Collisionless 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.

MMS Observation of Two‐Step Electron Acceleration at Earth's Bow Shock

AbstractWe use the Magnetospheric Multiscale mission to observe a bi‐directional electron acceleration event in the electron foreshock upstream of Earth's quasi‐perpendicular collisionless bow shock. The acceleration region is associated with a decrease in wave activity, inconsistent with common electron acceleration mechanisms such as Diffusive Shock Acceleration and Stochastic Shock Drift Acceleration. We propose a two‐step acceleration process where an electron field‐aligned beam acts as a seed population further accelerated by a shrinking magnetic bottle process, with the shock acting as the magnetic mirror(s).

Earth's magnetosphere and outer radiation belt under sub-Alfvénic solar wind.

The interaction between Earth's magnetic field and the solar wind results in the formation of a collisionless bow shock 60,000–100,000 km upstream of our planet, as long as the solar wind fast magnetosonic Mach (hereafter Mach) number exceeds unity. Here, we present one of those extremely rare instances, when the solar wind Mach number reached steady values <1 for several hours on 17 January 2013. Simultaneous measurements by more than ten spacecraft in the near-Earth environment reveal the evanescence of the bow shock, the sunward motion of the magnetopause and the extremely rapid and intense loss of electrons in the outer radiation belt. This study allows us to directly observe the state of the inner magnetosphere, including the radiation belts during a type of solar wind-magnetosphere coupling which is unusual for planets in our solar system but may be common for close-in extrasolar planets.

Kinetic structures of quasi-perpendicular shocks in global particle-in-cell simulations

We carried out global Particle-in-Cell simulations of the interaction between the solar wind and a magnetosphere to study the kinetic collisionless physics in super-critical quasi-perpendicular shocks. After an initial simulation transient, a collisionless bow shock forms as a result of the interaction of the solar wind and a planet magnetic dipole. The shock ramp has a thickness of approximately one ion skin depth and is followed by a trailing wave train in the shock downstream. At the downstream edge of the bow shock, whistler waves propagate along the magnetic field lines and the presence of electron cyclotron waves has been identified. A small part of the solar wind ion population is specularly reflected by the shock while a larger part is deflected and heated by the shock. Solar wind ions and electrons are heated in the perpendicular directions. Ions are accelerated in the perpendicular direction in the trailing wave train region. This work is an initial effort to study the electron and ion kinetic effects developed near the bow shock in a realistic magnetic field configuration.

Ordinary mode instability associated with thermal ring distribution

The purely growing ordinary (O) mode instability driven by excessive parallel temperature anisotropy has recently received renewed attention owing to its potential applicability to the solar wind plasma. Previous studies of O mode instability have assumed either bi-Maxwellian or counter-streaming velocity distributions. For solar wind plasma trapped in magnetic mirror-like geometry such as magnetic clouds or in the vicinity of the Earth's collisionless bow shock environment, however, the velocity distribution function may possess a loss-cone feature. The O-mode instability in such a case may be excited for cyclotron harmonics as well as the purely growing branch. The present paper investigates the O-mode instability for plasmas characterized by the parallel Maxwellian distribution and perpendicular thermal ring velocity distribution in order to understand the general stability characteristics.

Vlasiator: First global hybrid-Vlasov simulations of Earth's foreshock and magnetosheath

We present results from a new hybrid-Vlasov simulation code, Vlasiator, designed for global magnetospheric simulations. Vlasiator represents ions by a six-dimensional distribution function propagated using a finite volume approach. The distribution functions are self-consistently coupled to electromagnetic fields with electrons modeled as a charge-neutralizing fluid. A novel sparse representation of the distribution function reduces the computational demands of the problem by up to two orders of magnitude. The capabilities of the code are demonstrated by reproducing characteristics of the ion/ion right-hand resonant beam instability, as well as key features of the collisionless bow shock and magnetosheath in front of the Earth's magnetosphere in global five-dimensional (two in ordinary space, three in velocity space) simulations. We find that Vlasiator reproduces the ion velocity distribution functions with quality comparable to spacecraft observations.

Quantified energy dissipation rates in the terrestrial bow shock: 2. Waves and dissipation

AbstractWe present the first quantified measure of the energy dissipation rates, due to wave‐particle interactions, in the transition region of the Earth's collisionless bow shock using data from the Time History of Events and Macroscale Interactions during Substorms spacecraft. Our results show that wave‐particle interactions can regulate the global structure and dominate the energy dissipation of collisionless shocks. In every bow shock crossing examined, we observed both low‐frequency (&lt;10 Hz) and high‐frequency (10 Hz) electromagnetic waves throughout the entire transition region and into the magnetosheath. The low‐frequency waves were consistent with magnetosonic‐whistler waves. The high‐frequency waves were combinations of ion‐acoustic waves, electron cyclotron drift instability driven waves, electrostatic solitary waves, and whistler mode waves. The high‐frequency waves had the following: (1) peak amplitudes exceeding δB∼ 10 nT and δE∼ 300 mV/m, though more typical values were δB∼ 0.1–1.0 nT and δE∼ 10–50 mV/m; (2) Poynting fluxes in excess of 2000 μW m−2 (typical values were ∼1–10 μW m−2); (3) resistivities &gt; 9000 Ω m; and (4) associated energy dissipation rates &gt;10 μW m−3. The dissipation rates due to wave‐particle interactions exceeded rates necessary to explain the increase in entropy across the shock ramps for ∼90% of the wave burst durations. For ∼22% of these times, the wave‐particle interactions needed to only be ≤ 0.1% efficient to balance the nonlinear wave steepening that produced the shock waves. These results show that wave‐particle interactions have the capacity to regulate the global structure and dominate the energy dissipation of collisionless shocks.

Isothermal magnetosheath electrons due to nonlocal electron cross talk

Heating of the various plasma species at the Earth's collisionless bow shock is not fully understood. Although the total amount of heating is constrained by the one‐fluid Rankine‐Hugoniot relations in terms of local plasma conditions, the partition of energy between, e.g., electrons and ions, is influenced by particle kinetics which are not considered in the Rankine‐Hugoniot approach. Additionally, in this paper we demonstrate the impact of nonlocal effects. Here we model the effects of shock‐heated electrons which traverse the magnetosheath to arrive at another point on the bow shock surface. We construct the distribution of electrons immediately downstream of each point on the bow shock from two populations: local solar wind electrons entering the magnetosheath for the first time and previously shocked electrons which have traversed the magnetosheath. We determine the self‐consistent cross‐shock potential at each point such that the resulting electron distribution gives a downstream plasma which is neutral and has zero parallel current. This leads to very little variation in the downstream electron temperature everywhere around the curved bow shock, in spite of large differences in the total (Rankine‐Hugoniot) downstream temperature. Consequently, the partition of heating between electrons and ions at the shock, i.e., the equation of state, contains nonlocal contributions. We show that heating properties at the point where the shock is exactly perpendicular controls electron heating throughout the rest of the shock surface.

Active current sheets and candidate hot flow anomalies upstream of Mercury's bow shock

Hot flow anomalies (HFAs) represent a subset of solar wind discontinuities interacting with collisionless bow shocks. They are typically formed when the normal component of the motional (convective) electric field points toward the embedded current sheet on at least one of its sides. The core region of an HFA contains hot and highly deflected ion flows and rather low and turbulent magnetic field. In this paper, we report observations of possible HFA‐like events at Mercury identified over a course of two planetary years. Using data from the orbital phase of the MESSENGER mission, we identify a representative ensemble of active current sheets magnetically connected to Mercury's bow shock. We show that some of these events exhibit magnetic and particle signatures of HFAs similar to those observed at other planets, and present their key physical characteristics. Our analysis suggests that Mercury's bow shock does not only mediate the flow of supersonic solar wind plasma but also provides conditions for local particle acceleration and heating as predicted by previous numerical simulations. Together with earlier observations of HFA activity at Earth, Venus, Mars, and Saturn, our results confirm that hot flow anomalies could be a common property of planetary bow shocks and show that the characteristic size of these events is controlled by the bow shock standoff distance and/or local solar wind conditions.

Ion distributions upstream and downstream of the Earth's bow shock: first results from Vlasiator

Abstract. A novel hybrid-Vlasov code, Vlasiator, is developed for global simulations of magnetospheric plasma kinetics. The code is applied to model the collisionless bow shock on scales of the Earth's magnetosphere in two spatial dimensions and three dimensions in velocity space retrieving ion distribution functions over the entire foreshock and magnetosheath regions with unprecedented detail. The hybrid-Vlasov approach produces noise-free uniformly discretized ion distribution functions comparable to those measured in situ by spacecraft. Vlasiator can reproduce features of the ion foreshock and magnetosheath well known from spacecraft observations, such as compressional magnetosonic waves generated by backstreaming ion populations in the foreshock and mirror modes in the magnetosheath. An overview of ion distributions from various regions of the bow shock is presented, demonstrating the great opportunities for comparison with multi-spacecraft observations.

Application of a total variation diminishing scheme to electromagnetic hybrid particle-in-cell plasma simulation

A discretization procedure for a total variation diminishing (TVD) scheme is introduced to an electromagnetic hybrid particle-in-cell (PIC) plasma simulation code in order to improve the numerical stability and resolution when calculating the plasma flow field in which magnetic field discontinuities (for example, Rankine–Hugoniot jump conditions for shock waves) are generated. In the hybrid PIC code used in this study, ions are treated as particles and electrons are assumed to be an inertia-less (mass-less) fluid. In the numerical results of one-dimensional test simulations, the TVD scheme significantly prevents non-physical, numerical oscillations, which would ordinarily be produced in the solution when the convection term of the magnetic induction equation in the hybrid PIC code is discretized by central difference schemes at magnetic field discontinuities. Furthermore, a two-dimensional simulation of the global structure of a collision-less bow shock, which is suitable for practical use, makes it possible to clearly capture the bow shock by using the hybrid PIC code with the TVD scheme.

A Review of Density Holes Upstream of Earth's Bow Shock

Larmor size transient structures with density depletions as large as 99% of ambient solar wind density levels occur commonly upstream of Earth's collisionless bow shock. These “density holes” have a mean duration of 17.9±10.4 s but holes as short as 4 s have been observed. The average fractional density depletion (<I>δn/n</I>) inside the holes is 0.68±0.14. The density of the upstream edge moving in the sunward direction can be enhanced by five or more times the solar wind density. Particle distributions show the steepened edge can behave like a shock, and measured local field geometries and Mach number support this view. Similarly shaped magnetic holes accompany the density holes indicating strong coupling between fields and particles. Current densities as large as 150 nA·m^-2 are observed at the leading compressed edge. The waves are elliptically polarized and rotating in the sense of ions (left hand) in the plasma frame. The waves appear to grow and steepen as the density holes convect with the solar wind toward the Earth. The transient nature of density holes suggests that the temporal features could represent the different stages of nonlinear evolutionary processes that produce a shock-like structure. The density holes are only observed with upstream particles, suggesting that back-streaming particles interacting with the solar wind are important. The significance of these observations is still being investigated.

Analysis of Collisionless Shock Turbulence by Using Virtual Satellites in 2-D Full Particle-in-Cell Simulations

Two-dimensional full particle electromagnetic particle-in-cell simulations are used in order to reproduce and analyze in details the intrinsic turbulence of the terrestrial collisionless bow shock. In order to compare numerical results and local experimental measurements performed by the four-satellite space mission CLUSTER, one has developed ldquovirtual proberdquo techniques crossing the ldquonumericalrdquo shock in order to mimic the real CLUSTER mission. Numerical results shown in this paper illustrate the measurements of a turbulent macroscopic magnetic field obtained through a time-varying and inhomogeneous shock front.

Simulation study of magnetic holes at the Earth's collisionless bow shock

Recent observations by the Cluster and Double Star spacecraft at the Earth's bow shock have revealed localized magnetic field and density holes in the solar wind plasma. These structures are characterized by a local depletion of the magnetic field and the plasma density, and by a strong increase of the plasma temperature inside the magnetic and density cavities. Our objective here is to report results of a hybrid-Vlasov simulations of ion-Larmor-radius sized plasma density cavities with parameters that are representative of the high-beta solar wind plasma at the Earth's bow shock. We observe the asymmetric self-steepening and shock-formation of the cavity, and a strong localized temperature increase (by a factor of 5–7) of the plasma due to reflections and shock surfing of the ions against the collisionless shock. Temperature maxima are correlated with density minima, in agreement with Cluster observations. For oblique incidence of the solar wind, we observe efficient acceleration of ions along the magnetic field lines by the shock drift acceleration process.

Macrostructure of collisionless bow shocks: 2. ULF waves in the foreshock and magnetosheath

We perform global hybrid (kinetic ions and fluid electrons) simulations of the solar wind coupling with magnetic dipoles of different strength and study foreshock morphology and its influence on the bow shock and magnetosheath. The advantage of the hybrid code over fluid codes is that it treats ion‐scale microphysics in the context of the global interaction. We study the characteristics of the ultralow‐frequency (ULF) waves generated by kinetic instabilities and find two types of waves: (1) sinusoidal almost parallel propagating waves and (2) highly compressive obliquely propagating fluctuations. In contrast to suggestions made in the past, we show that compressive waves found near the shock do not evolve from the sinusoidal wave population but rather are generated by a different ion population. We find that the sinusoidal waves are generated by field‐aligned backstreaming ions, while the compressive waves near the shock are generated by gyrating ion beams closer to the shock. Our results show that, for low dipole magnetization, noncompressive waves dominate the foreshock, while compressive waves grow just in a very small region and do not have time to evolve, so no quasi‐parallel shock is formed. In contrast, when the system scale size is much larger than an ion inertial length, highly compressive waves convect into the quasi‐parallel region, evolving into large steepened structures that eventually form the shock transition. These waves play an active role in shock dissipation processes and eventually form part of the wave spectra in the magnetosheath. Comparison of our results with observations shows that the characteristics of sinusoidal waves in our simulations resemble the properties of 30‐s sinusoidal quasi‐monochromatic waves in the Earth's foreshock, while compressive waves have similar properties to the observed right‐handed steepened fluctuations. Downstream from the shock, the magnetosheath is permeated by a variety of waves that result from the convection of upstream waves and also from local generation. The wave characteristics are different in the quasi‐parallel and quasi‐perpendicular parts of the magnetosheath.

Macrostructure of collisionless bow shocks: 1. Scale lengths

The global structure of collisionless bow shocks is investigated using a 2.5‐dimensional electromagnetic hybrid code. This allows us to study the macrostructure of the shock while accounting for microphysical processes at the shock. The study entails the interaction of solar wind with magnetic dipoles of varying strength. For very weak dipoles the interaction does not lead to formation of a shock since the obstacle is not strong enough for the flow to become subsonic. For lager dipole strengths, a bow shock/wave is formed due to the presence of a plasma stagnation region in front of the dipole. It is found that the quasi‐perpendicular part of this boundary corresponds to a true shock wave, whereas the quasi‐parallel side consists of a magnetosonic wave followed by a rotational discontinuity. The backstreaming ions in the foreshock of this interaction lead to the generation of parallel propagating sinusoidal waves. These waves result in beam scattering, however, do not affect the solar wind. The formation of quasi‐parallel shock is tightly connected to the generation of oblique compressional waves. These waves are generated by backstreaming ions having a beam‐ring distribution function and are an inherent part of the shock dissipation processes. The results demonstrate that the two classes of 30 s ULF waves observed in the ion foreshock are unrelated. The results also demonstrate that at least in 2.5‐dimensional, plasma scales determine the nature of the bow shock to a large extent although system size can influence both particle acceleration and evolution of ULF waves.

Wavelength and decay length of density overshoot structure in supercritical, collisionless bow shocks

Above some critical Mach number, quasiperpendicular collisionless shocks are known to exhibit “overshoot” and “undershoot” structure thought to be associated with the motion of ions trapped at the shock front. Using spacecraft potential data from the Cluster spacecraft, the overshoot/undershoot density structure at 56 crossings of the quasiperpendicular bow shock is studied. The envelope of the absolute value of the density, in most cases, decays exponentially and these envelopes are fitted to a decaying function from which we calculate the decay length scale. The overshoot/undershoot wavelength is also estimated using the zero crossings of the density profile and a good correlation between the average wavelength and the convected ion gyroradius is found: the wavelength is approximately two to three times the ion gyroradius. There is no evidence of a strong correlation between the wavelength and the ion inertial length. Similar results are found for the decay length, which also seems to be ordered by the convected ion gyroradius.

Electrostatic Turbulence and Debye-Scale Structures Associated with Electron Thermalization at Collisionless Shocks

We analyze measurements of bipolar, Debye-scale electrostatic structures and turbulence measured in the transition region of the Earth's collisionless bow shock. In this region, the solar wind electron population is slowed and heated, and we show that this turbulence correlates well in amplitude with the measured electron temperature change. The observed bipolar structures are highly oblate and longitudinally polarized and may instantaneously carry up to 10% of the plasma energy ψ ≡ e/kbTe ≈ 0.1 before dissipating. The relationship between ψ and the field-aligned scale size Δ∥ of the Gaussian potential suggests that the bipolar structures are BGK trapped particle equilibria or electron hole modes. We suggest a generation scenario and a potential role in dissipation.

Upstream ULF waves and energetic electrons associated with the lunar wake: Detection of precursor activity

We present observations of precursor ULF wave activity and energetic electron flows detected by the WIND spacecraft just prior to entry of the lunar wake on 27 December 1994. This activity occurs upstream of the wake on field lines directly connected to the wake penumbra region. The activity ceases near the penumbra entrance. The observations of upstream ULF wave activity and solar wind counterstreaming electron flows is similar to observations made upstream of collisionless bow shocks. Analogously, the wake precursor region is characterized by thermalization and information propagation ahead of the wake structure.

Measurement of the potential drop across the Earth's collisionless bow shock

The normal component of the DC electric field measured on ISEE‐1 usually exhibits an enhancement of a few mV/m over both upstream and downstream values at the Earth's bow shock. Using the measured relative velocity between the shock and the spacecraft (from the ISEE‐1/2 time delay in the magnetometer data) we can transform the observed E enhancement to a potential drop (ΔØ). For a subcritical shock the potential drop was very close to the measured change of particle kinetic energy (ΔØ ≃ 280 V on Day 330, 1977), while for a supercritical shock the potential drop was only a fraction of the measured change of kinetic energy (ΔØ ≃ 140 V on Day 324, 1977). Overshooting of the potential is indicated in the data by a change in sign of the E enhancement.