Quasi-perpendicular Shock Research Articles

Direct Measurements of Synchrotron-emitting Electrons at Near-Sun Shocks

In this study, we present the first-ever direct measurements of synchrotron-emitting heliospheric traveling shocks, intercepted by the Parker Solar Probe (PSP) during its close encounters. Given that much of our understanding of powerful astrophysical shocks is derived from synchrotron radiation, these observations by PSP provide an unprecedented opportunity to explore how shocks accelerate relativistic electrons and the conditions under which they emit radiation. The probe’s unparalleled capabilities to measure both electromagnetic fields and energetic particles with high precision in the near-Sun environment has allowed us to directly correlate the distribution of relativistic electrons with the resulting photon emissions. Our findings reveal that strong quasi-parallel shocks emit radiation at significantly higher intensities than quasi-perpendicular shocks due to the efficient acceleration of ultrarelativistic electrons. These experimental results are consistent with theory and recent observations of supernova remnant shocks and advance our understanding of shock physics across diverse space environments.

Electron Shock Drift Acceleration at a Low-Mach-number, Low-plasma-beta Quasi-perpendicular Shock

Shock drift acceleration (SDA) 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 their escape from the shock’s loss cone. These electrons are then reflected by the shock and energized by SDA. In this way, the acceleration efficiency of SDA at low-plasma-beta quasi-perpendicular shocks is highly enhanced.

Modification of the turbulence properties at the bow shock: statistical results

Turbulent solar wind is known to be a main driver of the processes inside the magnetosphere, including geomagnetic storms and substorms. Experimental studies of the last decade demonstrate additional ways of interplanetary plasma transport to the magnetosphere, including small-scale processes in the magnetosphere boundary layers. This fact implies that properties of the solar wind turbulence can affect the geomagnetic activity. However, in front of the magnetosphere are a bow shock and a magnetosheath region which contribute to the changes in the properties of the solar wind turbulence and may result in destructions of the association between solar wind turbulence and the magnetosphere. The present study provides the statistics of two-point simultaneous measurements of the turbulence properties in the solar wind and the magnetosheath based on Wind and THEMIS spacecraft data. Changes in the turbulence properties are analyzed for different background conditions. Solar wind bulk speed and temperature are shown to be the main factors that influence the modification of turbulence at the quasi-perpendicular bow shock at frequencies higher than the break frequency (ion transition range). Inside the magnetosheath, significant steepening of spectra occurs with an increase in temperature anisotropy without a connection to the upstream spectrum scaling that underlines the crucial role of the instabilities in turbulence properties behind the bow shock.

Width of the quasi-perpendicular bow shock region at Mars

Width of the quasi-perpendicular bow shock region at Mars

Energy Transport and Conversion Within Earth's Supercritical Bow Shock: The Role of Intense Lower‐Hybrid Whistler Waves

AbstractDetailed analysis of a high Mach number quasiperpendicular Earth bow shock crossing by the Magnetospheric Multiscale (MMS) spacecraft fleet reveal that lower‐hybrid (LH) whistler waves generated in the shock foot region transport energy predominately along the shock surface and slightly toward the shock ramp in the shock normal incidence frame, where wave energy accumulates and is dissipated into the plasma. This suggests the LH whistlers play an integral role in energy reconfiguration at high Mach number collisionless shocks with ramifications to plasma heating. The multipoint observations are used to quantify the wave characteristic parameters (via interferometry), Poynting fluxes, and energy conversion rates D, and to assess their scale dependencies and spatial and temporal properties. The whistler associated energy transport and conversion are found to depend on scale and location within the layer. High‐frequency electrostatic waves yield largest values of D. However, the dominant net energy exchange contribution is from the LH whistlers. In the foot spatially temporally coherent net energy exchange from the plasma to whistlers is observed, whereas deeper in the ramp net wave energy dissipation to the plasma is observed exhibiting significant space‐time variability. These results are consistent with the modified two stream instability driven by the relative drift between reflected ions and electrons as the mechanism for wave growth in the foot. Owing to strong electron heating, whistler energy dissipation in the ramp is attributed to Landau damping, which out‐competes the destabilizing effect of the reflected ion and electron drift.

Drivers of Magnetic Field Amplification at Oblique Shocks: In Situ Observations

Collisionless shocks are ubiquitous structures throughout the Universe. Shock waves in space and astrophysical plasmas convert the energy of a fast-flowing plasma to other forms of energy, including thermal and magnetic energies. Plasma turbulence and high-amplitude electric and magnetic fluctuations are necessary for effective energy conversion and particle acceleration. We survey and characterize in situ observations of reflected ions and magnetic field amplification rates at quasiperpendicular shocks under a wide range of upstream conditions. We report magnetic amplification rates as high as 25 in our current data set. Reflected ions interacting with the incoming plasma create magnetic perturbations that cause magnetic amplification in upstream and downstream regions of quasiperpendicular shocks. Our observations show that, in general, magnetic amplification increases with the fraction of reflected ions, which itself increases with Mach number. Both parameters plateau once full reflection is reached. Magnetic amplification continuously increases with the inverse of the magnetization parameter of the upstream plasma. We find that the extended foot region upstream of shocks and nonlinear processes within that region are key factors for intense magnetic amplification. Our observations at nonrelativistic shocks provide the first experimental evidence that below a certain magnetization threshold, the magnetic amplification efficiency at quasiperpendicular shocks becomes comparable to that at the quasiparallel shocks.

Electron Heating in 2D Particle-in-cell Simulations of Quasi-perpendicular Low-beta Shocks

We measure the thermal electron energization in 1D and 2D particle-in-cell simulations of quasi-perpendicular, low-beta (β p = 0.25) collisionless ion–electron shocks with mass ratio m i/m e = 200, fast Mach number Mms=1 –4, and upstream magnetic field angle θ Bn = 55°–85° from the shock normal nˆ . It is known that shock electron heating is described by an ambipolar, B -parallel electric potential jump, Δϕ ∥, that scales roughly linearly with the electron temperature jump. Our simulations have Δϕ∥/(0.5miush2)∼0.1 –0.2 in units of the pre-shock ions’ bulk kinetic energy, in agreement with prior measurements and simulations. Different ways to measure ϕ ∥, including the use of de Hoffmann–Teller frame fields, agree to tens-of-percent accuracy. Neglecting off-diagonal electron pressure tensor terms can lead to a systematic underestimate of ϕ ∥ in our low-β p shocks. We further focus on two θ Bn = 65° shocks: a Ms=4 ( MA=1.8 ) case with a long, 30d i precursor of whistler waves along nˆ , and a Ms=7 ( MA=3.2 ) case with a shorter, 5d i precursor of whistlers oblique to both nˆ and B ; d i is the ion skin depth. Within the precursors, ϕ ∥ has a secular rise toward the shock along multiple whistler wavelengths and also has localized spikes within magnetic troughs. In a 1D simulation of the Ms=4 , θ Bn = 65° case, ϕ ∥ shows a weak dependence on the electron plasma-to-cyclotron frequency ratio ω pe/Ωce, and ϕ ∥ decreases by a factor of 2 as m i/m e is raised to the true proton–electron value of 1836.

Quasi-perpendicular shocks of galaxy clusters in hybrid kinetic simulations

Context. 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. Aims. 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. Methods. 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. Results. 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 Ms = 3, the magnetic structures and shock front density ripples grow and saturate at wavelengths reaching approximately four ion Larmor radii. Only shocks with Ms ≳ 2.3 develop ripples. At very weak shocks with Ms ≲ 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 Ms = 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.

Quantified Plasma Heating and Energy Dissipation in the Earth’s Quasi-perpendicular Bow Shock

The high-speed solar wind decelerates as it travels through the Earth’s bow shock, during which a portion of the incident flow energy is converted into the plasma thermal energy. However, the energy partition of plasma heating among different species, as well as the energy dissipation mechanism, remains elusive. In this paper, we quantify the plasma heating and the energy dissipation by calculating the pressure–strain interactions in 33 quasi-perpendicular bow shocks observed by the Magnetospheric Multiscale spacecraft. Our results show that the Joule dissipation measured by J·E′ and the quasi-viscous dissipation quantified by PiD are distinct in the examined shocks. We also reveal that ions gain more energy than electrons, and the compressive effect is more important than the incompressible channel in plasma heating. PiD contributed by the gyrotropic pressure tensor is consistently positive for electrons; however, there is no discernible distinction between the gyrotropic and nongyrotropic contribution to PiD for ions.

Nonlinear electron scattering by electrostatic waves in collisionless shocks

We present a theoretical analysis of electron pitch-angle scattering by ion-acoustic electrostatic fluctuations present in the Earth's bow shock and, presumably, collisionless shocks in general. We numerically simulate electron interaction with a single wave packet to demonstrate the scattering through phase bunching and phase trapping and quantify electron pitch-angle scattering in dependence on the wave amplitude and wave normal angle to the local magnetic field. The iterative mapping technique is used to model pitch-angle scattering of electrons by a large number of wave packets, which have been reported in the Earth's bow shock. Assuming that successive electron scatterings are not correlated, we revealed that the long-term dynamics of electrons is diffusive. The diffusion coefficient depends on the ratio $\varPhi _0/W$ between the wave packet amplitude and electron energy, $D\propto (\varPhi _0/W)^{\nu }$ . A quasi-linear scaling ( $\nu \approx 2$ ) is observed for sufficiently small wave amplitudes, $\varPhi _0\lesssim 10^{-3}W$ , while the diffusion is nonlinear ( $1<\nu <2$ ) above this threshold. We show that pitch-angle diffusion of ${\lesssim }1$ keV electrons in the Earth's bow shock can be nonlinear. The corresponding diffusion coefficient scales with the intensity $E_{w}^{2}$ of the electrostatic fluctuations in a nonlinear fashion, $D\propto E_{w}^{\nu }$ with $\nu <2$ , while its expected values in the Earth's bow shock are $D\sim 0.1\unicode{x2013}100$ $(T_{e}/W)^{\nu -1/2}\,{\rm rad}^{2}\,{\rm s}^{-1}$ . We speculate that in the Earth's quasi-perpendicular bow shock the stochastic shock drift acceleration mechanism with pitch-angle scattering provided by the electrostatic fluctuations can contribute to the acceleration of thermal electrons up to approximately 1 keV. The potential effects of a finite perpendicular coherence scale of the wave packets on the efficiency of electron scattering are discussed.

A 3D Parametric Venusian Bow Shock Model with the Effects of Mach Number and Interplanetary Magnetic Field

Using global magnetohydrodynamics simulations, we have developed a three-dimensional parametric model for the Venusian bow shock based on a generalized conic section function defined by six parameters, with the effects of the solar wind magnetosonic Mach number (M MS) and the interplanetary magnetic field (IMF) involved. The parametric model’s results reveal the following findings: (1) The size of the Venusian bow shock is primarily determined by M MS. An increase in M MS results in the bow shock moving closer to Venus and a reduction in its flaring angle. (2) Both the subsolar standoff distance and the bow shock’s flaring angle increase with the strength of the IMF components that are perpendicular to the solar wind flow direction (B Y and B Z in the Venus-centered solar orbital coordinate system), whereas the parallel IMF component (B X ) has a limited impact on the subsolar standoff distance but affects the flaring angle. (3) The cross section of the bow shock is elongated in the direction perpendicular to the IMF on the Y–Z plane, and the elongation degree is enhanced with increasing intensities of B Y and B Z . (4) The quasi-parallel bow shock locates closer to the planet as compared to the quasi-perpendicular bow shock. These findings are in alignment with prior empirical and theoretical models. The influences of M MS and IMF on the bow shock’s position and geometry are attributed to the propagation of fast magnetosonic waves, showing the nature of the formation of a collisionless bow shock under the interaction of magnetized flow with an atmospheric object.

A Comparison of Particle-in-cell and Hybrid Simulations of the Heliospheric Termination Shock

We compare hybrid (kinetic proton, fluid electron) and particle-in-cell (kinetic proton, kinetic electron) simulations of the solar wind termination shock with parameters similar to those observed by Voyager 2 during its crossing. The steady-state results show excellent agreement between the downstream variations in the density, plasma velocity, and magnetic field. The quasi-perpendicular shock accelerates interstellar pickup ions to a maximum energy limited by the size of the computational domain, with somewhat higher fluxes and maximal energies observed in the particle-in-cell simulation, likely due to differences in the cross-shock electric field arising from electron kinetic-scale effects. The higher fluxes may help address recent discrepancies noted between observations and large-scale hybrid simulations.

Formation of electron beam-like components in low-Mach-number quasi-perpendicular shock: Particle-in-cell simulation

Collisionless shocks with low Alfvénic Mach numbers are expected to accelerate electrons, but the underlying physics are still unsolved. Two-dimensional particle-in-cell simulation of low-Mach-number quasi-perpendicular shock in low-β is performed to study the physics of formation of beam-like components with respect to background magnetic fields. The incoming electrons can be trapped and scattered to have velocities along the shock surface by the electrostatic wave in the foot region owing to the free energy in the relative drift between shock reflected ions and upstream electrons. Then fractional electrons can be reflected by the mirror force at the shock overshoot when escaping from the loss cone. The reflection by the mirror force makes the electrons gain quasi-parallel velocities, and the electrons are accelerated in the quasi-parallel direction during trapping in the immediate downstream, forming a beam-like component with respect to magnetic fields. Our results shown in this paper explain the physics of beam formation and could be helpful for accounting for type II radio bursts.

Fast Particle Acceleration in 3D Hybrid Simulations of Quasiperpendicular Shocks.

Understanding the conditions conducive to particle acceleration at collisionless, nonrelativistic shocks is important for the origin of cosmic rays. We use hybrid (kinetic ions-fluid electrons) kinetic simulations to investigate particle acceleration and magnetic field amplification at nonrelativistic, weakly magnetized, quasiperpendicular shocks. So far, no self-consistent kinetic simulation has reported nonthermal tails at quasiperpendicular shocks. Unlike 2D simulations, 3D runs show that protons develop a nonthermal tail spontaneously (i.e., from the thermal bath and without preexisting magnetic turbulence). They are rapidly accelerated via shock drift acceleration up to a maximum energy determined by their escape upstream. We discuss the implications of our results for the phenomenology of heliospheric shocks, supernova remnants, and radio supernovae.

Properties of Electron-scale Magnetic Reconnection at a Quasi-perpendicular Shock

Recent spacecraft observations have shown that magnetic reconnection occurs commonly in turbulent environments at shocks. At quasi-perpendicular shocks, magnetic field lines are bent by the back-streaming reflected ions, which form a current sheet in the foot region, and then electron-scale reconnection occurs when the current sheet is fragmented at the shock front. Here we study magnetic reconnection at a quasi-perpendicular shock by using a two-dimensional particle-in-cell simulation. Collective properties of the reconnection sites from the shock transition to the downstream region are analyzed by adopting a statistical approach to the simulation data. Reconnecting current sheets are found to be densely distributed near the shock front, with a reconnection electric field larger than those in the downstream region. By tracing a reconnection site from its formation until it is convected downstream, we show the reconnection proceeds intermittently after an active stage near the shock front. Our tracing further shows that, in addition to being originated from the shock front, reconnection in the downstream region can also occur locally, driven by turbulent flows therein. The results help us better understand the evolution of electron-scale reconnection at a perpendicular shock.

Magnetohydrodynamic Shocks Revisited: Magnetically Constraining the Upstream Solar Wind Condition

Magnetohydrodynamic (MHD) shocks are commonly found in various space and astrophysical systems. One often encounters the problem that only the magnetic field data are available when studying interplanetary shocks and planetary bow shocks in the solar system, and not the plasma data due to instrumental and/or telemetry limitations. We aim to reveal the mathematical structure of the MHD Rankine–Hugoniot relation under the condition that magnetic field changes across the shock are known, which can be devised into a diagnosis tool to constrain the shock parameters. The perturbative solution is already known for the Rankine–Hugoniot equation. The solution is combined with the condition of the de Hoffmann–Teller frame for the vanishing convective electric field, and we obtain a two-dimensional matrix equation for the density jump and the Alfvén Mach number. The lesson is that the shock parameters (density jump and Alfvén Mach number) are analytically obtained by inverting the MHD Rankine–Hugoniot equation under the condition that the plasma beta is either a priori set or known. Further numerical studies indicate that the presented shock jump estimation works particularly well for quasi-perpendicular shocks. Moreover, a test case with the Earth bow shock crossing data supports our theoretical development. The presented method opens the door to determining or constraining the shock parameters even if the data are limited to the magnetic field only.

Effects of Coronal Magnetic Field Configuration on Particle Acceleration and Release during the Ground Level Enhancement Events in Solar Cycle 24

Ground level enhancements (GLEs) are extreme solar energetic particle (SEP) events that are of particular importance in space weather. In solar cycle 24, two GLEs were recorded on 2012 May 17 (GLE 71) and 2017 September 10 (GLE 72), respectively, using a range of advanced modern instruments. Here we conduct a comparative analysis of the two events by focusing on the effects of large-scale magnetic field configuration near active regions on particle acceleration and release. Although the active regions are both located near the western limb, temporal variations of SEP intensities and energy spectra measured in situ display different behaviors at early stages. By combining a potential field model, we find the coronal mass ejection (CME) in GLE 71 originated below the streamer belt, while in GLE 72 it originated near the edge of the streamer belt. We reconstruct the CME shock fronts with an ellipsoid model based on nearly simultaneous coronagraph images from multiple viewpoints and further derive the 3D shock geometry at the GLE onset. The highest-energy particles are primarily accelerated in the shock–streamer interaction regions, i.e., likely at the nose of the shock in GLE 71 and the eastern flank in GLE 72, due to quasi-perpendicular shock geometry and confinement of closed fields. Subsequently, they are released to the field lines connecting to near-Earth spacecraft when the shocks move through the streamer cusp region. This suggests that magnetic structures in the corona, especially shock–streamer interactions, may have played an important role in the acceleration and release of the highest-energy particles in the two events.

Intermittency at Earth's bow shock: Measures of turbulence in quasi-parallel and quasi-perpendicular shocks

Turbulent plasmas such as the solar wind and magnetosheath exhibit an energy cascade that is present across a broad range of scales, from the stirring scale at which energy is injected, down to the smallest scales where energy is dissipated through processes such as reconnection and wave–particle interactions. Recent observations of Earth's bow shock reveal a disordered or turbulent transition region exhibiting features of turbulent dissipation, like reconnecting current sheets. We used observations from magnetospheric multiscale (MMS) over four separate bow shock crossings of varying shock normal angle to characterize turbulence in the shock transition region and how it evolves toward the magnetosheath. These cases studies have been chosen to ensure validity of Taylor's hypothesis, which we discuss in depth. We observe the magnetic spectrum evolving by fitting power laws over many short intervals, finding that the power-law index in the shock transition region is separable from the upstream and downstream plasma, for both quasi-perpendicular and quasi-parallel shocks. Across the shock, we see a change in the breakpoint location between inertial and ion power-law slopes. We also observe the evolution of scale-independent kurtosis of magnetic fluctuations across the shock, finding a reduction of high kurtosis intervals downstream of the shock. Finally, we adapt a method for calculating correlation length to include a high-pass filter, allowing estimates for changes in correlation length across the shock. In a quasi-perpendicular shock, we find the correlation length to be significantly smaller in the magnetosheath than in solar wind; however, the opposite can occur for quasi-parallel shocks.

In Situ Observation of Electron Acceleration by a Double Layer in the Bow Shock

The importance of the electric potential along the field direction in the acceleration of electrons in the quasi-perpendicular bow shock has been proposed. Nevertheless, the mechanism by which electrons are accelerated in the bow shock remains unclear from the perspective of in situ observation. In this study, utilizing data obtained by the Magnetospheric Multiscale mission, we identify a double layer (DL) located within the transition layer of the quasi-perpendicular bow shock. It is found that the electric potential generated by this DL corresponds well with an increase in electron parallel temperature, suggesting that the DL can effectively accelerate the electrons in the bow shock. Furthermore, strong whistler emissions have been detected in the vicinity of this DL. It seems that the electrons accelerated by the DL could potentially supply the necessary free energy to excite the observed whistler waves. Thus, the presence of whistler waves provides indirect evidence of an electron beam generated by the DL in bow shock. Our observations demonstrate that the DL can accelerate electrons effectively and impact the electron dynamics within the bow shock.

Planar Magnetic Structures Downstream of Coronal Mass Ejection–driven Shocks in the Inner Heliosphere

Planar magnetic structures (PMSs), characterized by interplanetary magnetic field vectors remaining parallel to a specific plane, are commonly observed in the solar wind, especially in the sheath region of interplanetary coronal mass ejections (ICMEs). In this study, PMS events in the 2 hr regions downstream of ICME-driven shocks were investigated to reveal the relationship between PMS formation and shock environment using data collected by the Parker Solar Probe, Solar Orbiter, and Venus Express spacecraft in the inner heliosphere. PMS events are identified in the majority (around 93%) of the postshock 2 hr regions, with transit times ranging from 10 to 120 minutes, which demonstrates their common occurrence associated with ICME-driven shocks. About 33% of the detected PMS events cover the whole 2 hr intervals, called full PMS events. Most of the full PMS events are observed in the downstream region of quasi-perpendicular shocks. In addition, statistical results show that full PMS events occurring in the downstream region of quasi-perpendicular shocks are generally associated with higher magnetic compression ratios, which implies that full PMS events are more likely to be formed in the downstream region of strong quasi-perpendicular shocks.