Shocks in collisionless plasmas

We present the first direct measurements of the electric field and plasma density with high resolution in Short Large‐Amplitude Magnetic Structures (SLAMS) at a quasi‐parallel shock crossing. Cluster observations at the Earth's bow shock confirm the fast‐mode structure of SLAMS. Using the four Cluster spacecraft, we determine the velocity of the SLAMS vSLAMS and find that E = −vSLAMS × B. This indicates that locally the SLAMS is moving with the same velocity as the plasma, thus indicating trapping of ions. A small‐scale (electron gyroradius) electric field with E ≠ −vSLAMS × B is found at the leading edge of the SLAMS. Downstream of several SLAMS, a wake‐like decrease in the plasma density is observed suggesting the three‐dimensional structure of SLAMS. The scale length of these SLAMS is of the order, or larger, than the satellite separation of 600 km.

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.

Collisionless shocks are considered as one of the most efficient phenomena for the electron acceleration in space and astrophysical plasmas, yet the detailed acceleration process and heating mechanism remain unsolved. Various acceleration and heating mechanisms have so far been proposed and discussed to explain the spacecraft measurements in situ at Earth’s bow shock, involving the large-scale electromagnetic fields, plasma turbulence, and wave-particle interactions. A key element of the acceleration and heatingmechanisms is the spatial scale of the shock transition with respect to the gyro-radius of the electrons [1]. In the simplest picture, since the shock transition occurs on a spatial scale of ion gyro-radius, the electrons behave as magnetized at the shock transition. The cross-shock potential (electrostatic potential drop across the shock transition) plays two distinct roles in electron dynamics [2]. First, the cross-shock potential reduces a certain amount of the upstream flow kinetic energy (mostly carried by the ions due to their mass); Second, the kinetic energy is used to heat the electrons (DC heating). On the other hand, the electrons can also be scattered (or demagnetized) by high-amplitude, randomly-oscillating electromagnetic fields such as turbulence or strong inhomogeneities (AC heating). Space turbulence can potentially scatter the electrons randomly leaving upstream or downstream of the shock ramp region. For a quasiperpendicular shock, the electrons become scattered in a non-adiabatic sense perpendicular to the mean magnetic field (Figure 1). In this paper, the adiabaticity in collisionless shocks is addressed to the studies based on particlein-cell-simulation (PIC). Two important parameters enter a PIC simulation carried out for the study of a collisionless shock: the mass ratio mp/me between ions and electrons and the ratio of the electron plasma frequency to gyrofrequency ωpe/ce, see e.g., [3]. Due to the computational limitations, the usage of the realistic values for the both parameters is not yet possible. The common way to overcome this problem is to find a compromise for the two parameters that can mostly optimize the purpose of the study. The impact of using low frequency ratio of the electron plasma frequency to gyrofrequency in numerical simulations has been discussed in Krasnoselskikh et al. [4]: the electric field is considerably overestimated than it should be for a comparison with the Earth bow shock. Here, I address the question, “What is the consequence of using a smaller frequency ratio upon the adiabatic motion of the electrons”?

The Earth's quasi-parallel bow shock: Review of observations and perspectives for Cluster

We examine the origin of the intensity‐time profile characteristic of diffuse ion events upstream of the earth's bow shock. This profile is believed to result from a rotation of the interplanetary magnetic field which produces a systematic variation in the connection time of field lines with the bow shock. A plateau in the ion intensity is formed if the connection time exceeds the time needed to reach equilibrium between the shock acceleration and ion loss processes. This scenario is tested using the October 31, 1977, upstream diffuse ion event for which simultaneous magnetic field and ion intensity data have been published. We analyze this event using a two‐dimensional Gleeson‐Axford equation to describe the shock acceleration process and a model bow shock whose nose serves as a uniform source of ions injected into the acceleration process. Intensity‐time profiles are calculated for 30‐keV and 120‐keV protons for a range of diffusion coefficients, K∥ and K⊥, using connection times based upon the shock geometry and the magnetic field data. It is found that the calculated and observed profiles are in good general agreement during the growth phase but diverge during the decay. The best overall fit is achieved with diffusion coefficients, K∥(30 keV) ∼ 4×1017 cm² s−1, K∥(120 keV) ∼ 1.2×1018 cm² s−1, and K⊥(120 keV) ∼ 1016 cm² s−1. These values also produce cross‐field anisotropies at 0430 UT which are in satisfactory agreement with the observed anisotropies.

The electron heating at collisionless shocks in near‐Earth space is normally found to be relatively small. We report here on two sets of bow shock crossings observed by the ISEE 1 and ISEE 2 spacecraft in which very large electron temperature increases were found. The two sets of shocks are part of a larger set of 52 bow shock crossings compiled from the ISEE data set. When the shocks with the large electron heating are compared to the rest of the shocks in the compiled set, it is found that the only upstream parameter which is out of the ordinary is the upstream solar wind flow speed Vu. Indeed, for the entire shock set the only upstream parameters which correlate well with the electron heating are the solar wind speed and quantities derived from it. The best correlation among those tested is between the temperature increase (Ted ‐ Teu) and the difference in the square of the bulk flow speed (Vu² ‐ Vd²) across the shock, which is proportional to the total amount of bulk flow energy dissipated by the shock. A subsequent search for bow shock crossings which occur during intervals of high solar wind speed confirms that the electron heating is very large under high‐speed conditions. The first‐order dependence of the electron temperature increase on the available bulk flow energy is consistent with a heating process which is dominated by the macroscopic cross‐shock electrostatic potential jump. This study suggests that the temperature difference is the appropriate measure of electron heating at shocks (rather than the ratio Ted/Teu) and that the first‐order dependence on (Vu² ‐ Vd²) should be normalized out in future studies of electron heating at space shocks.

Energetic ion spectra measured by the Active Magnetospheric Particle Tracer Explorers/Charge Composition Explorer (AMPTE/CCE) downstream from the Earth's quasi‐parallel bow shock (in the quasi‐parallel magnetosheath) and in the plasma depletion layer are compared. In the latter region, energetic ions are from a single source, leakage of magnetospheric ions across the magnetopause and into the plasma depletion layer. In the former region, both the magnetospheric source and shock acceleration of the thermal solar wind population at the quasi‐parallel shock can contribute to the energetic ion spectra. The relative strengths of these two energetic ion sources are determined through the comparison of spectra from the two regions. It is found that magnetospheric leakage can provide an upper limit of 35% of the total energetic H+ population in the quasi‐parallel magnetosheath near the magnetopause in the energy range from ∼10 to ∼80 keV/e and substantially less than this limit for the energetic He2+ population. The rest of the energetic H+ population and nearly all of the energetic He2+ population are accelerated out of the thermal solar wind population through shock acceleration processes. By comparing the energetic and thermal He2+ and H+ populations in the quasi‐parallel magnetosheath, it is found that the quasi‐parallel bow shock is 2‐3 times more efficient at accelerating He2+ than H+. This result is consistent with previous estimates from shock acceleration theory and simulations.

A thorough understanding of collisionless shocks requires knowledge of how different ion species are accelerated across the shock. We investigate a bow shock crossing using the Magnetospheric Multiscale spacecraft after a coronal mass ejection crossed Earth, which led to solar wind consisting of protons, alpha particles, and singly charged helium ions. The three species are resolved upstream of the shock. The low Mach number of the bow shock enabled the ions to be partly distinguished downstream of the shock due to the relatively low ion heating. Some of the protons are specularly reflected and produce quasi‐periodic fine structures in the velocity distribution functions downstream of the shock. Heavier ions are shown to transit the shock without reflection. However, the gyromotion of the heavier ions partially obscures the fine structure of proton distributions. Additionally, the calculated proton moments are unreliable when the different ion species are not distinguished by the particle detector. The need for high time‐resolution mass‐resolving ion detectors when investigating collisionless shocks is discussed.

Using test particle trajectories in a simplified model of a supercritical, oblique, collisionless shock, we investigate the interaction of solar wind thermal ions with the earth's bow shock. We present results for shocks with shock angle (θBn) between 35° and 60° and show that their velocity space signatures are consistent with observations of many upstream ion events, particularly gyrating ions and field‐aligned ion beams. The shock is modeled as a finite, planar discontinuity in the magnetic field and in the electrostatic potential, which is also given an overshoot at the shock. We find that the shock can produce backstreaming ions by reflecting a small fraction of the incident distribution. The reflected particle trajectories are of three types: specularly reflected, multiple traversal, and multiple bounce. All backstreaming reflected ions are found to suffer specular reflection on their first encounter with the shock surface; their subsequent behavior is determined by the angle θBn and their initial conditions.

We present a statistical analysis of large-amplitude bipolar electrostatic structures measured by the Magnetospheric Multiscale spacecraft in the Earth's bow shock. The analysis is based on 371 large-amplitude bipolar structures collected in nine supercritical quasi-perpendicular Earth's bow shock crossings. We have found that 361 of the bipolar structures have negative electrostatic potentials, and only 10 structures (> 1, a parameter range typical of collisionless shocks in the heliosphere and various astrophysical environments. This analysis indicates that the original mechanism of electron surfing acceleration involving electron phase space holes is not likely to be efficient in realistic collisionless shocks.

Abstract– One transient heating mechanism that can potentially explain the formation of most meteoritic chondrules 1–3 Myr after CAIs is shock waves produced by planetary embryos perturbed into eccentric orbits via resonances with Jupiter following its formation. The mechanism includes both bow shocks upstream of resonant bodies and impact vapor plume shocks produced by high‐velocity collisions of the embryos with small nonresonant planetesimals. Here, we investigate the efficiency of both shock processes using an improved planetesimal accretion and orbital evolution code together with previous simulations of vapor plume expansion in the nebula. Only the standard version of the model (with Jupiter assumed to have its present semimajor axis and eccentricity) is considered. After several hundred thousand years of integration time, about 4–5% of remaining embryos have eccentricities greater than about 0.33 and shock velocities at 3 AU exceeding 6 km s−1, currently considered to be a minimum for melting submillimeter‐sized silicate precursors in bow shocks. Most embryos perturbed into highly eccentric orbits are relatively large—half as large as the Moon or larger. Bodies of this size could yield chondrule‐cooling rates during bow shock passage compatible with furnace experiment results. The cumulative area of the midplane that would be traversed by highly eccentric embryos and their associated bow shocks over a period of 1–2 Myr is <1% of the total area. However, future simulations that consider a radially migrating Jupiter and alternate initial distributions of the planetesimal swarm may yield higher efficiencies.

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.

In collisionless magnetosonic shock waves, ions are commonly thought to be decelerated by a dc electrostatic cross‐shock electric field along the shock normal , where γ is the effective polytrope index for electrons. By observation this ratio is ∼1/10 at the earth’s bow shock. When viewed in the de Hoffman‐Teller frame, corresponding changes in the ion kinematics occur. Since the e[ϕ*HT] is an order of magnitude smaller than the ion energy, the ions are not significantly affected by the electrostatic force. They are instead primarily retarded in this frame by the magnetic force. Since this latter force is proportional to the component of B out of the coplanarity plane, infinitesimally thin shock models may not be realistic for the study of the ion and electron dynamics in the de Hoffman‐Teller frame.

We describe experiments which throw light on the physics of high-Mach-number electrostatic shocks. A planar carbon target is irradiated with an 18-nsec laser pulse at a wavelength of 1.05 \ensuremath{\mu}m with an energy of 100--200 J. Carbon plasma ablates supersonically from the solid target at a velocity of 6\ifmmode\times\else\texttimes\fi{}${10}^{7}$ cm ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}1}$. A spherical carbon obstacle is placed in the ablating plasma at a distance of around 1 mm from the primary target where the density is ${10}^{18}$ electrons ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. The density structure of the plasma is probed by interferometry and schlieren photography, and shows a density jump which can be interpreted as a bow shock in a plasma flowing with a Mach number of around 2.2. Measurements of magnetic field imply a plasma \ensuremath{\beta} (8\ensuremath{\pi}nkT/${B}^{2}$) in excess of 100. The shock thickness is occasionally very thin (about 10 \ensuremath{\mu}m), but more usually 50 \ensuremath{\mu}m. In either case the shock thickness is much smaller than the electron and ion Coulomb mean free paths.

This paper provides a brief synthesis of certain aspects of the electric and magnetic field structure of a collisionless shock in the solar wind and outlines how electron heating and acceleration at the shock is related to that structure. Emphasis is on measurements obtained in the vicinity of Earth’s bow shock, although the results should have broad applicability to other shocks in the heliosphere.