Supercritical Quasi-perpendicular Shock Research Articles

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

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

On the Nature and Origin of Bipolar Electrostatic Structures in the Earth's Bow Shock

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.

Nonstationary Quasiperpendicular Shock and Ion Reflection at Mars

AbstractCollisionless shocks in space plasma are regions of heating and acceleration of charged particles and dissipation of kinetic energy. These accelerated particles are the source of electromagnetic emissions from supernova remnants and other astrophysical structures. At high Mach numbers, shocks can be inherently nonstationary and exhibit modulated energy transfer and recurring plasma compression areas in the form of reformation. We use data from the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft to study reformation of the Martian bow shock, which has a relatively high curvature compared to that at Earth, and the upstream solar wind is often mass loaded with a population of pickup ions. We show evidence of ion reflection effects in reformation of a supercritical quasiperpendicular shock.

TRANSPORT OF SOLAR WIND H+ AND He++ IONS ACROSS EARTH’S BOW SHOCK

ABSTRACT We have investigated the dependence of mass, energy, and charge of solar wind (SW) transport across Earth’s bow shock. An examination of 111 crossings during quiet SW in both quasi-perpendicular and quasi-parallel shock regions shows that 64 crossings had various degrees of heating and thermalization of SW. We found 22 crossings where the SW speed was <400 km s−1. The shock potential of a typical supercritical quasi-perpendicular shock estimated from deceleration of the SW and cutoff energy of electron flat top distribution is ∼50 Volts. We find that the temperatures of H+ and He++ beams that penetrate the shock can sometimes be nearly the same in the upstream and downstream regions, indicating little or no heating had occurred crossing the bow shock. None of the models predict that the SW can cross the bow shock without heating. Our observations are important constraints for new models of collisionless shocks.

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.

Dispersion of low frequency plasma waves upstream of the quasi-perpendicular terrestrial bow shock

Abstract. Low frequency waves in the foot of a supercritical quasi-perpendicular shock front have been observed since the very early in situ observations of the terrestrial bow shock (Guha et al., 1972). The great attention that has been devoted to these type of waves since the first observations is explained by the key role attributed to them in the processes of energy redistribution in the shock front by various theoretical models. In some models, these waves play the role of the intermediator between the ions and electrons. It is assumed that they are generated by plasma instability that exist due to the counter-streaming flows of incident and reflected ions. In the second type of models, these waves result from the evolution of the shock front itself in the quasi-periodic process of steepening and overturning of the magnetic ramp. However, the range of the observed frequencies in the spacecraft frame are not enough to distinguish the origin of the observed waves. It also requires the determination of the wave vectors and the plasma frame frequencies. Multipoint measurements within the wave coherence length are needed for an ambiguous determination of the wave vectors. In the main multi-point missions such as ISEE, AMPTE, Cluster and THEMIS, the spacecraft separation is too large for such a wave vector determination and therefore only very few case studies are published (mainly for AMPTE UKS AMPTE IRM pair). Here we present the observations of upstream low frequency waves by the Cluster spacecraft which took place on 19 February 2002. The spacecraft separation during the crossing of the bow shock was small enough to determine the wave vectors and allowed the identification of the plasma wave dispersion relation for the observed waves. Presented results are compared with whistler wave dispersion and it is shown that contrary to previous studies based on the AMPTE data, the phase velocity in the shock frame is directed downstream. The consequences of this finding for both types of models that were developed to explain the generation of these waves are discussed.

Heating heavy ions in the polar corona by collisionless shocks: A one-dimensional simulation

Recently a new model for explaining the observations of preferential heating of heavy ions in the polar solar corona was proposed ( Zimbardo, 2010, 2011). In that model the ion energization mechanism is the ion reflection off supercritical quasi-perpendicular collisionless shocks in the corona and the subsequent acceleration by the motional electric field E = − V × B/ c. The mechanism of heavy ion reflection is based on ion gyration in the magnetic overshoot of the shock. The acceleration due to the motional electric field is perpendicular to the magnetic field, giving rise to large temperature anisotropy with T ⊥ ≫ T ∥, in agreement with SoHO observations. Such a model is tested here by means of a one dimensional test particle simulation where ions are launched toward electric and magnetic profiles representing the shock transition. We study the dynamics of O 5+, as representative of coronal heavy ions for Alfvénic Mach numbers of 2–4, as appropriate to solar corona. It is found that O 5+ ions are easily reflected and gain more than mass proportional energy with respect to protons.

Acceleration of heavy ions by perpendicular collisionless shocks: Impact of the shock front nonstationarity

[1] Both hybrid/full particle simulations and recent experimental results have clearly evidenced that the front of a supercritical quasi-perpendicular shock can be nonstationary. One responsible mechanism proposed for this nonstationarity is the self-reformation of the front itself being due to the accumulation of reflected ions. Important consequences of this nonstationarity are that not only the amplitude but also the spatial scales of fields components at the shock front (ramp and foot) are strongly varying within each cycle of the self-reformation. On the other hand, several studies have been made on the acceleration and heating of heavy ions but most have been restricted to a stationary shock profile only. Herein, one-dimensional test particle simulations based on shock profiles fields produced in PIC simulation are performed in order to investigate the impact of the shock front nonstationarity on heavy ion acceleration (He, O, Fe). Reflection and acceleration mechanisms of heavy ions (with different initial thermal velocities and different charge-mass ratios) interacting with a nonstationary shock front (self-reformation) are analyzed in detail. Present preliminary results show that: (1) the heavy ions suffer both shock drift acceleration (SDA) and shock surfing acceleration (SSA) mechanisms; (2) the fraction of reflected heavy ions increases with initial thermal velocity, charge-mass ratio and decreasing shock front width at both stationary shocks (situation equivalent to fixed shock cases) and nonstationary shocks (situation equivalent to continuously time-evolving shock cases); (3) the shock front nonstationarity (time-evolving shock case) facilitates the reflection of heavy ions; (4) a striking feature is the formation of an injected monoenergetic heavy ions population which persists in the shock front spectrum for different initial thermal velocities and ions species. The impact of the shock front nonstationarity on the heavy ions spectra within the shock front region and the downstream region are detailed separately. Present results are compared with previous experimental analysis and theoretical models of solar energetic particles (SEP) events. The variations of Fe/O spectra in high energy part have been retrieved, and the nonstationary effects of shock front strongly amplify these variations.

Impact of the nonstationarity of a supercritical perpendicular collisionless shock on the dynamics and energy spectra of pickup ions

[1] Both hybrid and full particle simulations and recent experimental results have clearly evidenced that the front of a supercritical quasi-perpendicular shock can be nonstationary. One proposed mechanism responsible for this nonstationarity is the self-reformation of the shock front being due to the accumulation of reflected ions. On the other hand, a large number of studies have been made on the acceleration and heating of pickup ions (PIs) but most have been restricted to a stationary shock profile only. Herein, one-dimensional test particle simulations based on shock profiles issued from one-dimensional particle-in-cell simulation are performed in order to investigate the impact of the shock front nonstationarity (self-reformation) on the acceleration processes and the resulting energy spectra of PIs (protons H+) at a strictly perpendicular shock. PIs are represented by different shell distributions (variation of the shell velocity radius). The contribution of shock drift acceleration (SDA), shock surfing acceleration (SSA), and directly transmitted (DT) PI's components to the total energy spectra is analyzed. Present results show that (1) both SDA and SSA mechanisms can apply as preacceleration mechanisms for PIs, but their relative energization efficiency strongly differs; (2) SDA and SSA always work together at nonstationary shocks (equivalent to time-varying shock profiles) but SDA, and not SSA, is shown to dominate the formation of high-energy PIs in most cases; (3) the front nonstationarity reinforces the formation of SDA and SSA PIs in the sense that it increases both their maximum energy and their relative density, independently on the radius of PI's shell velocity; and (4) for high shell velocity around the shock velocity, the middle energy range of the total energy spectrum follows a power law Ek−1.5. This power law is supported by both SDA and DT ions (within two separate contributing energy ranges) for a stationary shock and mainly by SDA ions for a nonstationary shock. In both cases, the contribution of SSA ions is comparatively weak.

Heavy ion reflection and heating by collisionless shocks in polar solar corona

We propose a new model for explaining the observations of preferential heating of heavy ions in the polar solar corona. We consider that a large number of small scale shock waves can be present in the solar corona, as suggested by recent observations of polar coronal jets by the Hinode and STEREO spacecraft. The heavy ion energization mechanism is, essentially, the ion reflection off supercritical quasi-perpendicular collisionless shocks in the corona and the subsequent acceleration by the motional electric field E=−(1/ c) V × B. The acceleration due to E is perpendicular to the magnetic field, giving rise to large temperature anisotropy with T ⊥ ⪢ T ∥ , which can excite ion cyclotron waves. Also, heating is more than mass proportional with respect to protons, because the heavy ion orbit is mostly upstream of the quasi-perpendicular shock foot. The observed temperature ratios between O 5+ ions and protons in the polar corona, and between α particles and protons in the solar wind are easily recovered. We also discuss the mechanism of heavy ion reflection, which is based on ion gyration in the magnetic overshoot of the shock.

Heliosphere Termination Shock as a Transformer of Magnetic Field from Lognormal to Normal Distribution

A mechanism is proposed to demonstrate that the strength of magnetic field can be transformed from a lognormal to a normal distribution as the solar wind passes through the heliosphere termination shock (TS), which explains the recent Voyager 1 observations. The TS is approximated as a perpendicular MHD shock. Synthetic simulations using random picks of 3 × 107 upstream states generate the downstream magnetic field based on the Rankine-Hugoniot relation across the TS. Thus, it is implicitly implied that the magnetic fluctuations are parallel to the shock surface. A lognormal distribution is transformed to a normal distribution for small plasma beta (β10 = 0.1), but for larger beta (β10 = 10), the distribution of B2 remains a lognormal. The observation of a normal magnetic field distribution downstream of the TS provides an upper bound (β10 < 1) for the solar wind beta near the TS, which in turn provides an upper bound for the number density of interstellar neutral hydrogens. One of the TS crossings from the Voyager 2 magnetic field and plasma observations on 2007 September 1 was found to have reformation of the local structure when the upstream beta, β10, without including pickup protons equals 0.04, which is a low-beta supercritical quasi-perpendicular shock.

Structure and stationarity of quasi-perpendicular shocks: Numerical simulations

This paper presents an overview of numerical simulation studies of fast collisionless shocks and compares these simulation results with observations of the Earth's bow shock and theoretical works. Especially, we review the structure and stationarity of the supercritical quasi-perpendicular shocks. In situ observations indicate that these shocks are generally quasi-stationary whereas full particle simulations as well as hybrid simulations often present a strong nonstationary behavior, a shock self-reformation. The simulation results, along with theoretical and observational works, suggest that the classical models of the quasi-stationary structure generated by reflected protons or by dispersive whistlers are not generally applicable for the supercritical quasi-perpendicular shocks and other phenomena are to be included into the model to ensure the observed quasi-stationarity: The role of a small scale turbulence and shock ripples is investigated. The downstream turbulence and the electron dynamics in the quasi-perpendicular shocks are also discussed.

The Injection, Acceleration, And Dynamical Influence Of Interstellar Pickup Ions At The Solar Wind Termination Shock

The interaction of interstellar pickup ions with the solar wind termination shock is reviewed and assessed. The pickup ions mass and momentum load the wind and increase its pressure, effects which decrease the strength of the shock and its distance from the Sun. The pickup hydrogen may contribute substantially to the “reflected” ion population, which should provide most of the dissipation at the supercritical quasi-perpendicular shock. A fraction of the pickup ions impinging on the shock is “injected” into the process of diffusive shock acceleration to form the anomalous cosmic ray component. An injection mechanism which accounts for the apparent absence of solar wind ions in the anomalous component is “shock surfing”, in which pickup ions which approach the shock slowly may be trapped between the upstream Lorentz force and the shock potential and accelerated in the motional electric field beyond the energy threshold for diffusive shock acceleration. However, the simplest interpretation of shock surfing would favor less massive pickup ion species, in contradiction with Voyager observations of anomalous component composition. A possible extension of the shock surfing mechanism is considered, as well as other injection mechanisms. Finally, the pressure of the anomalous component may modify the structure of the termination shock, which in turn may influence injection rates.

Determination of the dispersion of low frequency waves downstream of a quasiperpendicular collisionless shock

Abstract. A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obtain the dispersion equation of the observed waves. It is shown that the low frequency turbulence mainly consists of waves observed below 1 Hz with a linear dependence between the absolute value of wave vector |k| and the plasma frame wave frequency. The phase velocity of these waves is close to the phase velocity of intermediate waves Vint = Vacos(θ).

Non-stationarity and low frequency turbulence at a quasiperpendicular shock front

Previous studies have shown that quasi-monochromatic waves in the frequency range 1–15 Hz are usually observed upstream of the ramp of supercritical quasi-perpendicular shocks. A number of models have been proposed to explain the origin of these waves. In order to differentiate between these models, one has to determine both the observed frequencies and also wave vectors of the measured waves. The present paper is devoted to the determination of the dispersion relation ω( k) of these waves, using simultaneous data from AMPTE UKS and AMPTE IRM.

Determination of the dispersion of low frequency waves downstream of a quasiperpendicular collisionless shock

A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obtain the dispersion equation of the observed waves. It is shown that the low frequency turbulence mainly consists of waves observed below 1 Hz with a linear dependence between the absolute value of wave vector |k| and the plasma frame wave frequency. The phase velocity of these waves is close to the phase velocity of intermediate waves Vint = Vacos(θ).

Heating and acceleration of electrons through the whistler precursor in 1-D and 2-D oblique shocks

Whistler wave precursors in sub- and super-critical quasi-perpendicular collisionless shocks are analyzed with 1-D and 2-D full particle simulations for similar plasma conditions. In addition to the Landau damping present in both kinds of simulations as the main process of dissipation, 2-D results emphasize the existence of the cross-field currents instabilities (self-consistently included) in the lower hybrid frequency domain both at the shock transition and in the whistler structure. The energy transfer from whistler electromagnetic components (electromagnetic energy) into electron dynamic (thermal energy) is more efficient along the parallel direction and leads to a slight electron preheating in front of the shock.

Nature and origin of wave modes in the dayside earth magnetosheath

The day side magnetosheath displays turbulence at frequencies lower than the local proton frequency. The nature of the waves modes is studied from ISEE-1-2 electron density and magnetic field data. We compare the polarization and the compressibility of the observed fluctuations to the polarization and the compressibility of the linear wave modes in a Maxwellian kinetic plasma model with an anisotropic proton temperature. Downstream of the undershoot of a supercritical quasi-perpendicular shock we successively observe Alfvén Ion Cyclotron (AIC) modes, mirror modes and then AIC modes. From the crossing of an oblique shock to the inner sheath we observe AIC modes propagating toward the magnetopause. Along the Sun-Earth line, from the inner sheath to the magnetopause, AIC modes are observed during one crossing while mirror modes are seen during another crossing. In the sheath depletion layer we observe right-hand polarized AIC modes. At 0600 LT and at equal distance from the magnetopause and from the shock both types of modes are observed, the mirror mode appearing when the magnetic field is draping the magnetopause. From these analysis we infer the source of the propagating AIC modes to be the magnetosheath frontier regions, while the mirror modes grow in situ in the inner magnetosheath when specific conditions are reached.

Ion heating by kinetic cross-field streaming instability due to reflected ions at a quasiperpendicular shock

The present paper shows that the reflected ion at a supercritical quasiperpendicular shock wave can excite a purely growing m9de propagating parallel to the ambient magnetic field (k∥B0). To discuss the ion heating by such an unstable mode, the self-consistent quasilinear kinetic equation is solved with the assumption that the present purely growing mode is the dominant unstable mode in the system. In the quasilinear analysis of the instability, two particular cases are considered—the case of low initial ion beta [βi(0)=0.1] and that of a high initial ion beta [βi(0)=1]. For each case of low and high initial betas, two values of initial turbulence level are used. One corresponds to δB2(0)/B20=0.1 and the other corresponding to δB2(0)/B20 =0.1. It is shown that for both low and high beta cases, the ion heating at the shock becomes more efficient for a higher value of δB2(0)/B20.

The interaction of quasiperpendicular shock waves in a collisionless plasma

Hybrid simulations with kinetic ions and massless fluid electrons are used to investigate the interaction of collisionless shocks. The interaction between pairs of sub- and supercritical shocks are studied for a wide range of parameters relevant to both the solar and interplanetary plasma. These parameters include the shock Mach number, the electron and ion plasma betas, and the angle between the shock normal and the magnetic field. In the collision of two subcritical quasiperpendicular shocks, the shock electromagnetic field structures pass through each other, but do not carry the plasma associated with them. When unequal shocks collide, there is no evidence of the contact discontinuity predicted by fluid theory. In the collision of supercritical quasiperpendicular shocks, significant acceleration of ions occurs. This acceleration arises when ions reflected at one shock encounter the electric fields of the other shock and takes place in a number of distinct phases. For a wide range of parameters, the maximum ion energy is roughly an order of magnitude larger than the ram kinetic energy of the colliding shocks. This ion energization will subsequently manifest itself as a high ion to electron temperature ratio in the doubly shocked plasma. Finally, it was found that the values of the Mach number and angle between the shock normal and magnetic field play a significant role in the collisions. For shock geometries significantly different from perpendicular, ions from each oncoming shock can escape upstream and undergo considerable acceleration.