Quasi-parallel Bow Shock Research Articles

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.

Electron Acceleration and Heating during Magnetic Reconnection in the Earth's Quasi-parallel Bow Shock

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.

Oblique propagation and temperature effects on the resonant right-hand ion beam instability

The resonant right-hand instability (RHI) is often the dominant mode driven by reflected ions upstream of Earth’s quasi-parallel bow shock. In the tradition of Peter Gary, this paper further explores the right-hand instability using numerical solutions of the plasma dispersion relation and non-linear kinetic simulations, with parameters inspired by observations from NASA’s Magnetospheric Multiscale (MMS) mission. Agreement is found between the ion distributions in the particle-in-cell simulations and Magnetospheric Multiscale spacecraft data, which show the gyrophase bunching characteristic of the instability. The non-linear structures created by right-hand instability tend to be stronger when the plasma beta is lower. These structures have sizes of around 100 to 200 ion inertial lengths perpendicular to the magnetic field, presenting planet-sized disturbances to the magnetosphere. 2d and 3D hybrid particle-in-cell simulations show that modes with a range of propagation angles oblique to the magnetic field are excited, providing a ground to understand previous statistical studies of observed foreshock waves.

Dynamics of Earth's bow shock under near-radial interplanetary magnetic field conditions

We investigate the dynamics of Earth's quasi-parallel terrestrial bow shock based on measurements from the Magnetospheric MultiScale (MMS) spacecraft constellation during a period of near-radial interplanetary magnetic conditions, when the interplanetary magnetic field and the solar wind (SW) velocity are nearly anti-parallel. High-speed earthward ion flows with properties that are similar to those of the pristine SW are observed to be embedded within the magnetosheath-like plasma. These flows are accompanied by Interplanetary Magnetic Field (IMF) intensity of less than about 10 nT, compared to nearby magnetosheath intensities of generally greater than 10 nT. The high-speed flow intervals are bounded at their leading and trailing edges by intense fluxes of more energetic ions and large amplitude quasi-sinusoidal magnetic oscillations, similar to ultra-low frequency waves known to steepen and pileup on approach toward Earth to form the quasi-parallel bow shock. The MMS string-of-pearls configuration is aligned with the outbound trajectory and provides inter-spacecraft separations of several hundred km along its near 103 length, allowing sequential observation of the plasma and magnetic field signatures during the event by the four spacecraft. The SW-like interval is most distinct at the outer-most MMS-2 and sequentially less distinct at each of the trailing MMS spacecraft. We discuss the interpretation of this event alternatively as MMS having observed a quasi-rigid bow shock contraction/expansion cycle, ripples or undulations propagating on the bow shock surface, or a more spatially local evolution in the context of either a deeply deformed shock surface or a porous shock surface, as in the three-dimensional patchwork concept of the quasi-parallel bow shock, under the extant near-radial IMF condition.

A global view of Pc3 wave activity in near-Earth space: Results from hybrid-Vlasov simulations

Ultra-low frequency (ULF) waves in the Pc3 range, with periods between 10–45 s, are routinely observed in Earth’s dayside magnetosphere. They are thought to originate in the foreshock, which extends upstream of the quasi-parallel bow shock and is populated with shock-reflected particles. The foreshock is permeated with ULF waves generated by ion beam instabilities, most notably the “30-s” waves whose periods match those of the Pc3 waves and which are carried earthward by the solar wind flow. However, the global picture of Pc3 wave activity from the foreshock to the magnetosphere and its response to changing solar wind conditions is still poorly understood. In this study, we investigate the global distribution and properties of Pc3 waves across near-Earth space using global simulations performed with the hybrid-Vlasov model Vlasiator. The simulations enable us to study the waves in their global context, and compare their properties in the foreshock, magnetosheath and dayside magnetosphere, for different sets of upstream solar wind conditions. We find that in all three regions the Pc3 wave power peaks at higher frequencies when the interplanetary magnetic field (IMF) strength is larger, consistent with previous studies. The Pc3 wave power is significantly enhanced in all three regions for higher solar wind Alfvén Mach number. As this parameter is known to affect the shock properties but has little impact inside the magnetosphere, this brings further support to the magnetospheric waves originating in the foreshock. Other parameters that are found to influence the foreshock wave power are the solar wind density and the IMF cone angle. Inside the magnetosphere, the wave power distribution depends strongly on the IMF orientation, which controls the foreshock position upstream of the bow shock. The wave power is largest when the angle between the IMF and the Sun-Earth line is smallest, suggesting that wave generation and transmission are most efficient in these conditions.

Large‐Scale High‐Speed Jets in Earth's Magnetosheath: Global Hybrid Simulations

AbstractHigh‐speed jets (HSJs) occur frequently in Earth's magnetosheath downstream of the quasiparallel bow shock. They have great impacts on the magnetosheath and the magnetosphere. Using two‐dimensional global hybrid simulations, we investigate the formation and evolution of HSJs with different solar wind conditions. When the quasi‐parallel shock is formed, HSJs begin to appear in the quasi‐parallel magnetosheath. Some elongated HSJs formed at the quasi‐parallel bow shock extend toward the quasi‐perpendicular magnetosheath along with the background magnetosheath flow. As the elongated HSJs moves in the magnetosheath, filamentary structures of the velocity, ion density, and temperature occur in the magnetosheath. The filamentary structures are the traces of HSJs moving in the magnetosheath. Moreover, the Kelvin‐Helmholtz instability can be excited at HSJs, which causes meandering of HSJs. When the interplanetary magnetic field is aligned to the solar wind velocity, the large‐scale HSJs with a parallel (perpendicular) scale size of about 2.5 RE (0.3 RE) are formed at the magnetosheath where the θBn is approaching zero. Then, some HSJs converge, leading to the formation of even larger HSJs with a parallel (perpendicular) scale size of 5 RE (0.6 RE).

Quasi-Parallel Shock Reformation Seen by Magnetospheric Multiscale and Ion-Kinetic Simulations.

Shock waves in collisionless plasmas are among the most efficient particle accelerators in space. Shock reformation is a process important to plasma heating and acceleration, but direct observations of reformation at quasi‐parallel shocks have been lacking. Here, we investigate Earth's quasi‐parallel bow shock with observations by the four Magnetospheric Multiscale spacecraft. The multi‐spacecraft observations provide evidence of short large‐amplitude magnetic structures (SLAMS) causing reformation of the quasi‐parallel shock. We perform an ion‐kinetic Vlasiator simulation of the bow shock and show that SLAMS reforming the bow shock recreates the multi‐spacecraft measurements. This provides a method for identifying shock reformation in the future.

Faster Form of Electron Magnetic Reconnection with a Finite Length X-Line.

Observations in Earth's turbulent magnetosheath downstream of a quasiparallel bow shock reveal a prevalence of electron-scale current sheets favorable for electron-only reconnection where ions are not coupled to the reconnecting magnetic fields. In small-scale turbulence, magnetic structures associated with intense current sheets are limited in all dimensions. And since the coupling of ions are constrained by a minimum length scale, the dynamics of electron reconnection is likely to be 3D. Here, both 2D and 3D kinetic particle-in-cell simulations are used to investigate electron-only reconnection, focusing on the reconnection rate and associated electron flows. A new form of 3D electron-only reconnection spontaneously develops where the magnetic X-line is localized in the out-of-plane (z) direction. The consequence is an enhancement of the reconnection rate compared with two dimensions, which results from differential mass flux out of the diffusion region along z, enabling a faster inflow velocity and thus a larger reconnection rate. This outflow along z is due to the magnetic tension force in z just as the conventional exhaust tension force, allowing particles to leave the diffusion region efficiently along z unlike the 2D configuration.

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.

Stochastic and Quasi-adiabatic Electron Heating in Quasi-parallel Shocks

Abstract Using Magnetospheric Multiscale observations at the Earth’s quasi-parallel bow shock we demonstrate that electrons are heated by two different mechanisms: a quasi-adiabatic heating process during magnetic field compression, characterized by the isotropic temperature relation T / B = ( T 0 / B 0 ) ( B 0 / B ) α with α = 2/3 when the electron heating function ∣ χ e ∣ < 1 , and a stochastic heating process when ∣ χ e ∣ > 1 . Both processes are controlled by the value of the stochastic heating function χ j = m j q j − 1 B − 2 div ( E ⊥ ) for particles with mass m j and charge q j in the electric and magnetic fields E and B . Test-particle simulations are used to show that the stochastic electron heating and acceleration in the studied shock are accomplished by waves at frequencies (0.4–5) f ce (electron gyrofrequency) for bulk heating, and waves f > 5 f ce for acceleration of the tail of the distribution function. Stochastic heating can give rise to flat-top electron distribution functions, frequently observed near shocks. It is also shown that obliquely polarized electric fields of electron cyclotron drift and ion acoustic instabilities scatter the electrons into the parallel direction and keep the isotropy of the electron distribution. The results reported in this paper may be relevant to electron heating and acceleration at interplanetary shocks and other astrophysical shocks.

Magnetic reconnection and kinetic waves generated in the Earth's quasi-parallel bow shock

Magnetic reconnection in quasi-parallel shocks, relevant to the Earth's bow shock, is studied by means of two-dimensional full particle-in-cell simulations. As the Alfvénic Mach number increases, the propagation direction of the waves excited in the transition region changes, and the shock becomes more turbulent with more reconnection sites. In the higher Mach number shock, abundant electron-only reconnection sites are generated with scales on the order of the ion skin depth or less. Non-reconnecting current sheets can also generate electron jets and energy dissipation can occur there as well. However, non-reconnecting current sheets with the magnetic field reversal typically show a smaller energy dissipation rate than reconnecting current sheets. In the shock transition region, two types of waves are responsible for driving reconnection: one has a wavelength around three ion skin depths (di), and the other has a wavelength less than 1 di. Electron and ion distribution functions show that in regions where the former type of waves is excited, there are two ion beams and a single-peaked electron distribution. In contrast, in regions where the latter type of waves is excited, there are multiple electron and ion beams. The waves propagating obliquely to the magnetic field bend the magnetic field lines, and magnetic reconnection occurs where oppositely directed field lines come into contact.

Dynamics of Plasma Turbulence at Earth’s Bow Shock and through the Magnetosheath

Abstract Earth’s magnetosheath can be treated as a natural laboratory to study turbulence development in confined space. The present study focuses on the characteristics of turbulent cascade downstream of the bow shock, where properties of turbulence are known to differ from those in the upstream solar wind. Characteristics of the turbulent spectrum are considered in two distinct points of the magnetosheath for two case studies. The analysis is based on high-resolution measurements of plasma parameters by the Spektr-R spacecraft and magnetic field data by the Themis/Arthemis mission. The measurements are performed for two distinct cases: in the dayside magnetosheath behind the quasi-perpendicular bow shock and in the nightside flank of the magnetosheath behind the quasi-parallel bow shock. The study focuses on the scales at which kinetic effects in plasma become significant and the turbulent spectrum is known to break. The analysis reveals that modification of the fluctuation spectrum at the bow shock is controlled by the distance of the measurement point from the bow shock’s nose. Also, performed statistical results suggest the influence of the large-scale parameters of the upstream solar wind and the type of the bow shock on the turbulent spectrum’s modification in the downstream region.

Magnetosheath Jets and Plasmoids: Characteristics and Formation Mechanisms from Hybrid Simulations

Abstract Magnetosheath jets and plasmoids are very common phenomena downstream of Earth’s quasi-parallel bow shock. As the increase of the dynamic pressure is one of the principal characteristics of magnetosheath jets, the embedded paramagnetic plasmoids have been considered as an special case of the former. Although the properties of both types of structures have been widely studied during the last 20 years, their formation mechanisms have not been examined thoroughly. In this work we perform a 2D local hybrid simulation (kinetic ions – fluid electrons) of a quasi-parallel (θ Bn = 15°), supercritical (M A = 7) collisionless shock in order to study these mechanisms. Specifically, we analyze the formation of one jet and one plasmoid, showing for the first time that they can be produced by different mechanisms related to the same shock. In our simulation, the magnetosheath jet is formed according to the mechanism proposed by Hietala, where at the shock ripples the upstream solar wind suffers locally less deceleration and the flow is focused in the downstream side, producing a compressed and high-velocity region that leads to an increase of dynamic pressure downstream of the shock. The formation of the plasmoid, however, follows a completely new scenario being generated by magnetic reconnection between two plasma layers with opposite B-field orientation in the region just behind the shock.

Classification of Magnetosheath Jets Using Neural Networks and High Resolution OMNI (HRO) Data

Magnetosheath jets are transient, localized dynamic pressure enhancements found downstream of the Earth's bow shock in the magnetosheath region. Using a pre-existing database of magnetosheath jets we train a neural network to distinguish between jets found downstream of a quasi-parallel bow shock θBn 45). The initial database was compiled using MMS measurements in the magnetosheath (downstream) to identify and classify them as "quasi-parallel" or "quasi-perpendicular", while the neural network uses only solar wind (upstream) measurements from the OMNIweb database. To evaluate the results, a comparison with three physics-based modeling approaches is done. It is shown that neural networks are systematically outperforming the other methods by achieving a ~93 agreement with the initial dataset, while the rest of the methods achieve around 80%. The better performance of the neural networks likely is due to the fact that they use information from more solar wind quantities than the physics-based models, even in the absence of certain upstream properties, such as IMF direction.

Non-locality of Earth's quasi-parallel bow shock: injection of thermal protons in a hybrid-Vlasov simulation

Abstract. We study the interaction of solar wind protons with Earth's quasi-parallel bow shock using a hybrid-Vlasov simulation. We employ the global hybrid model Vlasiator to include effects due to bow shock curvature, tenuous upstream populations, and foreshock waves. We investigate the uncertainty of the position of the quasi-parallel bow shock as a function of several plasma properties and find that regions of non-locality or uncertainty of the shock position form and propagate away from the shock nose. Our results support the notion of upstream structures causing the patchwork reconstruction of the quasi-parallel shock front in a non-uniform manner. We propose a novel method for spacecraft data to be used to analyse this quasi-parallel reformation. We combine our hybrid-Vlasov results with test-particle studies and show that proton energization, which is required for injection, takes place throughout a larger shock transition zone. The energization of particles is found regardless of the instantaneous non-locality of the shock front, in agreement with it taking place over a larger region. Distortion of magnetic fields in front of and at the shock is shown to have a significant effect on proton injection. We additionally show that the density of suprathermal reflected particles upstream of the shock may not be a useful metric for the probability of injection at the shock, as foreshock dynamics and particle trapping appear to have a significant effect on energetic-particle accumulation at a given position in space. Our results have implications for statistical and spacecraft studies of the shock injection problem.

Ultra-low-frequency waves in the ion foreshock of Mercury: a global hybrid modelling study

ABSTRACT We study the solar wind interaction with Mercury using a global three-dimensional hybrid model. In the analysed simulation run, we find a well-developed, dynamic Hermean ion foreshock ahead of the quasi-parallel bow shock under upstream solar wind and interplanetary magnetic field (IMF) conditions corresponding to the orbital perihelion of the planet. A portion of the incident solar wind ion flux is scattered back upstream near the quasi-parallel bow shock including both major solar wind ion species, protons and alphas. The scattered particles form the Hermean suprathermal foreshock ion population. A significant part of the suprathermal population is backstreaming with a velocity component towards the Sun in the near-foreshock at the planetocentric distance of few planetary radii in the plane of the IMF. The ion foreshock is associated with large-scale, oblique fast magnetosonic waves in the ultra-low-frequency (ULF) range convecting downstream with the solar wind. The ULF wave period is about 5 s in the analysed upstream condition case at Mercury, which corresponds to the 30-s foreshock waves at Earth when scaled by the IMF magnitude.

Jets in the magnetosheath: IMF control of where they occur

Abstract. Magnetosheath jets are localized regions of plasma that move faster towards the Earth than the surrounding magnetosheath plasma. Due to their high velocities, they can cause indentations when colliding into the magnetopause and trigger processes such as magnetic reconnection and magnetopause surface waves. We statistically study the occurrence of these jets in the subsolar magnetosheath using measurements from the five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft and OMNI solar wind data from 2008 to 2011. We present the observations in the BIMF–vSW plane and study the spatial distribution of jets during different interplanetary magnetic field (IMF) orientations. Jets occur downstream of the quasi-parallel bow shock approximately 9 times as often as downstream of the quasi-perpendicular shock, suggesting that foreshock processes are responsible for most jets. For an oblique IMF, with 30–60∘ cone angle, the occurrence increases monotonically from the quasi-perpendicular side to the quasi-parallel side. This study offers predictability for the numbers, locations, and magnetopause impact rates of jets observed during different IMF orientations, allowing us to better forecast the formation of these jets and their impact on the magnetosphere.

Observations of short large amplitude magnetic structures at the Kronian bow shock

We present observations of Short Large Amplitude Magnetic Structures (SLAMS) upstream of the quasi-parallel bow shock of Saturn. Cassini surveyed the quasi-parallel bow shock regime during 2004 and 2005, and from this time period we chose four events for a detailed study. For our analysis we used the measurements of the Cassini Plasma Spectrometer (CAPS) and the Magnetometer (MAG).Locally the SLAMS act as a fast mode shock wave, and we observed possible ion beam reflection, multiple beams, deceleration and plasma heating of the solar wind protons. These features are in agreement with the near Earth observations. We also detected whistler precursor waves multiple times, which was also documented in studies of the Earth's foreshock region. Since the frequency of the upstream ULF waves detected at Saturn is lower than it is at Earth, it also has an effect on the spatial extension of the SLAM structures, which arise from these waves. With only one spacecraft's measurements it is not possible to study the SLAMS with the same efficiency as with the four-point measurements of the CLUSTER probes, but the basic observational features and the description of their evolutional characteristics are summarized.

Autogenous and efficient acceleration of energetic ions upstream of Earth's bow shock.

Earth and its magnetosphere are immersed in the supersonic flow of the solar-wind plasma that fills interplanetary space. As the solar wind slows and deflects to flow around Earth, or any other obstacle, a 'bow shock' forms within the flow. Under almost all solar-wind conditions, planetary bow shocks such as Earth's are collisionless, supercritical shocks, meaning that they reflect and accelerate a fraction of the incident solar-wind ions as an energy dissipation mechanism1,2, which results in the formation of a region called the ion foreshock3. In the foreshock, large-scale, transient phenomena can develop, such as 'hot flow anomalies'4-9, which are concentrations of shock-reflected, suprathermal ions that are channelled and accumulated along certain structures in the upstream magnetic field. Hot flow anomalies evolve explosively, often resulting in the formation of new shocks along their upstream edges5,10, and potentially contribute to particle acceleration11-13, but there have hitherto been no observations to constrain this acceleration or to confirm the underlying mechanism. Here we report observations of a hot flow anomaly accelerating solar-wind ions from roughly 1-10 kiloelectronvolts up to almost 1,000 kiloelectronvolts. The acceleration mechanism depends on the mass and charge state of the ions and is consistent with first-order Fermi acceleration14,15. The acceleration that we observe results from only the interaction of Earth's bow shock with the solar wind, but produces a much, much larger number of energetic particles compared to what would typically be produced in the foreshock from acceleration at the bow shock. Such autogenous and efficient acceleration at quasi-parallel bow shocks (the normal direction of which are within about 45 degrees of the interplanetary magnetic field direction) provides a potential solution to Fermi's 'injection problem', which requires an as-yet-unexplained seed population of energetic particles, and implies that foreshock transients may be important in the generation of cosmic rays at astrophysical shocks throughout the cosmos.

Effect of Upstream ULF Waves on the Energetic Ion Diffusion at the Earth’s Foreshock. II. Observations

This study reports observations of energetic ions upstream of the Earth's quasi-parallel bow shock by Cluster at times when interspacecraft separation distances were large. We analyze two individual upstream ion events during high solar wind velocity conditions to compare the spatial evolution of partial energetic ion densities in front of the Earth's bow shock along the magnetic field line. Using a bow shock model, we determine the distance of SC1 and SC3 to the bow shock surface parallel to the magnetic field. The CIS-HIA instrument on board Cluster provides partial energetic ion densities in four energy channels between 10 and 32 keV. Using the differences of the partial energetic ion densities observed on SC1 and SC3, and the distances of the spacecraft to the bow shock, we determine the spatial gradient of partial energetic ion densities at various distances from the bow shock. We show, for the first time, that the e-folding distance and the diffusion coefficient of the diffuse ions become unusually small when these ions interact with high-intensity waves generated by a strong field-aligned beam.