Shock Drift Acceleration Research Articles

Nonthermal electron acceleration at collisionless quasi-perpendicular shocks

Shock waves propagating in collisionless heliospheric and astrophysical plasmas have been studied extensively over the decades. One prime motivation is to understand the nonthermal particle acceleration at shocks. Although the theory of diffusive shock acceleration (DSA) has long been the standard for cosmic-ray acceleration at shocks, plasma physical understanding of particle acceleration remains elusive. In this review, we discuss nonthermal electron acceleration mechanisms at quasi-perpendicular shocks, for which substantial progress has been made in recent years. The discussion presented in this review is restricted to the following three specific topics: The first is stochastic shock drift acceleration (SSDA), which is a relatively new mechanism for electron injection into DSA. The basic mechanism, related in-situ observations and kinetic simulations results, and how it is connected with DSA will be discussed. Second, we discuss shock surfing acceleration (SSA) at very high Mach number shocks relevant to young supernova remnants (SNRs). While the original proposal under the one-dimensional assumption is unrealistic, SSA has now been proven efficient by a fully three-dimensional kinetic simulation. We discuss the multidimensional nature of SSA and its role in electron injection. Finally, we discuss the current understanding of the magnetized Weibel-dominated shock. It is essentially a magnetized shock in which the reflected-gyrating ions dominate the formation of the shock structure but with a substantial magnetic field amplification by the ion-Weibel instability. Spontaneous magnetic reconnection of self-generated current sheets within the shock structure is an interesting consequence of Weibel-generated strong magnetic turbulence. Although the exact condition for active magnetic reconnection has not been clarified, we argue that high Mach number shocks with both Alfvén and sound Mach numbers exceeding 20–40 will likely behave as a Weibel-dominated shock. Despite a number of interesting recent findings, the relative roles of SSDA, SSA, and magnetic reconnection for electron acceleration at collisionless shocks and how the dominant particle acceleration mechanisms change depending on shock parameters remain to be answered.

Monte Carlo Simulations of Electron Acceleration at Bow Waves Driven by Fast Jets in the Earth’s Magnetosheath

The shocked solar wind flows around the Earth’s magnetosphere in the magnetosheath downstream of the Earth’s bow shock. Within this region, faster flows of plasma, called magnetosheath jets, are frequently observed. These jets have been shown to sometimes exhibit supermagnetosonic speeds relative to the magnetosheath flow and to develop bow waves or shocks of their own. Such jet-driven bow waves have been observed to accelerate ions and electrons. We model electron acceleration by magnetosheath jet-driven bow waves using test-particle Monte Carlo simulations. Our simulations suggest that the energy increase of electrons with energies of a few hundred eV to 10 keV can be explained by a collapsing magnetic trap forming between the bow wave and the magnetopause with shock drift acceleration at the moving bow wave. Our simulations allow us to estimate the efficiency of acceleration as a function of different jet and magnetosheath parameters. Electron acceleration by jet-driven bow waves can increase the total acceleration in the parent shock environment, most likely also at shocks other than the Earth’s bow shock.

Acceleration of Solar Wind Suprathermal Electrons at the Earth’s Bow Shock

We present a statistical study of the in situ acceleration of solar wind suprathermal electrons at the Earth’s bow shock, utilizing the Wind measurements in ambient solar wind and MMS1 measurements around the bow shock from 2015 September to 2017 December. All the selected 74 cases show significant suprathermal electron acceleration at the bow shock. The observed power-law indexes of accelerated electron energy spectra are significantly larger than the first-order Fermi acceleration prediction and the flux enhancement ratio peaks near a 90° pitch angle, suggesting that the shock drift acceleration (SDA) process plays a crucial role in accelerating suprathermal electrons at the bow shock. According to the observed electron spectral characteristics, the 74 cases can be classified into Types 1, 2, 3 and 4. The electron acceleration efficiency roughly increases from Type 1 to Type 4. For the Type 4 cases with strong electron acceleration, the shocked suprathermal electrons show a double-power-law energy spectrum bending downwards at a break near ∼65 keV with a low-energy spectral index of ∼3.1 and high-energy index of ∼7.6. The observed break energy is comparable to a critical electron energy with its cross-shock gyrodiameter equal to the shock’s ramp thickness D ramp. At energies below (above) , the accelerated electrons can be effectively confined into (can easily escape from) the SDA process with a roughly energy-independent (energy-decreasing) drift time and a probably conserved (nonadiabatically reduced) magnetic moment, since their gyrodiameter is less (greater) than D ramp. Therefore, such an SDA process could produce the observed double-power-law spectrum bending downwards at a break energy that is associated with D ramp.

Quantifying electron scattering by electrostatic solitary waves in the Earth's bow shock

The electrostatic fluctuations are always present in the Earth's bow shock at frequencies above about 100 Hz, but the effects of this wave activity on electron dynamics have not been quantified yet. In this paper, we quantify electron pitch-angle scattering by electrostatic solitary waves, which make up a substantial part of the electrostatic fluctuations in the Earth's bow shock and were recently shown to be predominantly ion holes. We present analytical estimates and test-particle simulations of electron pitch-angle scattering by ion holes typical of the Earth's bow shock and conclude that this scattering can be rather well quantified within the quasi-linear theory. We use the observed distributions of ion hole parameters to estimate pitch-angle scattering rates by the ensemble of ion holes typical of the Earth's bow shock. We use the recently proposed theory of stochastic shock drift acceleration to show that pitch-angle scattering of electrons by the electrostatic fluctuations can keep electrons in the shock transition region long enough to support acceleration of thermal electrons by a factor of a few tens, that is up to a few hundred eV. Importantly, the electrostatic fluctuations can be more efficient in pitch-angle scattering of ≲1 keV electrons, than typically observed whistler waves.

Theory of Electron Injection at Oblique Shock of Finite Thickness

Abstract A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion–convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of 0.1–1 MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high M A / cos θ Bn , where M A and θ Bn are the Alfvén Mach number and the shock obliquity, respectively. The theory suggests that efficient acceleration of electrons to ultrarelativistic energies will be more easily realized at high Mach number, young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.

Energetic pickup proton population downstream of the termination shock as revealed by IBEX-Hi data

ABSTRACT Pickup protons originate as a result of the ionization of hydrogen atoms in the supersonic solar wind, forming the suprathermal component of protons in the heliosphere. While they are being picked by the heliospheric magnetic field and convected into the heliosheath, the pickup protons may suffer stochastic acceleration from the solar wind turbulence in the region from the Sun up to the heliospheric termination shock, where they can also experience shock-drift acceleration or reflection from the cross-shock potential. These processes create a high-energy tail in the pickup ion energy distribution. The properties of this energetic pickup proton population are still not well defined, in spite of the fact that they are vital for models that simulate energetic neutral atom fluxes. We consider two scenarios for the pickup proton velocity distribution downstream of the heliospheric termination shock (a filled shell with an energetic power-law tail, and bi-Maxwellian). Based on a numerical kinetic model and observations of the energetic neutral atom fluxes from the inner heliosheath by the IBEX-Hi instrument, we characterize the pickup proton distribution and provide estimations of the properties of the energetic pickup proton population downstream of the termination shock.

Acceleration of Solar Energetic Particles by the Shock of Interplanetary Coronal Mass Ejection

Abstract Interplanetary coronal mass ejection (ICME) shocks are known to accelerate particles and contribute significantly to solar energetic particle events. We have performed magnetohydrodynamic-particle in cell simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel and quasi-perpendicular). We find that diffusive shock acceleration plays a significant role in accelerating particles in a parallel ICME shock. In contrast, shock drift acceleration (SDA) plays a pivotal role in a quasi-perpendicular shock. High-Mach shocks are seen to accelerate particles more efficiently. Our simulations suggest that background turbulence and local particle velocity distribution around the shock can indirectly hint at the acceleration mechanism. Our results also point toward a few possible in situ observations that could validate our understanding of the topic.

Electron Acceleration at Rippled Low-mach-number Shocks in High-beta Collisionless Cosmic Plasmas

Abstract 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 multiscale 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 ≈ 2.5, in agreement with observations.

Turbulent Acceleration of Interstellar Pickup Ions at the Heliospheric Termination Shock Forms the Global ENA Spectrum

Abstract The heliospheric energetic neutral atom spectrum observed by the Interstellar Boundary Explorer (IBEX) reveals that the heliosheath proton distribution is consistent with a power law. The origin of the spectrum is likely from interstellar pickup ions (PUIs) accelerated at the heliospheric termination shock (HTS). We present an explanation of the proton spectrum origin using a test particle simulation of PUIs accelerated at the HTS. PUIs experience preferential heating by the motional electric field in the shock foot, but do not develop a power-law tail without the presence of turbulence at wavenumbers (k) close to the PUI gyroradius scale (R g). Voyager 2 observations of the magnetic field downstream of the HTS indicate a moderate amount of turbulence at kR g ≅ 1, δ B / B 0 2 ≅ 0.01 , which we find to be sufficient for producing a downstream suprathermal PUI tail but not at intensities observed by IBEX. Within the shock ramp, however, Voyager observed the turbulence power at much smaller scales to be nearly 100 times stronger, suggesting the possibility of strong turbulence at the PUI gyroradius scale. We show that a proton distribution can develop a power law downstream of the HTS consistent with IBEX observations if δ B / B 0 2 ≳ 0.1 at kR g ≅ 1 in the shock foot. Shock drift acceleration of PUIs by the motional electric field is aided by interactions with turbulence upstream of the shock overshoot. Steepening of the IBEX proton spectrum in directions farther from the heliospheric nose suggests the HTS compression ratio and/or turbulence power weakens near the heliotail.

Local Acceleration of Protons to 100 keV in a Quasi‐Parallel Bow Shock

AbstractRecent observations in the quasi‐parallel bow shock by the Magnetospheric Multiscale spacecraft show rapid heating and acceleration of ions up to an energy of about 100 keV. It is demonstrated that a prominent acceleration mechanism is the nonlinear interaction with a spectrum of waves produced by gradient‐driven instabilities, including the lower hybrid drift (LHD) instability, modified two‐stream (MTS) instability, and electron cyclotron drift (ECD) instability. Test‐particle simulations show that the observed spectrum of waves can rapidly accelerate protons up to a few hundreds of keV by the ExB mechanism. The ExB wave mechanism is related to the surfatron mechanism at shocks, but through the coupling with the stochastic heating condition, it produces significant acceleration on much shorter temporal and spatial scales by the interaction with bursts of waves within a cyclotron period. The results of this study are built on the heritage of four‐point measurement techniques developed for the Cluster mission and imply that the concepts of Fermi acceleration, diffusive shock acceleration, and shock drift acceleration are not needed to explain proton acceleration to hundreds of keV at the Earth’s bow shock.

Trajectory Analysis of Galactic Cosmic Rays Invading into the Heliosphere

Abstract The trajectories of galactic cosmic-ray protons invading the heliosphere are investigated by using numerical simulations. A time stationary global heliosphere is first reproduced by using a high-resolution MHD simulation. Then, motions of a number of test particles (protons) distributed in the virtual heliosphere are numerically solved. When the initial particle Lorentz factor is 10 (∼10 GeV), the motions of particles are strongly affected by small-scale heliospheric structures reflecting the small gyroradii of the particles. Particles can enter the heliosphere from many parts (nose, flank, and tail) of the heliopause. Once they have entered, they expand in the region where the magnetic field is locally weak, such as the heliopause and the heliospheric current sheet. On the other hand, particles have difficulty invading upstream of the termination shock. We found a variety of invading particle trajectory patterns such as current sheet drift, polar drift, spiral motion, shock drift, and Fermi-like acceleration. In the latter two, particles are accelerated. When the initial particle Lorentz factor is 1000 (∼1 TeV), the particles are insensitive to the small-scale structures of the heliosphere due to their large gyroradii. Some particles show eccentric motions due to resonant interaction with the large-scale eddy in the heliotail. Some other particles passing by the heliosphere are mirror reflected due to the bottleneck structure of interstellar magnetic field surrounding the heliosphere and return back to enter the heliosphere.

Effects of Multiscale Plasma Waves on Electron Preacceleration at Weak Quasi-perpendicular Intracluster Shocks

Abstract Radio relics associated with merging galaxy clusters indicate the acceleration of relativistic electrons in merger-driven shocks with low sonic Mach numbers (M s ≲ 3) in the intracluster medium (ICM). Recent studies have suggested that electron injection to diffusive shock acceleration (DSA) could take place through the so-called Fermi-like acceleration in the shock foot of β = P gas/P B ≈ 20–100 shocks and the stochastic shock drift acceleration (SSDA) in the shock transition of β ≈ 1–5 shocks. Here, we explore how the SSDA can facilitate electron preacceleration in weak quasi-perpendicular (Q ⊥) shocks in β ≈ 20–100 plasmas by performing particle-in-cell simulations in a two-dimensional domain large enough to properly encompass ion-scale waves. We find that in supercritical shocks with M s ≳ M AIC * ∼ 2.3 , multiscale waves are excited by the ion and electron temperature anisotropies in the downstream of the shock ramp, and that through stochastic pitch-angle scattering off the induced waves, electrons are confined in the shock transition for an extended period. Gaining energy through the gradient-drift along the motional electric field, electrons could be preaccelerated all the way to injection to DSA at such ICM shocks. Our findings imply that the electron DSA process at weak ICM shocks could explain the origin of radio relics. However, a further investigation of electron acceleration at subcritical shocks with M s < 2.3 is called for, since the Mach numbers of some observed radio relic shocks derived from radio or X-ray observations are as low as M s ∼ 1.5.

A field–particle correlation analysis of a perpendicular magnetized collisionless shock

Using the field–particle correlation technique, we examine the particle energization in a three-dimensional (one spatial dimension and two velocity dimensions; 1D-2V) continuum Vlasov–Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field–particle correlation technique with the high-fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons arising from the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov–Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field–particle correlation technique to spacecraft measurements of collisionless shocks.

Particle acceleration by interstellar plasma shock waves in non-uniform background magnetic field

ABSTRACTParticle acceleration by plasma shock waves is investigated for a magnetized plasma cloud propagating in a non-uniform background magnetic field by means of analytical and numerical calculations. The mechanism studied here is mainly, magnetic trapping acceleration (MTA) which is previously investigated for a cloud moving through the uniform interstellar magnetic field (IMF). In this work, the acceleration is studied for a cloud moving in an antiparallel background field with spatial variations along the direction of motion. For negative variation, the cloud moves towards an antiparallel magnetic field with an increasing intensity, the trapped particle moves to locations with higher convective electric field and therefore gains more energy over time. For positive variation, the background field decreases to zero and changes into a parallel field with an increasing intensity. It is concluded that, when the background field vanishes, the MTA mechanism ceases and the particle escapes into the space. This leads to a bouncing acceleration which further increases energy of the gyrating particle. The two processes are followed by a shock drift acceleration, where due to the background magnetic field gradient, the particle drifts along the electric field and gains energy. Although for positive variation, three different mechanisms are involved, energy gain is less than in the case of a uniform background field.

Electron Acceleration in One-dimensional Nonrelativistic Quasi-perpendicular Collisionless Shocks

Abstract We study diffusive shock acceleration (DSA) of electrons in nonrelativistic quasi-perpendicular shocks using self-consistent one-dimensional particle-in-cell 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 nonresonant 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.

Suprathermal Electron Acceleration by a Quasi-perpendicular Shock: Simulations and Observations

Abstract The acceleration of suprathermal electrons in the solar wind is mainly associated with shocks driven by interplanetary coronal mass ejections (ICMEs). It is well known that the acceleration of electrons is much more efficient at quasi-perpendicular shocks than at quasi-parallel ones. Yang et al. studied the acceleration of suprathermal electrons with observations at a quasi-perpendicular ICME-driven shock event to claim the important role of shock-drift acceleration (SDA). Here, we perform test-particle simulations to study the acceleration of electrons in this event, by calculating the downstream electron intensity distribution for all energy channels assuming an initial distribution based on the average upstream intensities. Using simulations, we obtain the results similar to the observations from Yang et al. as follows. It is shown that the ratio of downstream to upstream intensities peaks at about 90° pitch angle. In addition, in each pitch angle direction the downstream electron energy spectral index is much larger than the theoretical index of diffusive shock acceleration. Furthermore, the estimated drift length is proportional to the electron energy but the drift time is almost energy independent. Finally, we use a theoretical model based on SDA to describe the drift length and drift time especially, to explain their energy dependence. These results indicate the importance of SDA in the acceleration of electrons by quasi-perpendicular shocks.

Electron Firehose Instabilities in High-β Intracluster Shocks

Abstract The preacceleration of electrons through reflection and shock drift acceleration (SDA) is essential for the diffusive shock acceleration of nonthermal electrons in collisionless shocks. Previous studies suggested that, in weak quasi-perpendicular (Q ⊥) shocks in the high-β ( ) intracluster medium (ICM), the temperature anisotropy due to SDA-reflected electrons can drive the electron firehose instability, which excites oblique nonpropagating waves in the shock foot. In this paper, we investigate, through a linear analysis and particle-in-cell simulations, the firehose instabilities driven by an electron temperature anisotropy (ETAFI) and also by a drifting electron beam (EBFI) in β ∼ 100 ICM plasmas. The EBFI should be more relevant to describing the self-excitation of upstream waves in Q ⊥-shocks, since backstreaming electrons in the shock foot behave more like an electron beam rather than an anisotropic bi-Maxwellian population. We find that the basic properties of the two instabilities, such as the growth rate, γ, and the wavenumber of fast-growing oblique modes, are similar in the ICM environment, with one exception; while the waves excited by the ETAFI are nonpropagating (ω r = 0), those excited by the EBFI have a nonzero frequency ( ). However, the frequency is small with ω r < γ. Thus, we conclude that the interpretation of previous studies for the nature of upstream waves based on the ETAFI remains valid in Q ⊥-shocks in the ICM.

Shock Drift Acceleration of Ions in an Interplanetary Shock Observed by MMS

Abstract An interplanetary (IP) shock wave was recorded crossing the Magnetospheric Multiscale constellation on 2018 January 8. Plasma measurements upstream of the shock indicate efficient proton acceleration in the IP shock ramp: 2–7 keV protons are observed upstream for about three minutes (∼8000 km) ahead of the IP shock ramp, outrunning the upstream waves. The differential energy flux of 2–7 keV protons decays slowly with distance from the ramp toward the upstream region (dropping by about half within 8 Earth radii from the ramp) and is lessened by a factor of about four in the downstream compared to the ramp (within a distance comparable to the gyroradius of ∼keV protons). Comparison with test-particle simulations has confirmed that the mechanism accelerating the solar wind protons and injecting them upstream is classical Shock Drift Acceleration (SDA). This example of observed proton acceleration by a low-Mach, quasi-perpendicular shock may be applicable to astrophysical contexts, such as supernova remnants or the acceleration of cosmic rays.

Observational Evidence for Stochastic Shock Drift Acceleration of Electrons at the Earth's Bow Shock.

The first-order Fermi acceleration of electrons requires an injection of electrons into a mildly relativistic energy range. However, the mechanism of injection has remained a puzzle both in theory and observation. We present direct evidence for a novel stochastic shock drift acceleration theory for the injection obtained with Magnetospheric Multiscale observations at the Earth's bow shock. The theoretical model can explain electron acceleration to mildly relativistic energies at high-speed astrophysical shocks, which may provide a solution to the long-standing issue of electron injection.

Case Study of Solar Wind Suprathermal Electron Acceleration at the Earth’s Bow Shock

Abstract We present a case study of the in situ acceleration of solar wind suprathermal electrons at the two quasi-perpendicular-bow-shock crossings on 2015 November 4, combining the Wind 3D Plasma and Energetic Particle measurements of ambient solar wind suprathermal electrons and Magnetospheric Multiscale mission measurements of shocked suprathermal electrons. In both cases, the omnidirectional differential fluxes of shocked suprathermal electrons in the downstream exhibit a double-power-law energy spectrum with a spectral index of ∼3 at energies below a downward break ε brk near 40 keV and index of ∼6 at energies above, different from the unshocked suprathermal electrons observed in the ambient solar wind. At energies below (above) ε brk, the observed electron flux ratio between the downstream and ambient solar wind, J D /J A , peaks near 90° PA (becomes roughly isotropic). Electrons at ε brk have an average electron gyrodiameter (across bow shock) comparable to the shock thickness. These suggest that the bow-shock acceleration of suprathermal electrons is likely dominated by the shock drift acceleration mechanism. For electrons at energies below (above) ε brk, their estimated drift time appears to be roughly energy independent (decrease with energy), leading to the formation of a double-power-law spectrum substantially steepening at a break that’s determined by the shock thickness.