlog γ. We confirm this functional form in our measurements of A(γ, t), which allows us to predict α(t) through the model relations. Our results suggest that the basic second-order Fermi acceleration model, which predicts D0 ∼ σ, may not be a complete description of NTPA in turbulent plasmas. These findings encourage further application of tracked particles and FP coefficients as a diagnostic in kinetic simulations of various astrophysically relevant plasma processes like collisionless shocks and magnetic reconnection.

Extreme TeV BL Lacs are a class of blazars with unique spectral and temporal features that are not easily reproducible using standard one-zone models based on single shock acceleration. To account for their peculiar properties, we elaborated a two-step acceleration model in which a recollimation shock and the subsequent downstream turbulence energize non-thermal electrons. We applied the model to a sample of extreme TeV BL Lacs with well-characterized spectral energy distributions. Since we used several sources, we automatized the exploration of the parameter space. This allowed us to derive the parameter distributions and study the correlations among them. We numerically solved a system of two coupled nonlinear differential equations to obtain the non-thermal particles and turbulence spectra. We calculated the spectral energy distribution via the synchrotron self-Compton emission model. The automatization of the parameter space exploration is possible through a Markov chain Monte Carlo (MCMC) ensemble sampler, in our case emcee We derived well-defined posterior distributions for the parameters, showing that the model is well constrained by available data and demonstrating the suitability of our method. The cross-correlations among some of the physical parameters are not trivial.\ Therefore, we conclude that MCMC sampling is a key instrument for characterizing the complexity of our multiparameter phenomenological model.

Turbulence is one of the products of the magnetic-reconnection process in the solar-flare plasma. It intensely shifts the dynamics of the magnetic-reconnection process and rapidly transfers energy that facilitates plasma heating by over 10 MK and particle energization. In this study, using the results of a Monte Carlo experiment through the Euler–Maruyama approximation of stochastic Lagrangian models for inhomogeneous hydrodynamic turbulence, we present the velocity and dissipation (relaxation rate) characteristics of stochastic motions of particles (particles obeying a Gaussian distribution) in the turbulence of the solar-flare plasma. A Monte Carlo experiment was performed for a turbulent kinetic energy of 1030 erg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{30}\text{ erg}$\end{document}, on a time scale of ten seconds and a length scale of the order of the full loop half-length [1010 cm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{10}\text{ cm}$\end{document}] of the solar flare. The results of the velocity and dissipation (relaxation rate) are presented and analyzed in both one and two dimensions. We observed that the positive value of relaxation rate of (1–8)×10−4 s−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(1\,\text{--}\,8) \times 10^{-4}\text{ s}^{-1} $\end{document} for ≈ five seconds of dispersion time could lead to energy transfer and dissipation of the energy in the turbulence of the solar flare. The Monte Carlo mean relaxation rate of 4.5×10−4 s−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$4.5 \times 10^{-4}\text{ s}^{-1}$\end{document} shows that it dissipates ≈4.5×1027 erg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\approx 4.5 \times 10^{27}\text{ erg}$\end{document} energy into thermal energy in ten seconds, which is equal to ≈ 0.5% of the total injected kinetic energy. Velocities of the stochastic particles in the turbulence show the random fluctuations, which are unsteadily dispersive in nature. The range and mean values of particle velocities are ≈(0.5–3)×106 cms−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\approx (0.5\,\text{--}\,3) \times 10^{6}\text{ cm}\,\text{s}^{-1} $\end{document} and 1.5×106 cms−1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1.5 \times 10^{6}\text{ cm}\,\text{s}^{-1} $\end{document}, respectively, which indicates low-atmospheric turbulence (chromosphere) in the solar flare. The results obtained are in agreement with observations. Our analysis thus demonstrates that the turbulence in the solar flare dissipates ≈ 0.5% of the injected energy into thermal energy and low-atmospheric turbulence (chromosphere) in the solar flare. We surmise that the rest of the turbulent kinetic energy goes to the non-thermal particle energization (particle acceleration), generation of the termination shock, and other dynamical processes in the solar flare.

Nature's most powerful high-energy sources are capable of accelerating particles to high energy and radiating 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∼1) within a few eddy turnover times. Low pitch-angle particles can significantly exceed the nominal radiation-reaction limit, before abruptly cooling down. The particle spectrum becomes even harder (p<1) over time owing to particle cooling with an energy-dependent pitch-angle anisotropy. The resulting synchrotron spectrum is hard (νF_{ν}∝ν^{s} with s∼1). Our findings have important implications for understanding the nonthermal emission from high-energy astrophysical sources, most notably the prompt phase of gamma-ray bursts and gamma-ray flares from the Crab nebula.

No abstract available

We employ first-principles, fully kinetic particle-in-cell simulations to investigate magnetic field-line curvature in magnetically dominated turbulent plasmas and its role in particle acceleration through curvature-drift motion along the motional electric field. By varying the fluctuation-to-mean-magnetic-field ratio δB0/B0, we examine curvature κ statistics and their connection to particle acceleration. The curvature probability densities display broad power-law wings, scaling linearly in κ below the peak and developing hard high-κ tails for δB0/B0 ≳ 1. As the mean field strengthens, the high-κ tails steepen, and large-curvature events are suppressed when δB0/B0 ≪ 1. The probability density functions of magnetic field-line contraction, vE · κ, with vE the field-line velocity, develop power-law tails well described by a symmetric Pareto distribution, characteristic of stochastic and intermittent energy exchanges, with the tails becoming harder as δB0/B0 increases. Our guiding-center analysis shows that curvature-drift acceleration accounts for a substantial fraction of the energization via the motional electric field, and that it strengthens with increasing δB0/B0. For well-magnetized particles, curvature-drift acceleration typically exceeds ∇B drift, polarization drift, and betatron contributions. These results identify curvature-drift acceleration as a principal pathway through which magnetized turbulence transfers energy to nonthermal particles in astrophysical plasmas.

No abstract available

Alfvénic turbulence is an effective mechanism for particle acceleration in strongly magnetized, relativistic plasma. In this study, we investigate a scenario where turbulent plasma is influenced by a strong guide magnetic field, resulting in highly anisotropic turbulent fluctuations. In such cases, the magnetic moments of particles are conserved, which means that acceleration can only occur along the direction of the magnetic field. Consistent with previous analytic studies, we find through particle-in-cell simulations of magnetically dominated pair plasma that the momenta of accelerated particles are closely aligned with the magnetic field lines. Notably, the alignment angle decreases as particle energy increases, potentially limited only by the inherent curvature and gradients of the turbulent magnetic fluctuations. This finding has significant implications for interpreting the synchrotron radiation emitted by highly accelerated particles.

Over three thousand pulsars have been discovered, but none have been confirmed to be younger than a few hundred years. Observing a pulsar after a supernova explosion will help us understand the properties of newborn ones, including their capability to produce gamma-ray bursts and fast radio bursts. Here, the possible youngest pulsar wind nebula (PWN) at the center of the SN 1986J remnant is studied. We demonstrate that the 5 GHz flux of ‘PWN 1986J’, increasing with time, is consistent with a stochastic acceleration model of PWNe developed to explain the flat radio spectrum of the Crab Nebula. We obtain an acceleration time-scale of electrons/positrons and a decay time-scale of the turbulence responsible for the stochastic acceleration as about 10 and 70 years, respectively. Our findings suggest that efficient stochastic acceleration and rising radio/submm light curves are characteristic signatures of the youngest PWNe. Follow-up ALMA observations of decades-old supernovae within a few tens of Mpc, including SN 1986J, are encouraged to reveal the origin of the flat radio spectrum of PWNe.

The excess broadening of high-temperature spectral lines, long observed near the tops of flare arcades, is widely considered to result from magnetohydrodynamic turbulence. According to different theories, plasma turbulence is also believed to be a candidate mechanism for particle acceleration during solar flares. However, the degree to which this broadening is connected to the acceleration of nonthermal electrons remains largely unexplored outside of recent work, and many observations have been limited by limited spatial resolution and cadence. Using the Interface Region Imaging Spectrometer, we present spatially resolved observations of loop-top (LT) broadenings using hot (≈11 MK) Fe xxi 1354.1 Å line emission at ≈9 s cadence during the 2022 March 30 X1.3 flare. We find nonthermal velocities upward of 65 km s−1 that decay linearly with time, indicating the presence and subsequent dissipation of plasma turbulence. Moreover, the initial Fe xxi signal was found to be cospatial and cotemporal with microwave emission measured by the Expanded Owens Valley Solar Array, placing a population of nonthermal electrons in the same region as the LT turbulence. Evidence of electron acceleration at this time is further supported by hard X-ray measurements from the Spectrometer/Telescope for Imaging X-rays on board Solar Orbiter. Using the decay of nonthermal broadenings as a proxy for turbulent dissipation, we found the rate of energy dissipation to be consistent with the power of nonthermal electrons deposited into the chromosphere, suggesting a possible connection between turbulence and electron acceleration.

We present 3D fully kinetic shearing-box simulations of pair-plasma magnetorotational turbulence with unprecedented macro-to-microscopic scale separation. While retrieving the expected fluid behavior of the plasma at large scales, we observe a steepening of turbulent spectra at kinetic scales and substantial angular-momentum transport linked with kinetic processes. For the first time, we provide a definitive demonstration of nonthermal particle acceleration in kinetic magnetorotational turbulence agnostically of shearing-box initial conditions by means of a novel strategy exploiting synchrotron cooling.

Strong magnetically dominated Alfvénic turbulence is an efficient engine of nonthermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations δ B 0 and the guide field B 0. If δ B 0 ≪ B 0, the particle magnetic moments are conserved, and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in log-normal tails of particle energy distribution functions. Conversely, if δ B 0 ≳ B 0, interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to power-law tails of the energy distribution functions.

High‐charge beams remain a key research focus in laser plasma acceleration, driven by the demands of extreme experimental conditions in nuclear physics, laboratory astrophysics, and fusion research. A distinct acceleration mechanism is presented in which the interaction between petawatt femtosecond laser pulses and the subcritical density (SCD) plasma produces electron beams with charges of hundreds of nanocoulomb (nC), far exceeding those typically achieved via conventional laser wakefield acceleration. The synergy between the multiwakefield structure in SCD plasma and the laser self‐steepening effect significantly enhances the electron injection rate to 100 nC ps−1, experimentally achieving the electron beam charge up to 245 nC. This mechanism operates by reducing the phase velocity of plasma waves and increasing electron momentum, allowing large numbers of electrons to exceed the wave‐breaking threshold and undergo efficient injection. Experiments and simulations consistently confirm the dependence of charge on plasma density and laser energy, with charge reaching a maximum at a specific plasma density. Such high‐charge, high‐density electron beams offer promising applications in high‐flux particle beam physics, large‐field‐of‐view industrial imaging, advanced light sources, and radiation‐hardness testing of electronic systems.

Collisionless shock waves have long been considered to be among the most prolific particle accelerators in the universe. Shocks alter the plasma they propagate through, and often exhibit complex evolution across multiple scales. Interplanetary (IP) traveling shocks have been recorded in situ for over half a century and act as a natural laboratory for experimentally verifying various aspects of large-scale collisionless shocks. A fundamentally interesting problem in both heliophysics and astrophysics is the acceleration of electrons to relativistic energies ($> 300$ keV) by traveling shocks. The reason for an incomplete understanding of electron acceleration at IP shocks is due to scale-related challenges and a lack of instrumental capabilities. This letter presents the first observations of field-aligned beams of relativistic electrons upstream of an IP shock, observed thanks to the instrumental capabilities of Solar Orbiter. This study presents the characteristics of the electron beams close to the source and contributes to the understanding of their acceleration mechanism. On 25 July 2022, Solar Orbiter encountered an IP shock at 0.98 AU. The shock was associated with an energetic storm particle event, which also featured upstream field-aligned relativistic electron beams observed 14 minutes prior to the actual shock crossing. The distance of the beam's origin was investigated using a velocity dispersion analysis (VDA). Peak-intensity energy spectra were anaylzed and compared with those obtained from a semi-analytical fast-Fermi acceleration model. By leveraging Solar Orbiter's high temporal resolution Energetic Particle Detector (EPD), we successfully showcase an IP shock's ability to accelerate relativistic electron beams. Our proposed acceleration mechanism offers an explanation for the observed electron beam and its characteristics, while we also explore the potential contributions of more complex mechanisms.

Collisionless shocks are pervasive in astrophysics and they are critical to understand cosmic ray acceleration. Laboratory experiments with intense lasers are now opening the way to explore and characterise the underlying microphysics, which determine the acceleration process of collisionless shocks. We determine the shock character – electrostatic or electromagnetic – based on the stability of electrostatic shocks to transverse electromagnetic fluctuations as a function of the electron temperature and flow velocity of the plasma components and we compare the analytical model with particle-in-cell simulations. By making the connection with the laser parameters driving the plasma flows, we demonstrate that shocks with different and distinct underlying microphysics can be explored in the laboratory with state-of-the-art laser systems.

The spatio-temporal and polarisation properties of intense light is important in wide-ranging topics at the forefront of extreme light-matter interactions, including ultrafast laser-driven particle acceleration, attosecond pulse generation, plasma photonics, high-field physics and laboratory astrophysics. Here, we experimentally demonstrate modifications to the polarisation and temporal properties of intense light measured at the rear of an ultrathin target foil irradiated by a relativistically intense laser pulse. The changes are shown to result from a superposition of coherent radiation, generated by a directly accelerated bipolar electron distribution, and the light transmitted due to the onset of relativistic self-induced transparency. Simulations show that the generated light has a high-order transverse electromagnetic mode structure in both the first and second laser harmonics that can evolve on intra-pulse time-scales. The mode structure and polarisation state vary with the interaction parameters, opening up the possibility of developing this approach to achieve dynamic control of structured light fields at ultrahigh intensities.

No abstract available

While the aurora has attracted attention for millennia, important questions remain unanswered. Foremost is how auroral electrons are accelerated before colliding with the ionosphere and producing auroral light. Powerful Alfvén waves are often found traveling Earthward above auroras with sufficient energy to generate auroras, but there has been no direct measurement of the processes by which Alfvén waves transfer their energy to auroral electrons. Here, we show laboratory measurements of the resonant transfer of energy from Alfvén waves to electrons under conditions relevant to the auroral zone. Experiments are performed by launching Alfvén waves and simultaneously recording the electron velocity distribution. Numerical simulations and analytical theory support that the measured energy transfer process produces accelerated electrons capable of reaching auroral energies. The experiments, theory, and simulations demonstrate a clear causal relationship between Alfvén waves and accelerated electrons that directly cause auroras. It was predicted that Alfvén waves can account for the acceleration of precipitating auroral electrons. Here, the authors show laboratory measurements of the resonant transfer of energy from Alfvén waves to electrons under conditions relevant to the auroral zone as a direct test.

No abstract available

Plasma wakefield acceleration represented a breakthrough in the field of particle accelerators by pushing beams to gigaelectronvolt energies within centimeter distances. The large electric fields excited by a driver pulse in the plasma can efficiently accelerate a trailing witness bunch paving the way toward the realization of laboratory-scale applications like free-electron lasers. However, while the accelerator size is tremendously reduced, upstream and downstream of it the beams are still handled with conventional magnetic optics with sizable footprints and rather long focal lengths. Here we show the operation of a compact device that integrates two active-plasma lenses with short focal lengths to assist the plasma accelerator stage. We demonstrate the focusing and energy gain of a witness bunch whose phase space is completely characterized in terms of energy and emittance. These results represent an important step toward the accelerator miniaturization and the development of next-generation table-top machines.

Collisionless shock waves, found in supernova remnants, interstellar, stellar, and planetary environments, and laboratories, are one of nature’s most powerful particle accelerators. This study combines in situ satellite measurements with recent theoretical developments to establish a reinforced shock acceleration model for relativistic electrons. Our model incorporates transient structures, wave-particle interactions, and variable stellar wind conditions, operating collectively in a multiscale set of processes. We show that the electron injection threshold is on the order of suprathermal range, obtainable through multiple different phenomena abundant in various plasma environments. Our analysis demonstrates that a typical shock can consistently accelerate electrons into very high (relativistic) energy ranges, refining our comprehension of shock acceleration while providing insight on the origin of electron cosmic rays. The mechanisms resulting in particle acceleration to relativistic energies in space plasmas are an open question. Here, the authors show a reinforced shock acceleration model which enables electrons to efficiently achieve relativistic energies and reveal a low electron injection threshold.

The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters.

No abstract available

We propose an efficient scheme to produce ultrahigh-brightness tens of MeV electron beams by designing a density-tailored plasma to induce a wakefield in the weakly nonlinear regime with a moderate laser energy of 120 mJ. In this scheme, the second bucket of the wakefield can have a much lower phase velocity at the steep plasma density down-ramp than the first bucket and can be exploited to implement longitudinal electron injection at a lower laser intensity, leading to the generation of bright electron beams with ultralow emittance together with low energy spread. Three-dimensional particle-in-cell simulations are carried out and demonstrate that high-quality electron beams with a peak energy of 50 MeV, ultralow emittance of ∼28 nm rad, energy spread of 1%, charge of 4.4 pC, and short duration less than 5 fs can be obtained within a 1-mm-long tailored plasma density, resulting in an ultrahigh six-dimensional brightness B6D,n of ∼2 × 1017 A/m2/0.1%. By changing the density parameters, tunable bright electron beams with peak energies ranging from 5 to 70 MeV, a small emittance of ≤0.1 mm mrad, and a low energy spread at a few-percent level can be obtained. These bright MeV-class electron beams have a variety of potential applications, for example, as ultrafast electron probes for diffraction and imaging, in laboratory astrophysics, in coherent radiation source generation, and as injectors for GeV particle accelerators.

The propagation of a relativistic electron-positron beam in a magnetized electron-ion plasma is studied, focusing on the polarization of the radiation generated in this case. Special emphasis is laid on investigating the polarization of the generated radiation for a range of beam-plasma parameters, transverse and longitudinal beam sizes, and the external magnetic fields. Our results not only help in understanding the high degrees of circular polarization observed in gamma-ray bursts, but they also help in distinguishing the different modes associated with the filamentation dynamics of the pair beam in laboratory astrophysics experiments.

The acceleration of electrons near three-dimensional (3D) magnetic nulls is crucial to the energy conversion mechanism in the 3D magnetic reconnection process. To explore electron acceleration in a 3D magnetic null topology, we constructed a pair of 3D magnetic nulls in the PKU Plasma Test (PPT) device and observed acceleration of electrons near magnetic nulls. This study measured the plasma floating potential and ion density profiles around the 3D magnetic null. The potential wells near nulls may be related to the energy variations of electrons, so we measured the electron distribution functions (EDFs) at different spatial positions. The axial variation of EDF shows that the electrons deviate from the Maxwell distribution near magnetic nulls. With scanning probes that can directionally measure and theoretically analyze based on curve fitting, the variations of EDFs are linked to the changes of plasma potential under 3D magnetic null topology. The kinetic energy of electrons accelerated by the electric field is 6 eV ( ) and the scale of the region where accelerating electrons exist is in the order of serval electron skin depths.

Low-density meter-scale plasma waveguides produced in meter-scale supersonic gas jets have paved the way for recent demonstrations of all-optical multi-gigaelectronvolt laser wakefield acceleration (LWFA). This paper reviews recent advances by the University of Maryland, which have enabled these results, focusing on the development of elongated supersonic gas jets up to ∼1 m in length, experimental and simulation studies of plasma waveguide formation, and a new three-stage model for relativistic pulse propagation dynamics in these waveguides. We also present results from recent LWFA experiments conducted at the Laboratory for Advanced Lasers and Extreme Photonics at Colorado State University demonstrating high charge, low divergence electron bunches to ∼10 GeV, with laser-to-electron beam efficiency of at least ∼30%.

The smallest characteristic scales, at which electron dynamics determines the plasma behaviour, are the next frontier in space and astrophysical plasma research. The analysis of astrophysical processes at these scales lies at the heart of the research theme of electron-astrophysics. Electron scales are the ultimate bottleneck for dissipation of plasma turbulence, which is a fundamental process not understood in the electron-kinetic regime. In addition, plasma electrons often play an important role for the spatial transfer of thermal energy due to the high heat flux associated with their velocity distribution. The regulation of this electron heat flux is likewise not understood. By focussing on these and other fundamental electron processes, the research theme of electron-astrophysics links outstanding science questions of great importance to the fields of space physics, astrophysics, and laboratory plasma physics. In this White Paper, submitted to ESA in response to the Voyage 2050 call, we review a selection of these outstanding questions, discuss their importance, and present a roadmap for answering them through novel space-mission concepts.

In this Letter, we report on the experimental generation of high energy (10 GeV), ultrashort (femtosecond-duration), ultrahigh current (∼0.1  MA), petawatt peak power electron beams in a particle accelerator. These extreme beams enable the exploration of a new frontier of high-intensity beam-light and beam-matter interactions broadly relevant across fields ranging from laboratory astrophysics to strong field quantum electrodynamics and ultrafast quantum chemistry. We demonstrate our ability to generate and control the properties of these electron beams by means of a laser-electron beam shaping technique. This experimental demonstration opens the door to on-the-fly customization of extreme beam current profiles for desired experiments and is poised to benefit a broad swath of cross-cutting applications of relativistic electron beams.

No abstract available

Here is reported in situ observation of energetic electrons (~100-500 keV) associated with magnetic reconnection in the solar wind by the ACE and Wind spacecraft. The properties of this magnetic cloud driving reconnection and the associated energetic electron acceleration problem are discussed. Further analyses indicate that the electric field acceleration and Fermi type mechanism are two fundamental elements in the electron acceleration processes and the trapping effect of the specific magnetic field configuration maintains the acceleration status that increases the totally gained energy.

The kinetic features of plasmoid chain formation and evolution are investigated by two dimensional Particle-in-Cell simulations. Magnetic reconnection is initiated in multiple X points by the tearing instability. Plasmoids form and grow in size by continuously coalescing. Each chain plasmoid exhibits a strong out-of plane core magnetic field and an out-of-plane electron current that drives the coalescing process. The disappearance of the X points in the coalescence process are due to anti-reconnection, a magnetic reconnection where the plasma inflow and outflow are reversed with respect to the original reconnection flow pattern. Anti-reconnection is characterized by the Hall magnetic field quadrupole signature. Two new kinetic features, not reported by previous studies of plasmoid chain evolution, are here revealed. First, intense electric fields develop in-plane normally to the separatrices and drive the ion dynamics in the plasmoids. Second, several bipolar electric field structures are localized in proximity of the plasmoid chain. The analysis of the electron distribution function and phase space reveals the presence of counter-streaming electron beams, unstable to the two stream instability, and phase space electron holes along the reconnection separatrices.

Magnetic reconnection is a basic plasma process of dramatic rearrangement of magnetic topology, often leading to a violent release of magnetic energy. It is important in magnetic fusion and in space and solar physics --- areas that have so far provided the context for most of reconnection research. Importantly, these environments consist just of electrons and ions and the dissipated energy always stays with the plasma. In contrast, in this paper I introduce a new direction of research, motivated by several important problems in high-energy astrophysics --- reconnection in high energy density (HED) radiative plasmas, where radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. I identify the key processes distinguishing HED reconnection: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and Compton resistivity); and, at the most extreme end, QED effects, including pair creation. I then discuss the main astrophysical applications --- situations with magnetar-strength fields (exceeding the quantum critical field of about 4 x 10^13 G): giant SGR flares and magnetically-powered central engines and jets of GRBs. Here, magnetic energy density is so high that its dissipation heats the plasma to MeV temperatures. Electron-positron pairs are then copiously produced, making the reconnection layer highly collisional and dressing it in a thick pair coat that traps radiation. The pressure is dominated by radiation and pairs. Yet, radiation diffusion across the layer may be faster than the global Alfvén transit time; then, radiative cooling governs the thermodynamics and reconnection becomes a radiative transfer problem, greatly affected by the ultra-strong magnetic field. This overall picture is very different from our traditional picture of reconnection and thus represents a new frontier in reconnection research.

The Magnetic cloud boundary layer (BL) is a dynamic region formed by the interaction of the magnetic cloud (MC) and the ambient solar wind. In the present study, we comparatively investigate the proton and electron mean flux variations in the BL, in the interplanetary reconnection exhaust (RE) and across the MC-driven shock by using the Wind 3DP and MFI data from 1995 to 2006. In general, the proton flux has higher increments at lower energy bands compared with the ambient solar wind. Inside the BL, the core electron flux increases quasi-isotropically and the increments decrease monotonously with energy from ~30% (at 18 eV) to ~10% (at 70 eV); the suprathermal electron flux usually increases in either parallel or antiparallel direction; the correlation coefficient of electron flux variations in parallel and antiparallel directions changes sharply from ~0.8 below 70 eV to ~0 above 70 eV. Similar results are also found for RE. However, different phenomena are found across the shock where the electron flux variations first increase and then decrease with a peak increment (>200%) near 100 eV. The correlation coefficient of electron flux variations in parallel and antiparallel directions is always around 0.8. The similar behavior of flux variations in BL and RE suggests that reconnection may commonly occur in BL. Our work also implies that the strong energy dependence and direction selectivity of electron flux variations, which are previously thought to have no enough relevance to magnetic reconnection, could be considered as an important signature of solar wind reconnection in the statistical point of view.

By means of fully kinetic simulations, we investigate electron acceleration during magnetic reconnection in a nonrelativistic proton--electron plasma with conditions similar to solar corona and flares. We demonstrate that reconnection leads to a nonthermally dominated electron acceleration with a power-law energy distribution in the nonrelativistic low-$β$ regime but not in the high-$β$ regime, where $β$ is the ratio of the plasma thermal pressure and the magnetic pressure. The accelerated electrons contain most of the dissipated magnetic energy in the low-$β$ regime. A guiding-center current description is used to reveal the role of electron drift motions during the bulk nonthermal energization. We find that the main acceleration mechanism is a \textit{Fermi}-type acceleration accomplished by the particle curvature drift motion along the electric field induced by the reconnection outflows. Although the acceleration mechanism is similar for different plasma $β$, low-$β$ reconnection drives fast acceleration on Alfvénic timescales and develops power laws out of thermal distribution. The nonthermally dominated acceleration resulting from magnetic reconnection in low-$β$ plasma may have strong implications for the highly efficient electron acceleration in solar flares and other astrophysical systems.

Recent space based observations of the Sun revealed that magnetic reconnection is ubiquitous in the solar atmosphere, ranging from small scale reconnection (observed as nanoflares) to large scale one (observed as long duration flares or giant arcades). Often the magnetic reconnection events are associated with mass ejections or jets, which seem to be closely related to multiple plasmoid ejections from fractal current sheet. The bursty radio and hard X-ray emissions from flares also suggest the fractal reconnection and associated particle acceleration. We shall discuss recent observations and theories related to the plasmoid-induced-reconnection and the fractal reconnection in solar flares, and their implication to reconnection physics and particle acceleration. Recent findings of many superflares on solar type stars that has extended the applicability of the fractal reconnection model of solar flares to much a wider parameter space suitable for stellar flares are also discussed.

We discuss that energetic electrons are generated near the X-type magnetic reconnection region due to a surfing acceleration mechanism. In a thin plasma sheet, the polarization electric fields pointing towards the neutral sheet are induced around the boundary between the lobe and plasma sheet in association with the Hall electric current. By using a particle-in-cell simulation, we demonstrate that the polarization electric fields are strongly enhanced in an externally driven reconnection system, and some electrons can be trapped by the electrostatic potential well of the polarization field. During the trapping phase, the electrons can gain their energies from the convection/inductive reconnection electric fields. We discuss that relativistic electrons with MeV energies are quickly generated in and around the X-type neutral region by utilizing the surfing acceleration.

We report a newly found two-stage mechanism of electron acceleration near X-lines of 3D collisionless guide-field magnetic reconnection in the non-relativistic regime typical, e.g., for stellar coronae. We found that after electrons are first pre-accelerated during the linear growth of reconnection, they become additionally accelerated in the course of the nonlinear stage of 3D guide-field magnetic reconnection. This additional acceleration is due to the filamentation of electric and magnetic fields caused by streaming instabilities. In addition to enhanced parallel electric fields, the filamentation leads to additional curvature-driven electron acceleration in the guide-field direction. As a result, part of the the accelerated electron spectra becomes a power law with a spectral index of $\sim-1.6$ near the X-line. This second stage of acceleration due to nonlinear reconnection is relevant for the production of energetic electrons in, e.g., thin current sheets of stellar coronae.

The interactions between magnetic islands are considered to play an important role in electron acceleration during magnetic reconnection. In this paper, two-dimensional (2-D) particle-in-cell (PIC) simulations are performed to study electron acceleration during multiple X line reconnection with a guide field. The electrons remain almost magnetized, and we can then analyze the contributions of the parallel electric field, Fermi and betatron mechanisms to electron acceleration during the evolution of magnetic reconnection by comparing with a guide-center theory. The results show that with the proceeding of magnetic reconnection, two magnetic islands are formed in the simulation domain. The electrons are accelerated by both the parallel electric field in the vicinity of the X lines and Fermi mechanism due to the contraction of the two magnetic islands. Then the two magnetic islands begin to merge into one, and in such a process electrons can be accelerated by the parallel electric field and betatron mechanisms. During the betatron acceleration, the electrons are locally accelerated in the regions where the magnetic field is piled up by the high-speed flow from the X line. At last, when the coalescence of the two islands into a big one finishes, electrons can further be accelerated by the Fermi mechanism because of the contraction of the big island. With the increase of the guide field, the contributions of Fermi and betatron mechanisms to electron acceleration become less and less important. When the guide field is sufficiently large, the contributions of Fermi and betatron mechanisms are almost negligible.

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.

Non-thermal electron acceleration via magnetic reconnection is thought to play an important role in powering the variable X-ray emission from radiatively inefficient accretion flows around black holes. The trans-relativistic regime of magnetic reconnection, where the magnetization $σ$, defined as the ratio of magnetic energy density to enthalpy density, is $\sim 1$, is frequently encountered in such flows. By means of a large suite of two-dimensional particle-in-cell simulations, we investigate electron and proton acceleration in the trans-relativistic regime. We focus on the dependence of the electron energy spectrum on $σ$ and the proton $β$ (i.e., the ratio of proton thermal pressure to magnetic pressure). We find that the electron spectrum in the reconnection region is non-thermal and can be generally modeled as a power law. At $β\lesssim 3 \times 10^{-3}$, the slope, $p$, is independent of $β$ and it hardens with increasing $σ$ as $p\simeq 1.8 +0.7/\sqrtσ$. Electrons are primarily accelerated by the non-ideal electric field at X-points, either in the initial current layer or in current sheets generated in between merging magnetic islands. At higher values of $β$, the electron power law steepens for all values of $σ$. At values of $β$ near $β_{\rm max}\approx1/4σ$, when both electrons and protons are relativistically hot prior to reconnection, the spectra of both species display an additional component at high energies, containing a few percent of particles. These particles are accelerated via a Fermi-like process by bouncing in between the reconnection outflow and a stationary magnetic island. We provide an empirical prescription for the dependence of the power-law slope and the acceleration efficiency on $β$ and $σ$, which can be used in global simulations of collisionless accretion disks.

Both analytical and numerical works show that magnetic reconnection must occur in hot accretion flows. This process will effectively heat and accelerate electrons. In this paper we use the numerical hybrid simulation of magnetic reconnection plus test-electron method to investigate the electron acceleration and heating due to magnetic reconnection in hot accretion flows. We consider fiducial values of density, temperature, and magnetic parameter $β_e$ (defined as the ratio of the electron pressure to the magnetic pressure) of the accretion flow as $n_{0} \sim 10^{6} {\rm cm^{-3}}$, $T_{e}^0\sim 2\times 10^9 {\rm K}$, and $β_e=1$. We find that electrons are heated to a higher temperature $T_{e}=5\times 10^9$K, and a fraction $η\sim 8%$ of electrons are accelerated into a broken power-law distribution, $dN(γ)\propto γ^{-p}$, with $p\approx 1.5$ and 4 below and above $\sim 1$ MeV, respectively. We also investigate the effect of varying $β$ and $n_0$. We find that when $β_e$ is smaller or $n_0$ is larger, i.e, the magnetic field is stronger, $T_e$, $η$, and $p$ all become larger.

One of the key unresolved problems in the study of space plasmas is to explain the production of energetic electrons as magnetic field lines `reconnect' and release energy in a exposive manner. Recent observations suggest possible roles played by small scale magnetic islands in the reconnection region, but their precise roles and the exact mechanism of electron energization have remained unclear. Here we show that secondary islands generated in the reconnection region are indeed efficient electron accelerators. We found that, when electrons are trapped inside the islands, they are energized continuously by the reconnection electric field prevalent in the reconnection diffusion region. The size and the propagation speed of the secondary islands are similar to those of islands observed in the magnetotail containing energertic electrons.

In space and astrophysical plasmas, like in planetary magnetospheres, as that of Mercury,energetic electrons are often found near current sheets (CSs), which hints at electron acceleration by magnetic reconnection. Unfortunately, electron acceleration by reconnection is not well understood, yet. In particular, acceleration by turbulent plasmoid reconnection. We have investigated electron acceleration by turbulent plasmoid reconnection, described by MHD simulations, via test particle calculations. In order to avoid resolving all relevant turbulence scales down to the dissipation scales, a mean-field turbulence model is used to describe the turbulence of sub-grid scales (SGS) and their effects via a turbulent electromotive force (EMF). The mean-field model describes the turbulent EMF as a function of the mean values of current density, vorticity, magnetic field as well as of the energy, cross-helicity and residual helicity of the turbulence. We found that, mainly around X-points of turbulent reconnection, strongly enhanced localized EMFs most efficiently accelerated electrons and caused the formation of power-law spectra. Magnetic-field-aligned EMFs, caused by the turbulence, dominate the electron acceleration process. Scaling the acceleration processes to parameters of the Hermean magnetotail, electron energies up to 60 keV can be reached by turbulent plasmoid reconnection through the thermal plasma.

The heating of electrons in collisionless magnetic reconnection is explored in particle-in-cell (PIC) simulations with non-zero guide fields so that electrons remain magnetized. In this regime electric fields parallel to B accelerate particles directly while those perpendicular to B do so through gradient-B and curvature drifts. The curvature drift drives parallel heating through Fermi reflection while the gradient B drift changes the perpendicular energy through betatron acceleration. We present simulations in which we evaluate each of these mechanisms in space and time in order to quantify their role in electron heating. For a case with a small guide field (20 % of the magnitude of the reconnecting component) the curvature drift is the dominant source of electron heating. However, for a larger guide field (equal to the magnitude of the reconnecting component) electron acceleration by the curvature drift is comparable to that of the parallel electric field. In both cases the heating by the gradient B drift is negligible in magnitude. Heating by the curvature-drift dominates in the outflow exhausts where bent field lines expand to relax their tension and is therefore distributed over a large area. In contrast, the parallel electric field is localized near X-lines. Acceleration by parallel electric fields may play a smaller role in large systems where the X-line occupies a vanishing fraction of the system. The curvature drift and the parallel electric field dominate the dynamics and drive parallel heating. A consequence is that the electron energy spectrum becomes extremely anisotropic at late time, which has important implications for quantifying the limits of electron acceleration due to synchrotron emission. An upper limit on electron energy gain that is substantially higher than earlier estimates is obtained by balancing reconnection drive with radiative loss.

Kinetic simulations of 3D collisionless magnetic reconnection with a guide field show a dramatic enhancement of energetic electron production when compared with 2D systems. In the 2D systems, electrons are trapped in magnetic islands that limit their energy gain, whereas in the 3D systems the filamentation of the current layer leads to a stochastic magnetic field that enables the electrons to access volume-filling acceleration regions. The dominant accelerator of the most energetic electrons is a Fermi-like mechanism associated with reflection of charged particles from contracting field lines.

By means of fully kinetic particle-in-cell simulations, we study whether the proton-to-electron mass ratio $m_i/m_e$ influences the energy spectrum and underlying acceleration mechanism during magnetic reconnection. While kinetic simulations are essential for studying particle acceleration during magnetic reconnection, a reduced $m_i/m_e$ is often used to alleviate the demanding computing resources, which leads to artificial scale separation between electron and proton scales. Recent kinetic simulations with high-mass-ratio have suggested new regimes of reconnection, as electron pressure anisotropy develops in the exhaust region and supports extended current layers. In this work, we study whether different $m_i/m_e$ changes the particle acceleration processes by performing a series of simulations with different mass ratio ($m_i/m_e=25-400$) and guide-field strength in a low-$β$ plasma. We find that mass ratio does not strongly influence reconnection rate, magnetic energy conversion, ion internal energy gain, plasma energization processes, ion energy spectra, and the acceleration mechanisms for high-energy ions. Simulations with different mass ratios are different in electron acceleration processes, including electron internal energy gain, electron energy spectrum and the acceleration efficiencies for high-energy electrons. We find that high-energy electron acceleration becomes less efficient when the mass ratio gets larger because the \textit{Fermi}-like mechanism associated with particle curvature drift becomes less efficient. These results indicate that when particle curvature drift dominates high-energy particle acceleration, the further the particle kinetic scales are from the magnetic field curvature scales ($\sim d_i$), the weaker the acceleration will be.

Aims: We investigate the electron acceleration in convective electric fields of cascading magnetic reconnection in a flaring solar corona and show the resulting hard X-ray (HXR) radiation spectra caused by Bremsstrahlung for the coronal source. Methods: We perform test particle calculation of electron motions in the framework of a guiding center approximation. The electromagnetic fields and their derivatives along electron trajectories are obtained by linearly interpolating the results of high-resolution adaptive mesh refinement (AMR) MHD simulations of cascading magnetic reconnection. Hard X-ray (HXR) spectra are calculated using an optically thin Bremsstrahlung model. Results: Magnetic gradients and curvatures in cascading reconnection current sheet accelerate electrons: trapped in magnetic islands, precipitating to the chromosphere and ejected into the interplanetary space. The final location of an electron is determined by its initial position, pitch angle and velocity. These initial conditions also influence electron acceleration efficiency. Most of electrons have enhanced perpendicular energy. Trapped electrons are considered to cause the observed bright spots along coronal mass ejection CME-trailing current sheets as well as the flare loop-top HXR emissions.

Magnetic reconnection is a ubiquitous astrophysical process that rapidly converts magnetic energy into some combination of plasma flow energy, thermal energy, and non-thermal energetic particles, including energetic electrons. Various reconnection acceleration mechanisms in different low-$β$ (plasma-to-magnetic pressure ratio) and collisionless environments have been proposed theoretically and studied numerically, including first- and second-order Fermi acceleration, betatron acceleration, parallel electric field acceleration along magnetic fields, and direct acceleration by the reconnection electric field. However, none of them have been heretofore confirmed experimentally, as the direct observation of non-thermal particle acceleration in laboratory experiments has been difficult due to short Debye lengths for \textit{in-situ} measurements and short mean free paths for \textit{ex-situ} measurements. Here we report the direct measurement of accelerated non-thermal electrons from low-$β$ magnetically driven reconnection in experiments using a laser-powered capacitor coil platform. We use kiloJoule lasers to drive parallel currents to reconnect MegaGauss-level magnetic fields in a quasi-axisymmetric geometry. The angular dependence of the measured electron energy spectrum and the resulting accelerated energies, supported by particle-in-cell simulations, indicate that the mechanism of direct electric field acceleration by the out-of-plane reconnection electric field is at work. Scaled energies using this mechanism show direct relevance to astrophysical observations. Our results therefore validate one of the proposed acceleration mechanisms by reconnection, and establish a new approach to study reconnection particle acceleration with laboratory experiments in relevant regimes.

Magnetic reconnection in current sheets converts magnetic energy into particle energy. The process may play an important role in the acceleration and heating of the solar wind close to the Sun. Observations from Parker Solar Probe provide a new opportunity to study this problem, as it measures the solar wind at unprecedented close distances to the Sun. During the 1st orbit, PSP encountered a large number of current sheets in the solar wind through perihelion at 35.7 solar radii. We performed a comprehensive survey of these current sheets and found evidence for 21 reconnection exhausts. These exhausts were observed in heliospheric current sheets, coronal mass ejections, and regular solar wind. However, we find that the majority of current sheets encountered around perihelion, where the magnetic field was strongest and plasma beta was lowest, were Alfvénic structures associated with bursty radial jets and these current sheets did not appear to be undergoing local reconnection. We examined conditions around current sheets to address why some current sheets reconnected, while others did not. A key difference appears to be the degree of plasma velocity shear across the current sheets: The median velocity shear for the 21 reconnection exhausts was 24% of the Alfvén velocity shear, whereas the median shear across 43 Alfvénic current sheets examined was 71% of the Alfvén velocity shear. This finding could suggest that large, albeit sub-Alfvénic, velocity shears suppress reconnection. An alternative interpretation is that the Alfvénic current sheets are isolated rotational discontinuities which do not undergo local reconnection.

Diffusive shock acceleration (DSA) at relativistic shocks is expected to be an important acceleration mechanism in a variety of astrophysical objects including extragalactic jets in active galactic nuclei and gamma ray bursts. These sources remain strong and interesting candidate sites for the generation of ultra-high energy cosmic rays. In this paper, key predictions of DSA at relativistic shocks that are salient to the issue of cosmic ray ion and electron production are outlined. Results from a Monte Carlo simulation of such diffusive acceleration in test-particle, relativistic, oblique, MHD shocks are presented. Simulation output is described for both large angle and small angle scattering scenarios, and a variety of shock obliquities including superluminal regimes when the de Hoffman-Teller frame does not exist. The distribution function power-law indices compare favorably with results from other techniques. They are found to depend sensitively on the mean magnetic field orientation in the shock, and the nature of MHD turbulence that propagates along fields in shock environs. An interesting regime of flat spectrum generation is addressed, providing evidence for its origin being due to shock drift acceleration. The impact of these theoretical results on gamma-ray burst and blazar science is outlined. Specifically, Fermi gamma-ray observations of these cosmic sources are already providing significant constraints on important environmental quantities for relativistic shocks, namely the frequency of scattering and the level of field turbulence.

Collisionless plasma shock theory, which applies for example to the afterglow of gamma ray bursts, still contains key issues that are poorly understood. In this paper we study charged particle dynamics in a highly relativistic collisionless shock numerically using ~10^9 particles. We find a power law distribution of accelerated electrons, which upon detailed investigation turns out to originate from an acceleration mechanism that is decidedly different from Fermi acceleration. Electrons are accelerated by strong filamentation instabilities in the shocked interpenetrating plasmas and coincide spatially with the power law distributed current filamentary structures. These structures are an inevitable consequence of the now well established Weibel-like two-stream instability that operates in relativistic collisionless shocks. The electrons are accelerated and decelerated instantaneously and locally; a scenery that differs qualitatively from recursive acceleration mechanisms such as Fermi acceleration. The slopes of the electron distribution power laws are in concordance with the particle power law spectra inferred from observed afterglow synchrotron radiation in gamma ray bursts, and the mechanism can possibly explain more generally the origin of non-thermal radiation from shocked inter- and circum-stellar regions and from relativistic jets.

We propose a novel electron acceleration mechanism, which we call stochastic shock drift acceleration (SSDA), that extends the standard shock drift acceleration (SDA) for low-energy electrons at a quasi-perpendicular shock to include the effect of stochastic pitch-angle scattering. We demonstrate that the steady-state energy spectrum of electrons accelerated within the shock transition region becomes a power-law in the limit of strong scattering. The spectral index is independent of the pitch-angle scattering coefficient. On the other hand, the maximum energy attainable through the mechanism scales linearly with the pitch-angle scattering coefficient. These results have been confirmed by Monte Carlo simulations that include finite pitch-angle anisotropy. We find that the theory can reasonably well explain in-situ observations of quasi-perpendicular Earth's bow shock. Theoretical scaling law suggests that the maximum energy increases in proportion to the square of the shock speed, indicating that the thermal electrons may be accelerated up to mildly relativistic energies by the SSDA at quasi-perpendicular supernova remnant shocks. Therefore, the mechanism provides a plausible solution to the long-standing electron injection problem.

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 transition region exhibits a clear power-law distribution with spectral index of $2.0 {\rm -} 2.5$. By analyzing the trajectories of accelerated electrons, we find that the acceleration mechanism is very similar to shock surfing acceleration of ions. In contrast to the ion shock surfing, however, the energetic electrons are reflected by electron-scale electrostatic fluctuations in the shock transition region, but not by the ion-scale cross-shock electrostatic potential. The reflected electrons are then accelerated by the convective electric field in front of the shock. We conclude that the multidimensional effects as well as the self-consistent shock structure are essential for the strong electron acceleration at high Mach number shocks.

We propose semi-analytic models for the electron momentum distribution in weak shocks that accounts for both in situ acceleration and re-acceleration through diffusive shock acceleration (DSA). In the former case, a small fraction of incoming electrons are assumed to be reflected at the shock ramp and pre-accelerated to the so-called injection momentum, $p_{\rm inj}$, above which particles can diffuse across the shock transition and participate in the DSA process. This leads to the DSA power-law distribution extending from the smallest momentum of reflected electrons, $p_{\rm ref}$, all the way to the cutoff momentum, $p_{\rm eq}$, constrained by radiative cooling. In the later case, fossil electrons, specified by a power-law spectrum with a cutoff, are assumed to be re-accelerated also from $p_{\rm ref}$ up to $p_{\rm eq}$ via DSA. We then show that, in the in situ acceleration model, the amplitude of radio synchrotron emission depends strongly on the shock Mach number, whereas it varies rather weakly in the re-acceleration model. Considering rather turbulent nature of shocks in the intracluster medium, such extreme dependence for the in situ acceleration might not be compatible with relatively smooth surface brightness of observed radio relics.

The direct current (DC) electric field near the reconnection region has been proposed as an effective mechanism to accelerate protons and electrons in solar flares. A power-law energy spectrum was generally claimed in the simulations of electron acceleration by the reconnection electric field. However in most of the literature, the electric and magnetic fields were chosen independently. In this paper, we perform test-particle simulations of electron acceleration in a reconnecting magnetic field, where both the electric and magnetic fields are adopted from numerical simulations of the MHD equations. It is found that the accelerated electrons present a truncated power-law energy spectrum with an exponential tail at high energies, which is analogous to the case of diffusive shock acceleration. The influences of reconnection parameters on the spectral feature are also investigated, such as the longitudinal and transverse components of the magnetic field and the size of the current sheet. It is suggested that the DC electric field alone might not be able to reproduce the observed single or double power-law distributions.

We investigate shock structure and particle acceleration in relativistic magnetized collisionless electron-ion shocks by means of 2.5D particle-in-cell simulations with ion-to-electron mass ratios (m_i/m_e) ranging from 16 to 1000. We explore a range of inclination angles between the pre-shock magnetic field and the shock normal. In "subluminal" shocks, where relativistic particles can escape ahead of the shock along the magnetic field lines, ions are efficiently accelerated via a Fermi-like mechanism. The downstream ion spectrum consists of a relativistic Maxwellian and a high-energy power-law tail, which contains ~5% of ions and ~30% of ion energy. Its slope is -2.1. Upstream electrons enter the shock with lower energy than ions, so they are more strongly tied to the field. As a result, only ~1% of the incoming electrons are Fermi-accelerated at the shock before being advected downstream, where they populate a steep power-law tail (with slope -3.5). For "superluminal" shocks, where relativistic particles cannot outrun the shock along the field, the self-generated turbulence is not strong enough to permit efficient Fermi acceleration, and the ion and electron downstream spectra are consistent with thermal distributions. The incoming electrons are heated up to equipartition with ions, due to strong electromagnetic waves emitted by the shock into the upstream. Thus, efficient electron heating (>15% of the upstream ion energy) is the universal property of relativistic electron-ion shocks, but significant nonthermal acceleration of electrons (>2% by number, >10% by energy, with slope flatter than -2.5) is hard to achieve in magnetized flows and requires weakly magnetized shocks (magnetization <1e-3). These findings place important constraints on the models of AGN jets and Gamma Ray Bursts that invoke particle acceleration in relativistic magnetized electron-ion shocks.

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 electric field with long time particles staying near the shock front for shock drift acceleration (SDA). In addition, at parallel shocks the electron acceleration efficiency is increasing with the increasing of $\left(b/B_0\right)^2$, and at $\left(b/B_0\right)^2=10.0$ the acceleration is very strong due to sufficient pitch-angle scattering for first-order Fermi acceleration, as well as due to large local component of magnetic field perpendicular to shock normal angle for SDA. On the other hand, the high perpendicular shock acceleration with $\left(b/B_0\right)^2=0.01$ is stronger than the high parallel shock acceleration with ($\left(b/B_0\right)^2=10.0$), the reason might be the assumption that SDA is more efficient than first-order Fermi acceleration. Furthermore, for oblique shocks, the acceleration efficiency is small no matter the turbulence level is low or high. Moreover, for the effect of shock thickness on electron acceleration at perpendicular shocks, we show that there exists the bend-over thickness, $L_{\text{diff,b}}$. The acceleration efficiency does not change evidently if the shock thickness is much smaller than $L_{\text{diff,b}}$. However, if the shock thickness is much larger than $L_{\text{diff,b}}$, the acceleration efficiency starts to drop abruptly.

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 undergo multiple cycles of shock drift acceleration before the injection into DSA. Strong current-driven waves also temporarily change the shock obliquity and cause mild proton pre-acceleration even in quasi-perpendicular shocks, which otherwise do not accelerate protons. These results can be used to understand nonthermal emission in supernova remnants and intracluster medium in galaxy clusters.

Electron acceleration to non-thermal energies in low Mach number (M<5) shocks is revealed by radio and X-ray observations of galaxy clusters and solar flares, but the electron acceleration mechanism remains poorly understood. Diffusive shock acceleration, also known as first-order Fermi acceleration, cannot be directly invoked to explain the acceleration of electrons. Rather, an additional mechanism is required to pre-accelerate the electrons from thermal to supra-thermal energies, so they can then participate in the Fermi process. In this work, we use two- and three-dimensional particle-in-cell plasma simulations to study electron acceleration in low Mach number shocks. We focus on the particle energy spectra and the acceleration mechanism in a reference run with M=3 and a quasi-perpendicular pre-shock magnetic field. We find that about 15 percent of the electrons can be efficiently accelerated, forming a non-thermal power-law tail in the energy spectrum with a slope of p~2.4. Initially, thermal electrons are energized at the shock front via shock drift acceleration. The accelerated electrons are then reflected back upstream, where their interaction with the incoming flow generates magnetic waves. In turn, the waves scatter the electrons propagating upstream back toward the shock, for further energization via shock drift acceleration. In summary, the self-generated waves allow for repeated cycles of shock drift acceleration, similarly to a sustained Fermi-like process. This mechanism offers a natural solution to the conflict between the bright radio synchrotron emission observed from the outskirts of galaxy clusters and the low electron acceleration efficiency usually expected in low Mach number shocks.

We study the suprathermal electron acceleration mechanism in a perpendicular magnetosonic shock wave in a high Mach number regime by using a particle-in-cell simulation. We find that shock surfing/surftron acceleration producing the suprathermal electrons occurs in the shock transition region where a series of large amplitude electrostatic solitary waves (ESWs) are excited by Buneman instability under the interaction between the reflected ions and the incoming electrons. It is shown that the electrons are likely to be trapped by ESWs, and during the trapping phase they can be effectively accelerated by the shock motional/convection electric field. We discuss that suprathermal electrons can be accelerated up to $m_i c^2 (v_0/c)$, where $m_i c^2$ is the ion rest mass energy and $v_0$ is the shock upstream flow velocity. Furthermore, some of these suprathermal electrons may be effectively trapped for infinitely long time when Alfvén Mach number $M_A$ exceeds several 10, and they are accelerated up to the shock potential energy determined by the global shock size.

Radio relics could be generated by multiple shocks induced in the turbulent intracluster medium during galaxy mergers. Kang (2021) demonstrated that the re-acceleration of cosmic ray (CR) protons via diffusive shock acceleration (DSA) by multiple shocks could enhance the acceleration efficiency and flatten the CR spectrum, compared to a single episode of DSA. Here we examine the CR electron acceleration through multiple re-acceleration by considering energy losses and decompression of the particle distribution and magnetic fields in the postshock region between consecutive shock passages. We find that the accumulated effects of repeated re-acceleration are significant, if preceding shocks are stronger than the last shock and the shock passage interval is $\lesssim20$ Myr. In such cases, both the CR spectrum and the ensuing radiation spectrum behind the last shock are enhanced and become flatter than the canonical DSA power-law forms. As a result, the shock Mach number estimated from radio observations tends be higher than the actual Mach number of the last shock. Thus, multiple episodes of DSA may explain the enhanced acceleration efficiency for CR electrons and the discrepancy of shock Mach numbers, $M_{\rm X} \lesssim M_{\rm rad}$, inferred for some observed radio relics.

With a test-particle simulation, we investigate the effect of large-scale coronal magnetic fields on electron acceleration at an outward-propagating coronal shock with a circular front. The coronal field is approximated by an analytical solution with a streamer-like magnetic field featured by partially open magnetic field and a current sheet at the equator atop the closed region. We show that the large-scale shock-field configuration, especially the relative curvature of the shock and the magnetic field line across which the shock is sweeping, plays an important role in the efficiency of electron acceleration. At low shock altitudes, when the shock curvature is larger than that of magnetic field lines, the electrons are mainly accelerated at the shock flanks; at higher altitudes, when the shock curvature is smaller, the electrons are mainly accelerated at the shock nose around the top of closed field lines. The above process reveals the shift of efficient electron acceleration region along the shock front during its propagation. It is also found that in general the electron acceleration at the shock flank is not so efficient as that at the top of closed field since at the top a collapsing magnetic trap can be formed. In addition, we find that the energy spectra of electrons is power-law like, first hardening then softening with the spectral index varying in a range of -3 to -6. Physical interpretations of the results and implications on the study of solar radio bursts are discussed.

An extreme case of electron shock drift acceleration in low Mach number collisionless shocks is investigated as a plausible mechanism of initial acceleration of relativistic electrons in large-scale shocks in galaxy clusters where upstream plasma temperature is of the order of 10 keV and a degree of magnetization is not too small. One-dimensional electromagnetic full particle simulations reveal that, even though a shock is rather moderate, a part of thermal incoming electrons are accelerated and reflected through relativistic shock drift acceleration and form a local nonthermal population just upstream of the shock. The accelerated electrons can self-generate local coherent waves and further be back-scattered toward the shock by those waves. This may be a scenario for the first stage of the electron shock acceleration occurring at the large-scale shocks in galaxy clusters such as CIZA J2242.8+5301 which has well defined radio relics.

Energetic electrons are a common feature of interplanetary shocks and planetary bow shocks, and they are invoked as a key component of models of nonthermal radio emission, such as solar radio bursts. A simulation study is carried out of electron acceleration for high Mach number, quasi-perpendicular shocks, typical of the shocks in the solar wind. Two dimensional self-consistent hybrid shock simulations provide the electric and magnetic fields in which test particle electrons are followed. A range of different shock types, shock normal angles, and injection energies are studied. When the Mach number is low, or the simulation configuration suppresses fluctuations along the magnetic field direction, the results agree with theory assuming magnetic moment conserving reflection (or Fast Fermi acceleration), with electron energy gains of a factor only 2 - 3. For high Mach number, with a realistic simulation configuration, the shock front has a dynamic rippled character. The corresponding electron energization is radically different: Energy spectra display: (1) considerably higher maximum energies than Fast Fermi acceleration; (2) a plateau, or shallow sloped region, at intermediate energies 2 - 5 times the injection energy; (3) power law fall off with increasing energy, for both upstream and downstream particles, with a slope decreasing as the shock normal angle approaches perpendicular; (4) sustained flux levels over a broader region of shock normal angle than for adiabatic reflection. All these features are in good qualitative agreement with observations, and show that dynamic structure in the shock surface at ion scales produces effective scattering and can be responsible for making high Mach number shocks effective sites for electron acceleration.

Relativistic shocks propagating into a medium with low magnetization are generated and sustained by small-scale but very strong magnetic field turbulence. This so-called "microturbulence" modifies the typical shock acceleration process, and in particular that of electrons. In this work we perform Monte Carlo (MC) simulations of electrons encountering shocks with microturbulent fields. The simulations cover a three-dimensional parameter space in shock speed, acceleration efficiency, and peak magnetic field strength. From these, a Markov Chain Monte Carlo (MCMC) method was employed to estimate the maximum electron momentum from the MC-simulated electron spectra. Having estimated this quantity at many points well-distributed over an astrophysically relevant parameter space, an MCMC method was again used to estimate the parameters of an empirical formula that computes the maximum momentum of a Fermi-accelerated electron population anywhere in this parameter space. The maximum energy is well-approximated as a broken power-law in shock speed, with the break occurring when the shock decelerates to the point where electrons can begin to escape upstream from the shock.

Thermal electrons cannot directly participate in the process of diffusive acceleration at electron-ion shocks because their Larmor radii are smaller than the shock transition width: this is the well-known electron injection problem of diffusive shock acceleration. Instead, an efficient pre-acceleration process must exist that scatters electrons off of electromagnetic fluctuations on scales much shorter than the ion gyro radius. The recently found intermediate-scale instability provides a natural way to produce such fluctuations in parallel shocks. The instability drives comoving (with the upstream plasma) ion-cyclotron waves at the shock front and only operates when the drift speed is smaller than half of the electron Alfven speed. Here, we perform particle-in-cell simulations with the SHARP code to study the impact of this instability on electron acceleration at parallel non-relativistic, electron-ion shocks. To this end, we compare a shock simulation in which the intermediate-scale instability is expected to grow to simulations where it is suppressed. In particular, the simulation with an Alfvenic Mach number large enough to quench the intermediate instability shows a great reduction (by two orders of magnitude) of the electron acceleration efficiency. Moreover, the simulation with a reduced ion-to-electron mass ratio (where the intermediate instability is also suppressed) not only artificially precludes electron acceleration but also results in erroneous electron and ion heating in the downstream and shock transition regions. This finding opens up a promising route for a plasma physical understanding of diffusive shock acceleration of electrons, which necessarily requires realistic mass ratios in simulations of collisionless electron-ion shocks.

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 magnetic turbulence at the shock transition and the region immediately behind the main shock overshoot is essential for electron energization. Wide-energy non-thermal electron distributions are formed both upstream and downstream of the shock. The maximum energy of the electrons is sufficient for their injection into diffusive shock acceleration. We show for the first time that the downstream electron spectrum has a~power-law form with index $p\approx 2.5$, in agreement with observations.

The early acceleration of protons and electrons in the nonrelativistic collisionless shocks with three obliquities are investigated through 1D particle-in-cell simulations. In the simulations, the charged particles possessing a velocity of $0.2\, c$ flow towards a reflecting boundary, and the shocks with a sonic Mach number of $13.4$ and a Alfven Mach number of $16.5$ in the downstream shock frame are generated. In these quasi-parallel shocks with the obliquity angles $θ= 15^\circ$, $30^\circ$, and $45^\circ$, some of the protons and the electrons can be injected into the acceleration processes, and their downstream spectra in the momentum space show a power law tail at a time of $1.89\times10^5 ω_{\rm pe}^{-1}$, where $ω_{\rm pe}$ is the electron plasma frequency. Moreover, the charged particles reflected at the shock excite magnetic waves upstream of the shock. The shock drift acceleration is more prominent with a larger obliquity angle for the shocks, but the accelerated particles diffuse parallel to the shock propagation direction more easily to participate in the diffusive shock acceleration. At the time still in the early acceleration stage, more energetic protons and electrons appear in the downstream of the shock for $θ= 15^\circ$ compared with the other two obliquities; moreover, in the upstream region, the spectrum of the accelerated electrons is the hardest for $θ_{\rm nB} = 45^\circ$ among the three obliquities, whereas the proton spectra for $θ_{\rm nB} = 15^\circ$ and $45^\circ$ are similar as a result of the competition of the effectiveness of the shock drift acceleration and the diffusive shock acceleration.

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 electric field is excited at the shock front in association with the ion-scale rippling, and that reflected ions are accelerated upstream at a localized region where the shock-normal electric field of the rippled structure is polarized upstream. The current-driven instability caused by the highly-accelerated reflected ions has a high growth rate to large-amplitude electrostatic waves. Energetic electrons are then generated by the large-amplitude electrostatic waves via electron surfing acceleration at the leading edge of the shock transition region. The present result suggests that the electron surfing acceleration is also a common feature at low-Mach-number perpendicular collisionless shocks.

Shock drift acceleration plays an important role in generating high-energy electrons at quasi-perpendicular shocks, but its efficiency in low beta plasmas is questionable. In this article, we perform a two-dimensional particle-in-cell simulation of a low-Mach-number low-plasma-beta quasi-perpendicular shock, and find that the electron cyclotron drift instability is unstable at the leading edge of the shock foot, which is excited by the relative drift between the shock-reflected ions and the incident electrons. The electrostatic waves triggered by the electron cyclotron drift instability can scatter and heat the incident electrons, which facilitates them to escape from the shock's loss cone. These electrons are then reflected by the shock and energized by shock drift acceleration. In this way, the acceleration efficiency of shock drift acceleration at low-plasma-beta quasi-perpendicular shocks is highly enhanced.

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 approximately thermal with a limited supra-thermal power-law component. Our results are discussed in the context of wakefield acceleration and the modelling of electromagnetic radiation from blazar cores.

In the present paper, we use a coarse-graining approach to investigate the nonlinear redistribution of free energy in both position and scale space for weakly collisional magnetised plasma turbulence. For this purpose, we use high-resolution numerical simulations of gyrokinetic (GK) turbulence that span the proton-electron range of scales, in a straight magnetic guide field geometry. Accounting for the averaged effect of the particles' fast gyro-motion on the slow plasma fluctuations, the GK approximation captures the dominant energy redistribution mechanisms in strongly magnetised plasma turbulence. Here, the GK system is coarse-grained with respect to a cut-off scale, separating in real space the contributions to the nonlinear interactions from the coarse-grid-scales and the sub-grid-scales (SGS). We concentrate on the analysis of nonlinear SGS effects. Not only that this allows us to investigate the flux of free energy across the scales, but also to now analyse its spatial density. We find that the net value of scale flux is an order of magnitude smaller than both the positive and negative flux density contributions. The dependence of the results on the filter type is also analysed. Moreover, we investigate the advection of energy in position space. This rather novel approach for GK turbulence can help in the development of SGS models that account for advective unstable structures for space and fusion plasmas, and with the analysis of the turbulent transport saturation.

It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is applied to derive two scalar equations that govern the nonlinear evolution of the Alfvenic and pseudo-Alfvenic components of ideal incompressible magnetohydrodynamic (MHD) plasma turbulence. The mathematical form of these equations makes clear the inherently three-dimensional nature of plasma turbulence, enabling an analysis of the nonlinear properties of two-dimensional limits often used to study plasma turbulence. In the anisotropic limit k_perp >>k_parallel that naturally arises in magnetized plasma systems, the perpendicular 2D limit retains the dominant nonlinearities that are mediated only by the Alfvenic fluctuations but lacks the wave physics associated with the linear term that is necessary to capture the anisotropic cascade of turbulent energy. In the in-plane 2D limit, the nonlinear energy transfer is controlled instead by the pseudo-Alfven waves, with the Alfven waves relegated to a passive role. In the oblique 2D limit, an unavoidable azimuthal dependence connecting the wavevector components will likely cause artificial azimuthal asymmetries in the resulting turbulent dynamics. Therefore, none of these 2D limits is sufficient to capture fully the rich three-dimensional nonlinear dynamics critical to the evolution of plasma turbulence.

This paper summarises some of the recent progress that has been made in understanding astrophysical plasma turbulence in the solar wind, from in situ spacecraft observations. At large scales, where the turbulence is predominantly Alfvenic, measurements of critical balance, residual energy, and 3D structure are discussed, along with comparison to recent models of strong Alfvenic turbulence. At these scales, a few percent of the energy is also in compressive fluctuations, and their nature, anisotropy, and relation to the Alfvenic component is described. In the small scale kinetic range, below the ion gyroscale, the turbulence becomes predominantly kinetic Alfven in nature, and measurements of the spectra, anisotropy, and intermittency of this turbulence are discussed with respect to recent cascade models. One of the major remaining questions is how the turbulent energy is dissipated, and some recent work on this question, in addition to future space missions which will help to answer it, are briefly discussed.

We have previously generated elongated Taylor double-helix flux rope plasmas in the SSX MHD wind tunnel. These plasmas are remarkable in their rapid relaxation (about one Alfvén time) and their description by simple analytical Taylor force-free theory despite their high plasma beta and high internal flow speeds. We report on the turbulent features observed in these plasmas including frequency spectra, autocorrelation function, and probability distribution functions of increments. We discuss here the possibility that the turbulence facilitating access to the final state supports coherent structures and intermittency revealed by non-Gaussian signatures in the statistics. Comparisons to a Hall-MHD simulation of the SSX MHD wind tunnel show similarity in several statistical measures.

A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al. 2009) for pressure-anisotropic plasmas, allowing for species drifts---a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas (e.g. intracluster medium). Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g., the Alfven ratio) are order-unity modified compared to the more commonly considered Maxwellian case, and so a quantitative theory is developed to support quantitative measurements now possible in the solar wind. The main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvenic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvenic cascade is fluid, satisfying RMHD equations (with the Alfven speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping. Secondly, the organising principle of this turbulence is elucidated in the form of a generalised kinetic free-energy invariant. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses; these changes influence the partitioning of free energy amongst the various cascade channels. As the firehose or mirror instability thresholds are approached, the dynamics of the plasma are modified so as to reduce the energetic cost of bending magnetic-field lines or of compressing/rarefying them. Finally, it is shown that this theory can be derived as a long-wavelength limit of non-Maxwellian slab gyrokinetics.

We analyze the motion of the plasma critical layer by two different processes in the relativistic-electron laser-plasma interaction regime ($a_0>1$). The differences are highlighted when the critical layer ions are stationary in contrast to when they move with it. Controlling the speed of the plasma critical layer in this regime is essential for creating low-$β$ traveling acceleration structures of sufficient laser-excited potential for laser ion accelerators (LIA). In Relativistically Induced Transparency Acceleration (RITA) scheme the heavy plasma-ions are fixed and only trace-density light-ions are accelerated. The relativistic critical layer and the acceleration structure move longitudinally forward by laser inducing transparency through apparent relativistic increase in electron mass. In the Radiation Pressure Acceleration (RPA) scheme the whole plasma is longitudinally pushed forward under the action of the laser radiation pressure, possible only when plasma ions co-propagate with the laser front. In RPA the acceleration structure velocity critically depends upon plasma-ion mass in addition to the laser intensity and plasma density. In RITA, mass of the heavy immobile plasma-ions does not affect the speed of the critical layer. Inertia of the bared immobile ions in RITA excites the charge separation potential whereas RPA is not possible when ions are stationary.

In this article, we concentrate on the basic physics of relativistic plasma wave accelerators. The generation of relativistic plasma waves by intense lasers or electron beams in low-density plasmas is important in the quest for producing ultra-high acceleration gradients for accelerators. A number of methods are being pursued vigorously to achieve ultra-high acceleration gradients using various plasma wave drivers; these include wakefield accelerators driven by photon, electron, and ion beams. We describe the basic equations and show how intense beams can generate a large-amplitude relativistic plasma wave capable of accelerating particles to high energies. We also demonstrate how these same relativistic electron waves can accelerate photons in plasmas.

Plasma injection schemes are crucial for producing high-quality electron beams in laser-plasma accelerators. This article introduces the general concepts of plasma injection. First, a Hamiltonian model for particle trapping and acceleration in plasma waves is introduced; ionization injection and colliding-pulse injection are described in the framework of this Hamiltonian model. We then proceed to consider injection in plasma density gradients.

Observational aspects of solar flares relevant to the acceleration process of electrons and protons are reviewed and it is shown that most of these observations can be explained by the interaction with flare plasma of a power law energy distribution of electrons (and protons) that are injected at the top of a flaring loop, in the so-called thick target model. Some new observations that do not agree with this model are described and it is shown that these can be explained most naturally if most of the energy released by the reconnection process goes first into the generation of plasma turbulence, which accelerates, scatters and traps the ambient electrons near the top of the loop stochastically. The resultant bremsstrahlung photon spectral and spatial distributions agree with the new observations. This model is also justified by some theoretical arguments. Results from numerical evaluation of the spectra of the accelerated electrons and their bremsstrahlung emission are compared with observations and shown how one can constrain the model parameters describing the flare plasma and the spectrum and the energy density of the turbulence.

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.

Dissipative processes cause collisionless plasmas in many systems to develop nonthermal particle distributions with broad power-law tails. The prevalence of power-law energy distributions in space/astrophysical observations and kinetic simulations of systems with a variety of acceleration and trapping (or escape) mechanisms poses a deep mystery. We consider the possibility that such distributions can be modeled from maximum-entropy principles, when accounting for generalizations beyond the Boltzmann-Gibbs entropy. Using a dimensional representation of entropy (related to the Renyi and Tsallis entropies), we derive generalized maximum-entropy distributions with a power-law tail determined by the characteristic energy scale at which irreversible dissipation occurs. By assuming that particles are typically energized by an amount comparable to the free energy (per particle) before equilibrating, we derive a formula for the power-law index as a function of plasma parameters for magnetic dissipation in systems with sufficiently complex topologies. The model reproduces several results from kinetic simulations of relativistic turbulence and magnetic reconnection.

We briefly give some of the characteristics of the beam-driven, plasma-based particle accelerator known as the plasma wakefield accelerator (PWFA). We also mention some of the major results that have been obtained since the birth of the concept. We focus on high-energy particle beams where possible.

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices, and the fundamental processes of turbulence, magnetic reconnection, and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfven wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

It is shown that two circularly polarised Alfvén waves that propagate along the ambient magnetic field in an uniform plasma trigger non oscillating electromagnetic field components when they cross each other. The non-oscilliating field components can accelerate ions and electrons with great efficiency. This work is based on particle-in-cell (PIC) numerical simulations and on analytical non-linear computations. The analytical computations are done for two counter-propagating monochromatic waves. The simulations are done with monochromatic waves and with wave packets. The simulations show parallel electromagnetic fields consistent with the theory, and they show that the particle acceleration result in plasma cavities and, if the waves amplitudes are high enough, in ion beams. These acceleration processes could be relevant in space plasmas. For instance, they could be at work in the auroral zone and in the radiation belts of the Earth magnetosphere. In particular, they may explain the origin of the deep plasma cavities observed in the Earth auroral zone.

We present a novel mechanism in which plasma electrons and ions optically acquire angular momentum during local pump depletion of an azimuthally polarized laser, despite the laser carrying none. Using theoretical considerations and multi-dimensional particle-in-cell simulations, we find that this process is enabled by a strong frequency downshift at the gradually eroding laser pulse front. We further show that the angular momentum gained by the plasma electrons is compensated by the ions and by the combined electromagnetic fields of the laser and nonlinear plasma wave. By varying key laser parameters such as phase, frequency, and polarization, we demonstrate that the transverse momentum of high-energy electrons can be effectively controlled.

In situ particle acceleration is probably occuring in cluster radio haloes. This is suggested by the uniformity and extent of the haloes, given that spatial diffusion is slow and that radiative losses limit particle lifetimes. Stochastic acceleration by plasma turbulence is the most likely mechanism. Alfven wave turbulence has been suggested as the means of acceleration, but it is too slow to be important in the cluster environment. We propose, instead, that acceleration occurs via strong lower-hybrid wave turbulence. We find that particle acceleration will be effective in clusters if only a small fraction of the cluster energy density is in this form.

Space plasmas are known to be out of (local) thermodynamic equilibrium, as observations show direct or indirect evidences of non-thermal velocity distributions of plasma particles. Prominent are the anisotropies relative to the magnetic field, anisotropic temperatures, field-aligned beams or drifting populations, but also, the suprathermal populations enhancing the high-energy tails of the observed distributions. Drifting bi-Kappa distribution functions can provide a good representation of these features and enable for a kinetic fundamental description of the dispersion and stability of these collision-poor plasmas, where particle-particle collisions are rare but wave-particle interactions appears to play a dominant role in the dynamic. In the present paper we derive the full set of components of the dispersion tensor for magnetized plasma populations modeled by drifting bi-Kappa distributions. A new solver called DIS-K (DIspersion Solver for Kappa plasmas) is proposed to solve numerically the dispersion relations of high complexity. The solver is validated by comparing to the damped and unstable wave solutions obtained with other codes, operating in the limits of drifting Maxwellian and non-drifting Kappa models. These new theoretical tools enable more realistic characterizations, both analytical and numerical, of wave fluctuations and instabilities in complex kinetic configurations measured in-situ in space plasmas.

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the observation and theory of chaos and complexity in plasmas, and elucidate their links to intermittent plasma turbulence. First, we present evidence of magnetic reconnection and intermittent magnetic turbulence in coronal mass ejections in the solar corona and solar wind via remote and in situ observations. The signatures of turbulent magnetic reconnection, i.e., bifurcated current sheet, reconnecting jet, parallel/anti-parallel Alfvén waves, and spiky dynamical pressure pulse, as well as fully-developed Kolmogorov intermittent turbulence, are detected at the leading edge of an interplanetary coronal mass ejection and the interface region of two interplanetary magnetic flux ropes. Methods for quantifying the degree of coherence, amplitude-phase synchronization, and multifractality of nonlinear multiscale fluctuations are discussed. The stochastic chaotic nature of Alfvén intermittent structures driven by magnetic reconnection is determined by a complexity-entropy analysis. Next, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave-wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. Two types of plasma chaos are considered: type-I Pomeau-Manneville intermittency and crisis-induced intermittency. The role of transient structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied.

Suprathermal electrons and inertial drifting electrons, so called electron beam, are crucial to the nonlinear dynamics of electrostatic solitary waves observed in several astrophysical plasmas. In this paper, the propagation of electron-acoustic solitary waves is investigated in a collisionless, unmagnetized plasma consisting of cool inertial background electrons, hot suprathermal electrons (modeled by a $κ$-type distribution), and stationary ions. The plasma is penetrated by a cool electron beam component. A linear dispersion relation is derived to describe small-amplitude wave structures that shows a weak dependence of the phase speed on the electron beam velocity and density. A (Sagdeev-type) pseudopotential approach is employed to obtain the existence domain of large-amplitude solitary waves, and investigate how their nonlinear structures depend on the kinematic and physical properties of the electron beam and the suprathermality (described by $κ$) of the hot electrons. The results indicate that the electron beam can largely alter the electron-acoustic solitary waves, but can only produce negative polarity solitary waves in this model. While the electron beam co-propagates with the solitary waves, the soliton existence domain (Mach number range) becomes narrower (nearly down to nil) with increasing the beam speed and the beam-to-hot electron temperature ratio, and decreasing the beam-to-cool electron density ratio in high suprathermality (low $κ$). It is found that the electric potential amplitude largely declines with increasing the beam speed and the beam-to-cool electron density ratio for co-propagating solitary waves, but is slightly decreased by raising the beam-to-hot electron temperature ratio.

The prospects of using extreme relativistic laser-matter interactions for laboratory astrophysics are discussed. Laser-driven process simulation of matter dynamics at ultra-high energy density is proposed for the studies of astrophysical compact objects and the early universe.

The Euler equations of ideal gas dynamics posess a remarkable nonlinear involutional symmetry which allows one to factor out an arbitrary uniform expansion or contraction of the system. The nature of this symmetry (called by cosmologists the transformation to supercomoving variables) is discussed and its origin clarified. It is pointed out that this symmetry allows one to map an explosion problem to a dual implosion problem and vice versa. The application to laboratory simulations of supernova remnants is considered; in principle this duality allows the complete three-dimensional evolution of highly structured explosion ejecta to be modelled using a static target in an implosion facility.

The absence of other viable momentum sources for collimated flows leads to the likelihood that magnetic fields play a fundamental role in jet launch and/or collimation in astrophysical jets. To best understand the physics of jets, it is useful to distinguish between the launch region where the jet is accelerated and the larger scales where the jet propagates as a collimated structure. Observations presently resolve jet propagation, but not the launch region. Simulations typically probe the launch and propagation regions separately, but not both together. Here, I identify some of the physics of jet launch vs. propagation and what laboratory jet experiments to date have probed. Reproducing an astrophysical jet in the lab is unrealistic, so maximizing the benefit of the experiments requires clarifying the astrophysical connection.

We consider the acceleration of particles due to a velocity shear in relativistic astrophysical flows. The basic physical picture and the formation of power law momentum spectra is discussed for a non-relativistic velocity field using a microscopic approach. We identify possible sites for shear acceleration in relativistic astrophysical jets and analyze their associated acceleration timescales. It is shown in particular that for a mean scattering time $τ$ scaling with the gyro-radius, the acceleration timescale for gradual shear scales in the same manner as the synchrotron cooling timescale, so that losses may no longer be able to stop the acceleration once it has started to work efficiently. Finally, the possible role of shear acceleration is discussed with reference to the relativistic jet in the quasar 3C~273.

We consider the acceleration of energetic particles by Fermi processes (i.e., diffusive shock acceleration, second order Fermi acceleration, and gradual shear acceleration) in relativistic astrophysical jets, with particular attention given to recent progress in the field of viscous shear acceleration. We analyze the associated acceleration timescales and the resulting particle distributions, and discuss the relevance of these processes for the acceleration of charged particles in the jets of AGNs, GRBs and microquasars, showing that multi-component powerlaw-type particle distributions are likely to occur.

Jets and outflows are thought to be an integral part of accretion phenomena and are associated with a large variety of objects. In these systems, the interaction of magnetic fields with an accretion disk and/or a magnetized central object is thought to be responsible for the acceleration and collimation of plasma into jets and wider angle flows. In this paper we present three-dimensional MHD simulations of magnetically driven, radiatively cooled laboratory jets that are produced on the MAGPIE experimental facility. The general outflow structure comprises an expanding magnetic cavity which is collimated by the pressure of an extended plasma background medium, and a magnetically confined jet which develops within the magnetic cavity. Although this structure is intrinsically transient and instabilities in the jet and disruption of the magnetic cavity ultimately lead to its break-up, a well collimated, knotty jet still emerges from the system; such clumpy morphology is reminiscent of that observed in many astrophysical jets. The possible introduction in the experiments of angular momentum and axial magnetic field will also be discussed.

We have shown the generation/amplification of fast macro-scale plasma flows in the degenerate two-fluid astrophysical systems with initial turbulent (micro--scale) magnetic/velocity fields due to the Unified Reverse Dynamo/Dynamo mechanism. This process is simultaneous with and complementary to the micro-scale unified dynamo. It is found that the generation of macro--scale flows is an essential consequence of the magneto-fluid coupling; the generation of macro--scale fast flows and magnetic fields are simultaneous, they grow proportionately. The resulting dynamical flow acceleration is directly proportional to the initial turbulent magnetic (kinetic/magnetic) energy in degenerate e-i (degenerate e-p) astrophysical plasma; the process is very sensitive to both the degeneracy level of the system and the magneto-fluid coupling. In case of degenerate e-p plasma, for realistic physical parameters, there always exists such a real solution of dispersion relation for which the formation of strong macro-scale flow/outflow is guaranteed; the generated/accelerated locally super-Alfvénic flows are extremely fast with Alfvén Mach number $> 10^3$ as observed in a variety of astrophysical outflows