Quasi-perpendicular Shock Research Articles

Transit time thermalization and the stochastic wave energization of ions in quasi-perpendicular shocks

ABSTRACT It is shown that the ratio of the proton convective gyroradius rEp, to the width of the shock ramp D, controls the thermalization process of ions in quasi-perpendicular shocks. When rEp/D > 1, the solar wind beam energy is rapidly converted to gyration (thermal) energy by a universal, transit time thermalization (TTT) mechanism that does not require any collisions, waves, or instabilities. The TTT of ions on magnetic field gradients is followed by stochastic wave energization (SWE) on electric field gradients. Ions heated by TTT and SWE processes are subject to additional ballistic surfing acceleration caused by the convection field in the shock front. These three fundamental ion energization mechanisms are studied with test-particle simulations in a realistic shock model, and are shown to be consistent with magnetospheric multiscale measurements in the Earth’s bow shock. It is also shown that shock reflected ions are produced by the SWE process and not by the cross-shock potential. An explanation for downstream oscillations in quasi-perpendicular shocks is also provided.

Particle-in-cell simulations of collisionless perpendicular shocks driven at a laser-plasma device

Experiments of generation of quasi-perpendicular collisionless shocks driven by laser plasma were performed at the Shenguang-II laser facility with intense lasers. Here, using a 1D particle-in-cell simulation code including protons, carbon ions, and electrons, we investigate the experimental shock formation via the interaction between the laser-ablated piston and ambient plasma magnetized by a large pre-existing magnetic field and the associated ion dynamics in more detail. Simulation results show that, given enough time and space, ambient protons and carbon ions can be reflected at the piston–ambient interface successively, which leads to the formation of corresponding shocks before the piston and interface. Electric fields associated with the initial interaction known as Larmor coupling and the shocks may accelerate ambient protons, carbon ions reflected at the interface or shocks, and piston ones transmitted to the ambient region before shock formation.

Isolation and phase-space energization analysis of the instabilities in collisionless shocks

We analyse the generation of kinetic instabilities and their effect on the energization of ions in non-relativistic, oblique collisionless shocks using a 3D-3V (three spatial with three velocity components) simulation by dHybridR, a hybrid particle-in-cell code. At sufficiently high Mach number, quasi-perpendicular and oblique shocks can experience rippling of the shock surface caused by kinetic instabilities arising from free energy in the ion velocity distribution due to the combination of the incoming ion beam and the population of ions reflected at the shock front. To understand the role of the ripple on particle energization, we devise a new instability isolation method to identify the unstable modes underlying the ripple and interpret the results in terms of the governing kinetic instability. We generate velocity-space signatures using the field–particle correlation technique to look at energy transfer in phase space from the isolated instability driving the shock ripple, providing a viewpoint on the different dynamics of distinct populations of ions in phase space. Together, the field–particle correlation technique and our new instability isolation method provide a unique viewpoint on the different dynamics of distinct populations of ions in phase space and allow us to completely characterize the energetics of the collisionless shock under investigation.

Electron heating mechanisms at quasi-perpendicular shocks – revisited with magnetospheric multiscale measurements

ABSTRACTWe demonstrate that measurements obtained from NASA’s magnetospheric multiscale (MMS) mission support quasi-adiabatic electron heating in quasi-perpendicular shocks with temperature Te⊥ ∝ B1 + α, where B is the magnetic field strength and α represents departure from adiabaticity. Adiabatic heating (α = 0) results from the conservation of magnetic moment on spatially increasing magnetic field inside the shock ramp. Negative α < 0 is observed in most situations, where perpendicular energy gain from adiabatic heating is redistributed by interactions with waves to the parallel direction leading to a lower isotropic temperature increase. Positive α is observed when the stochastic heating of electrons is activated by the E × B wave acceleration mechanism by electrostatic waves leading to a higher temperature increase. By using test-particle simulations in a realistic shock model we have elucidated the process of stochastic wave acceleration. We have also shown the equivalence of adiabatic heating and acceleration by gradient B drift at shocks with low Mach numbers and demonstrated that the cross-shock potential does not contribute to the electron heating. Signatures of quasi-adiabatic heating and/or stochastic heating of electrons are observed in all shocks analysed with measurements by the MMS.

Large-Scale Solar Wind Phenomena Affecting the Turbulent Cascade Evolution behind the Quasi-Perpendicular Bow Shock

The Earth’s magnetosphere is permanently influenced by the solar wind. When supersonic and superalfvenic plasma flow interacts with the magnetosphere, the magnetosheath region is formed, which is filled with shocked turbulent plasma. Varying SW parameters influence the mechanisms of formation of this boundary layer, including the dynamics of turbulence behind the bow shock. The effect of the solar wind on the development of turbulence in the magnetosheath was demonstrated recently based on broad statistics of spacecraft measurements. The present study considers the multipoint observations of turbulent fluctuations in the solar wind, in the dayside magnetosheath and at the flanks, to analyze the evolution of the turbulent cascade while the solar wind plasma enters the magnetosheath. Observations of the magnetosheath behind the quasi-perpendicular bow shock are analyzed to exclude the influence of the bow shock topology from consideration. Three basic types of solar wind flows are considered: slow undisturbed solar wind, compressed regions, and interplanetary manifestations of coronal mass ejections. The results show surviving Kolmogorov scaling behind the bow shock for steady solar wind flow and amplification of the compressive fluctuations at the kinetic scales at the magnetosheath flanks for the solar wind associated with compressed plasma streams. During interplanetary manifestations of the coronal mass ejection, the spectra in the dayside magnetosheath substantially deviate from those observed in the solar wind (including the absence of Kolmogorov scaling and steepening at the kinetic scales) and restore at the flanks.

Properties of a Supercritical Quasi-perpendicular Interplanetary Shock Propagating in the Terrestrial Foreshock Region

We investigate the properties of an interplanetary (IP) shock (M f = 2.1, θ = 80°) that was detected by Wind on 1999 September 12 and was magnetically connected to the terrestrial bow shock. Key results are obtained concerning how the IP shock modifies the terrestrial foreshock electron and ion dynamics: (1) Intensive Langmuir waves were detected downstream of the IP shock due to the enhanced penetrating terrestrial foreshock electron beams. (2) Whistler heat flux instabilities associated with the oblique precursor whistler pitch-angle scatter the suprathermal electrons, together with the normal betatron acceleration that occurs across the IP shock. (3) The IP shock interacts with the antisunward propagating Alfvén waves/fluctuations, and the shocked plasma shows both Alfvénic and mirror-mode features where Alfvén waves were separated into two parts propagating in opposite directions. (4) Intense specularly reflected gyrating ions were detected around the IP shock, which indicates that the energy dissipation effects at the IP shock depend on both reflected ions and the waves intrinsic to the shock. These results provide new insights into the interaction between an IP shock and the terrestrial foreshock.

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.

Quasi-perpendicular Shock Acceleration and Tidal Disruption Event Radio Flares

Delayed radio flares of optical tidal disruption events (TDEs) indicate the existence of nonrelativistic outflows accompanying TDEs. The interaction of TDE outflows with the surrounding circumnuclear medium creates quasi-perpendicular shocks in the presence of toroidal magnetic fields. Because of the large shock obliquity and large outflow velocity, we find that the shock acceleration induced by TDE outflows generally leads to a steep particle energy spectrum, with the power-law index significantly larger than the “universal” index for a parallel shock. The measured synchrotron spectral indices of recently detected TDE radio flares are consistent with our theoretical expectation. It suggests that the particle acceleration at quasi-perpendicular shocks can be the general acceleration mechanism accounting for the delayed radio emission of TDEs.

Electron Kinetic Entropy across Quasi-Perpendicular Shocks.

We use Magnetospheric Multiscale (MMS) data to study electron kinetic entropy per particle across Earth’s quasi-perpendicular bow shock. We have selected 22 shock crossings covering a wide range of shock conditions. Measured distribution functions are calibrated and corrected for spacecraft potential, secondary electron contamination, lack of measurements at the lowest energies and electron density measurements based on plasma frequency measurements. All crossings display an increase in electron kinetic entropy across the shock being positive or zero within their error margin. There is a strong dependence of on the change in electron temperature, , and the upstream electron plasma beta, . Shocks with large have large . Shocks with smaller are associated with larger . We use the values of , and density change to determine the effective adiabatic index of electrons for each shock crossing. The average effective adiabatic index is .

Electron Acceleration by Moderate-Mach-number Low-β Shocks: Particle-in-Cell Simulations

Particle acceleration is ubiquitous at shock waves, occurring on scales ranging from supernova remnants in the universe to coronal-mass-ejection-driven shocks and planetary bow shocks in the heliosphere. The most promising mechanism responsible for the almost universally observed power-law spectra is diffusive shock acceleration (DSA). However, how electrons are preaccelerated by different shocks to the energy required by the DSA theory is still unclear. In this paper, we perform two-dimensional particle-in-cell plasma simulations to investigate how the magnetic field orientations, with respect to simulation planes, affect electron preacceleration in moderate-Mach-number low- β shocks. Simulation results show that instabilities can be different as the simulation planes capture different trajectories of particles. For magnetic fields perpendicular to the simulation plane, electron cyclotron drift instability dominates in the foot. Electrons can be trapped by the electrostatic wave and undergo shock-surfing acceleration. For magnetic fields lying in the simulation plane, whistler waves produced by modified two-stream instability dominate in the foot and scatter the electrons. In both cases, electrons undergo multistage acceleration in the foot, shock surface, and immediate downstream, during which process shock-surfing acceleration takes place as part of the preacceleration mechanism in moderate-Mach-number quasi-perpendicular shocks.

Analysis of multiscale structures at the quasi-perpendicular Venus bow shock

Context.Solar Orbiter is a European Space Agency mission with a suite of in situ and remote sensing instruments to investigate the physical processes across the inner heliosphere. During the mission, the spacecraft is expected to perform multiple Venus gravity assist maneuvers while providing measurements of the Venusian plasma environment. The first of these occurred on 27 December 2020, in which the spacecraft measured the regions such as the distant and near Venus magnetotail, magnetosheath, and bow shock.Aims.This study aims to investigate the outbound Venus bow shock crossing measured by Solar Orbiter during the first flyby. We study the complex features of the bow shock traversal in which multiple large amplitude magnetic field and density structures were observed as well as higher frequency waves. Our aim is to understand the physical mechanisms responsible for these high amplitude structures, characterize the higher frequency waves, determine the source of the waves, and put these results into context with terrestrial bow shock observations.Methods.High cadence magnetic field, electric field, and electron density measurements were employed to characterize the properties of the large amplitude structures and identify the relevant physical process. Minimum variance analysis, theoretical shock descriptions, coherency analysis, and singular value decomposition were used to study the properties of the higher frequency waves to compare and identify the wave mode.Results.The non-planar features of the bow shock are consistent with shock rippling and/or large amplitude whistler waves. Higher frequency waves are identified as whistler-mode waves, but their properties across the shock imply they may be generated by electron beams and temperature anisotropies.Conclusions.The Venus bow shock at a moderately high Mach number (∼5) in the quasi-perpendicular regime exhibits complex features similar to the Earth’s bow shock at comparable Mach numbers. The study highlights the need to be able to distinguish between large amplitude waves and spatial structures such as shock rippling. The simultaneous high frequency observations also demonstrate the complex nature of energy dissipation at the shock and the important question of understanding cross-scale coupling in these complex regions. These observations will be important to interpreting future planetary missions and additional gravity assist maneuvers.

High-power laser experiment forming a supercritical collisionless shock in a magnetized uniform plasma at rest

We present an experimental method to generate quasiperpendicular supercritical magnetized collisionless shocks. In our experiment, ambient nitrogen (N) plasma is at rest and well magnetized, and it has uniform mass density. The plasma is pushed by laser-driven ablation aluminum (Al) plasma. Streaked optical pyrometry and spatially resolved laser collective Thomson scattering clarify structures of plasma density and temperatures, which are compared with one-dimensional particle-in-cell simulations. It is indicated that just after the laser irradiation, the Al plasma is magnetized by a self-generated Biermann battery field, and the plasma slaps the incident N plasma. The compressed external field in the N plasma reflects N ions, leading to counterstreaming magnetized N flows. Namely, we identify the edge of the reflected N ions. Such interacting plasmas form a magnetized collisionless shock.

Making Waves: Mirror Mode Structures Around Mars Observed by the MAVEN Spacecraft.

We present an in‐depth analysis of a time interval when quasi‐linear mirror mode structures were detected by magnetic field and plasma measurements as observed by the NASA/Mars Atmosphere and Volatile EvolutioN spacecraft. We employ ion and electron spectrometers in tandem to support the magnetic field measurements and confirm that the signatures are indeed mirror modes. Wedged against the magnetic pile‐up boundary, the low‐frequency signatures last on average ∼10 s with corresponding sizes of the order of 15–30 upstream solar wind proton thermal gyroradii, or 10–20 proton gyroradii in the immediate wake of the quasi‐perpendicular bow shock. Their peak‐to‐peak amplitudes are of the order of 30–35 nT with respect to the background field, and appear as a mixture of dips and peaks, suggesting that they may have been at different stages in their evolution. Situated in a marginally stable plasma with β ‖ ∼ 1, we hypothesize that these so‐called magnetic bottles, containing a relatively higher energy and denser ion population with respect to the background plasma, are formed upstream of the spacecraft behind the quasi‐perpendicular shock. These signatures are very reminiscent of magnetic bottles found at other unmagnetized objects such as Venus and comets, also interpreted as mirror modes. Our case study constitutes the first unmistakable identification and characterization of mirror modes at Mars from the joint points of view of magnetic field, electron and ion measurements. Up until now, the lack of high‐temporal resolution plasma measurements has prevented such an in‐depth study.

Collisionless Shocks in the Heliosphere: Foot Width Revisited

Abstract For single-point measurements of quasi-perpendicular shocks, analytical measurements of the foot width are often used to evaluate the velocity of the shock relative to the satellite. This velocity is of crucial importance for in situ observations because it enables the identification of the spatial scale of other regions of the shock front such as a magnetic ramp for which the comprehensive understanding of their formation is not yet achieved. Knowledge of the spatial scale is one of the key parameters for the validation of theoretical models that are developed to explain the formation of these regions. Previously available estimates of the foot width for a quasi-perpendicular shock are based on several simplifications such as zero upstream ion temperature and specular ion reflection by the cross-shock electrostatic potential. The occurrence of specular reflection implies high values of the cross-shock electrostatic potential that significantly exceed the values obtained from in situ measurements. In this paper the effects of nonzero ion temperature and nonspecular ion reflection on the foot width are investigated. It is shown that in the case of nonspecular reflection the foot width can be as small as half of the size of the standard widely used estimate. Results presented here enable more reliable identification of the shock velocity from single-point observations.

Electron Preacceleration at Weak Quasi-perpendicular Intracluster Shocks: Effects of Preexisting Nonthermal Electrons

Abstract Radio relics in the outskirts of galaxy clusters imply the diffusive shock acceleration (DSA) of electrons at merger-driven shocks with Mach number M s ≲ 3–4 in the intracluster medium (ICM). Recent studies have suggested that electron preacceleration and injection, prerequisite steps for DSA, could occur at supercritical shocks with M s ≳ 2.3 in the ICM, thanks to the generation of multiscale waves by microinstabilities such as the Alfvén ion cyclotron (AIC) instability, the electron firehose instability (EFI), and the whistler instability (WI). On the other hand, some relics are observed to have subcritical shocks with M s ≲ 2.3, leaving DSA at such weak shocks as an outstanding problem. Reacceleration of preexisting nonthermal electrons has been contemplated as one of possible solutions for that puzzle. To explore this idea, we perform particle-in-cell simulations for weak quasi-perpendicular shocks in high-β (β = P gas/P B ) plasmas with power-law suprathermal electrons in addition to Maxwellian thermal electrons. We find that suprathermal electrons enhance the excitation of electron-scale waves via the EFI and WI. However, they do not affect the ion reflection and the ensuing generation of ion-scale waves via the AIC instability. The presence of ion-scale waves is the key for the preacceleration of electrons up to the injection momentum; thus, the shock criticality condition for electron injection to DSA is preserved. Based on the results, we conclude that preexisting nonthermal electrons in the preshock region alone would not resolve the issue of electron preacceleration at subcritical ICM shocks.

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.

Ne/O and Fe/O Characteristics of Large Solar Energetic Particle Events during Solar Cycles 23 and 24

Abstract We have examined the Ne/O and Fe/O characteristics of large solar energetic particle (SEP) events at the ion energy range of 3–40 MeV nucleon−1 during solar cycles 23 and 24. In each cycle, the solar activity displays an ∼3 yr rising phase and a longer declining phase. While Fe-poor events only appeared in the declining phase of cycle 23, the properties of Fe-rich events were similar in the rising phases of both cycles. Also, very few Fe-rich events were seen in the declining phase of cycle 24. In addition, the Ne/O data in the corona, solar wind, and SEP events consistently reveal that the characteristics of SEP events are mainly governed by the solar wind turbulence status that exhibits a significant difference between slow and fast streams. During the rising phase of the solar cycles, slow streams are dominated by the two-dimensional turbulence component, which significantly reduces the injection energy of the quasi-perpendicular (Q-Perp) shock acceleration. Also, slow streams have an increased Ne/O ratio and hence enhanced temperature of coronal suprathermals, favoring the occurrence of Fe-rich events. In contrast, in the declining phase of the solar cycles, the fast streams are dominated by the slab turbulence component, which could significantly increase the injection energy of the Q-Perp shock acceleration. Consequently, in fast streams, most Fe-rich events originate from jet suprathermals. The coronal suprathermals may produce the Fe-poor events having abnormally low Ne/O ratios provided the speed of the associated coronal mass ejection is large enough.

Generation of High-frequency Whistler Waves in the Earth’s Quasi-perpendicular Bow Shock

Abstract We use observations from the Magnetospheric Multiscale spacecraft to identify a free energy source for high-frequency whistler waves in the Earth’s quasi-perpendicular bow shock. In the considered measurements, whistlers propagate both parallel and antiparallel to the background magnetic field B 0 with frequencies around 100 Hz (0.15 f ce, where f ce is the electron cyclotron frequency) and amplitudes between 0.1 and 1 nT. Their growth can be attributed to localized pitch angle anisotropy in the electron velocity distribution function that cannot be precisely described by macroscopic parameters like heat flux or temperature anisotropy. However, the presence of heat flux along − B 0 does create preferential conditions for the high-frequency whistler waves that propagate in this direction. These waves are directed partially toward the shock, meaning they can scatter electrons that are streaming from the shock. This prolongs the time the electrons spend in the shock transition region and thereby promotes electron energization.

Ion acceleration to 100 keV by the ExB wave mechanism in collision-less shocks

ABSTRACTIt is shown that ions can be accelerated to about 100 keV in the direction perpendicular to the magnetic field by the ExB mechanism of electrostatic waves. The acceleration occurs in discrete steps of duration being a small fraction of the gyroperiod and can explain observations of ion energization to 10 keV at quasi-perpendicular shocks and to hundreds keV at quasi-parallel shocks. A general expression is provided for the maximum energy of ions accelerated in shocks of arbitrary configuration. The waves involved in the acceleration are related to three cross-field current-driven instabilities: the lower hybrid drift (LHD) instability induced by the density gradients in shocks and shocklets, followed by the modified two-stream (MTS) and electron cyclotron drift (ECD) instabilities, induced by the ExB drift of electrons in the strong LHD wave electric field. The ExB wave mechanism accelerates heavy ions to energies proportional to the atomic mass number, which is consistent with satellite observations upstream of the bow shock and also with observations of post-shocks in supernovae remnants. The results are compared with other acceleration mechanisms traditionally discussed in the literature.

Development of a Turbulent Cascade behind the Bow Shock under Quiet Conditions in the Solar Wind

The bow shock crossing by the solar wind can lead in a number of cases to significant changes in the development of the turbulent cascade. Individual cases previously studied on the basis of experimental measurements of the characteristics of turbulence in the magnetosheath have not yet identified the factors that have the greatest influence on the modification of the turbulent cascade behind the bow shock. In this paper, we consider several observation cases of spectra of the compressible component in magnetosheath fluctuations on two satellites separated in space under calm conditions in the solar wind. This makes it possible to estimate the influence of the magnetosheath boundaries and the bow shock topology on the dynamics of a turbulent cascade when the plasma moves behind the bow shock. It is shown that there is a significant redistribution of energy in the turbulent cascade immediately behind the quasi perpendicular bow shock in the daytime part of the magnetosheath. This affects the magnetohydrodynamic scales, and the cascade properties are restored upon further propagation of the plasma towards the flanks. At the same time, behind the quasi parallel bow shock, the characteristics of the turbulent cascade upon the entry of plasma into the magnetosheath change only on subionic scales.