Earth's Bow Shock Research Articles

Nonlinear Development of Shocklike Structure in the Solar Wind

We report first in situ multispacecraft observations of nonlinear steepening of compressional pulses in the solar wind upstream of Earth's bow shock. The magnetic field of a compressional pulse formed at the upstream edge of density holes is shown to suddenly break and steepen into a shocklike structure. During the early phase of development thermalization of ions is insignificant. Substantial thermalization of ions occurs as gyrating ions are observed at the steepened edge. These observations indicate that the mechanisms causing the dissipation of magnetic fields (currents) and ions are different in the early phase of shock development.

STEREO/SEPT observations of upstream particle events: almost monoenergetic ion beams

Abstract. We present observations of Almost Monoenergetic Ion (AMI) events in the energy range of 100–1200 keV detected with the Solar Electron and Proton Telescope (SEPT) onboard both STEREO spacecraft. The energy spectrum of AMI events contain 1, 2, or 3 narrow peaks with the relative width at half maximum of 0.1–0.7 and their energy maxima varies for different events from 120 to 1200 keV. These events were detected close to the bow-shock (STEREO-A&B) and to the magnetopause at STEREO-B as well as unexpectedly far upstream of the bow-shock and far away from the magnetotail at distances up to 1100 RE (STEREO-B) and 1900 RE (STEREO-A). We discuss the origin of AMI events, the connection to the Earth's bow-shock and to the magnetosphere, and the conditions of the interplanetary medium and magnetosphere under which these AMI bursts occur. Evidence that the detected spectral peaks were caused by quasi-monoenergetic beams of protons, helium, and heavier ions are given. Furthermore, we present the spatial distribution of all AMI events from December 2006 until August 2007.

Plasma waves above the ion cyclotron frequency in the solar wind: a review on observations

Abstract. Since the very beginning of the space venture, discrepancies between hydrodynamic models and observations have raised the attention to the kinetic effects taking place in the interplanetary medium. After discussing some of these constraints, a review on the state of the art knowledge on the waves in the range fci<f<fpe (fci – about 10−1 Hz – is the ion cyclotron frequency, and fpe – a few 10 kHz – the electron plasma frequency) observed in the free solar wind, i.e., not magnetically connected to the Earth's bow shock, is addressed.

Cluster and ACE observations of phase synchronization in intermittent magnetic field turbulence: a comparative study of shocked and unshocked solar wind

Abstract. We apply two distinct nonlinear techniques, kurtosis and phase coherence index, to analyze the modulus of interplanetary magnetic field data |B| measured by Cluster and ACE spacecraft from 1 to 3 February 2002. High degree of phase synchronization is found across a wide range of time scales, from 1 s to 104 s, in the magnetic field fluctuations, both in the shocked solar wind upstream of Earth's bow shock and in the unshocked ambient solar wind at the L1 Lagrangian point. This is the first direct measurement of phase coherence in the ambient solar wind turbulence. We show that phase synchronization related to nonlinear multiscale interactions is the origin of the departure from Gaussianity in the intermittent magnetic field turbulence. In particular, we demonstrate that at small scales near the spectral break the intermittency level of Cluster is lower than ACE, which may be a signature of the reflected ions from the shock.

A ONE-SIDED ASPECT OF ALFVENIC FLUCTUATIONS IN THE SOLAR WIND

Using Advanced Composition Explorer (ACE) 64 s data at 1 AU we find that Alfvenic fluctuations propagating outward from the Sun along the magnetic field, B , in the solar wind often produce one-sided variations in one of the equatorial components of B and velocity, V . This is a natural consequence of the fact that the Alfvenic fluctuations are transverse fluctuations in which |B| remains nearly constant. Thus, fluctuations in the field component that defines the underlying background field direction are always relative to a base value rather than to an average value. This suggests that conclusions derived from statistical analyses of fluctuations in the solar wind that assume the fluctuations in all field components are relative to average values need to be re-examined. We also find that discrete, sunward-propagating Alfvenic fluctuations or rotational discontinuities are extremely rare in the pristine solar wind; thus far we have identified such discrete events in ACE data only in association with events identified as magnetic reconnection exhausts and/or in association with backstreaming ions from reverse shocks, including Earth's bow shock.

Contribution from the Earth's Bow Shock to Region 1 Current under Low Alfvén Mach Numbers

Using global MHD simulations of the solar wind–magnetosphere–ionosphere system, we investigate the dependence of the contribution from the Earth's bow shock (I1bs) to ionospheric region 1 field aligned current (FAC) (I1). It is found that I1bs increases with increasing southward interplanetary magnetic field (IMF) strength Bs, if the Alfvén Mach number MA of the solar wind exceeds 2, a similar result as obtained by previous authors. However, if MA becomes close to or falls below 2, I1bs will decrease with Bs in both magnitude and percentage (i.e., I1bs/I1) because of the resultant reduction of the bow shock strength. Both the surface current density Jbs at the nose of the bow shock and the total bow shock current Ibs share nearly the same relationship with MA, and vary non-monotonically with MA or Bs. The maximum point is found to be located at MA = 2.7. Three conclusions are then made as follows: (1) The surface current density at the nose, which is much easier to be evaluated, may be used to largely describe the behaviour of the bow shock instead of the total bow shock current. (2) The peak of the total bow shock current is reached at about MA = 2.7 when only Bs is adjusted. (3) The non-monotonic variation of the bow shock current with MA causes a similar variation of its contribution to region 1 FAC. The turning point for such contribution is found to be nearly MA = 2. The implication of these conclusions to the saturation of the ionospheric transpolar potential is briefly discussed.

Remote sensing of local structure of the quasi-perpendicular Earth's bow shock by using field-aligned beams

Abstract. Field-aligned ion beams (FABs) originate at the quasi-perpendicular Earth's bow shock and constitute an important ion population in the foreshock region. The bulk velocity of these FABs depends significantly on the shock normal angle, which is the angle between shock normal and upstream interplanetary magnetic field (IMF). This dependency may therefore be taken as an indicator of the local structure of the shock. Applying the direct reflection model to Cluster measurements, we have developed a method that uses proton FABs in the foreshock region for remote sensing of the local shock structure. The comparison of the model results with the multi-spacecraft observations of FAB events shows very good agreement in terms of wave amplitude and frequency of surface waves at the shock front.

Multipoint observations of ions in the 30–160 keV energy range upstream of the Earth's bow shock

We use multipoint observation data by Cluster during time periods when the interspacecraft separation distance was between 1 and 1.5 Earth radii in order to study the physical processes related to diffuse ions at <200 keV/e. For our analysis we use data from the Research with Adaptive Particle Imaging Detectors (RAPID) experiment onboard Cluster SC1 and SC3. We determine spatial ion density gradients by using proton intensities in the 27.7–159.7 keV energy range and helium intensities in the 137.8–235.1 keV energy range as a function of distance from the bow shock along the magnetic field. Our results show that the diffuse ions are subject to diffusive transport and the ion partial densities decrease exponentially with increasing distance from the bow shock. By complementing RAPID data with Cluster Ion Spectrometry measurements at lower energies (from 10 to 32 keV) from the same upstream ion event we find that the e‐folding distance of energetic ion density increases almost linearly with energy. This effect is also seen in the hardening of the particle spectra with increasing distance from the bow shock. We determine the spatial diffusion mean free path and the diffusion coefficient as a function of ion energy by assuming that upstream diffusion is balanced by downstream convection.

Deformation and evolution of solar wind discontinuities through their interactions with the Earth's bow shock

The present study examines the interaction of solar wind discontinuities with the Earth's bow shock, using multipoint observations in the magnetosheath by Time History of Events and Macroscale Interactions During Substorms (THEMIS), Cluster, and Double Star TC1. We focus on the deformation and evolution of two discontinuities observed on 21 June 2007, one of which involves a density increase and a magnetic field decrease, while the other is accompanied by a density decrease and a magnetic field increase. In the magnetosheath, the discontinuities are deformed into a concave shape; that is, the normal is inclined toward dusk (dawn) on the dawnside (duskside). The density‐increase (‐decrease) discontinuity is being compressed (expanded) as it propagates in the magnetosheath. We conclude that the compression (expansion) is due to antisunward (sunward) motion of the bow shock which is initiated or enhanced by the impact of the discontinuity on the bow shock. The steepening of Bz reversal followed by an overshoot of the total magnetic field, which appears at the trailing edge of the density‐decrease discontinuity, is also discussed.

Dynamic motion of the bow shock and the magnetopause observed by THEMIS spacecraft

We present an observational study of the dynamic motion of the bow shock and the magnetopause and suggest that the dynamic motion of the bow shock is due to the interaction of an interplanetary shock with the Earth's bow shock. THEMIS B spacecraft crossed the magnetopause, a discontinuity and the bow shock successively in 5 min during its outbound journey on 10 July 2007. Following THEMIS B, THEMIS C, D, E and A consecutively crossed the magnetopause and the discontinuity but not the bow shock. Timing analysis shows that the magnetopause and the discontinuity were moving earthward with speeds of ∼47 km/s and ∼90 km/s, respectively. There is a trend that the discontinuity decelerates as it propagates toward the magnetopause. We suggest that the dynamic motion and the discontinuity are results of the interaction of a weak (MA = 1.4) interplanetary shock with the Earth's bow shock. After the interaction, the transmitted interplanetary shock took the form of a discontinuity where total magnetic field and density increase and the temperature decreases. The rotation of the magnetic field across this discontinuity was similar to that of the interplanetary shock. The expected fast shock ahead of the discontinuity for shock‐shock interaction was not observed.

The statistics of foreshock cavities: results of a Cluster survey

Abstract. We use Cluster magnetic field, thermal ion, and energetic particle observations upstream of the Earth's bow shock to investigate the occurrence patterns of foreshock cavities. Such cavities are thought to form when bundles of magnetic field connect to the quasi-parallel bow shock. Shock-processed suprathermal ions can then stream along the field, back against the flow of the solar wind. These suprathermals enhance the pressure on shock-connected field lines causing them to expand into the surrounding ambient solar wind plasma. Foreshock cavities exhibit depressions in magnetic field magnitude and thermal ion density, associated with enhanced fluxes of energetic ions. We find typical cavity duration to be few minutes with interior densities and magnetic field magnitudes dropping to ~60% of those in the surrounding solar wind. Cavities are found to occur preferentially in fast, moderate magnetic field strength solar wind streams. Cavities are observed in all parts of the Cluster orbit upstream of the bow shock. When localised in a coordinate system organised by the underlying physical processes in the foreshock, there is a systematic change in foreshock cavity location with IMF cone angle. At low (high) cone angles foreshock cavities are observed outside (inside) the expected upstream boundary of the intermediate ion foreshock.

On nonlinear waves in Hall–MHD plasma

AbstractLow-frequency magnetic field fluctuations are observed in space plasmas, e.g. as upstream waves at the Earth's bow shock. Such upstream waves can steepen into very large amplitude wave phenomena, e.g. short large-amplitude magnetic structures (or SLAMS for short), shocklets or discrete wave packets. Such observations motivated us to study the nonlinear behavior of low-frequency and large-amplitude plasma waves in terms of the full nonlinear Hall–MHD framework. In the case of stationary (nonlinear) waves, the Hall–MHD equations can be rewritten in the so-called Sakai–Sonnerup system of equations that describe this plasma state and provide oscillatory and solitary types of solutions. An overall parameter study on the polarization characteristics, together with the magnetic field components and density variations of the different ranges of solutions, is presented here. These results can be further on applied to the theoretical treatment of particle interaction with such waves, e.g. at shocks in space plasmas, possibly leading to particle acceleration.

Cluster observations of fast shocks in the magnetosheath launched as a tangential discontinuity with a pressure increase crossed the bow shock

The interaction of a tangential discontinuity (TD) and accompanying dynamic pressure increase with the Earth's bow shock launches a fast shock that travels ahead of the TD in the magnetosheath and carries a significant portion of the pressure change. In this event study, we use observations from the Cluster spacecraft and magnetohydrodynamic simulations to identify the fast shock and its properties and to track the TD in the magnetosheath. Velocities of the fast shock and the TD were determined by triangulation using the four distant Cluster spacecraft. The fast shock is a planar structure, traveling nearly perpendicular to B at the magnetosonic speed in the plasma rest frame. Changes in density and ∣B∣ are correlated, with about a 20% increase in each. A current was observed tangential to the plane of the fast shock, and the positive E •J there provided an electromagnetic energy source for the observed heating of the ions. The fast shock is generated by the pressure change and determines the timing of the initial response of the magnetopause to that change. The TD was moving nearly in the −XGSE direction and was being compressed as it moved inward. The passage of the TD ushered in large‐scale compressive structure in the magnetosheath magnetic field, which satisfied the mirror mode instability criterion. Velocities of a fast rarefaction wave, reflected from the magnetopause, and an additional slow‐mode structure, which was not a product of the initial interaction with the bow shock, were determined by triangulation.

On nonstationarity and rippling of the quasiperpendicular zone of the Earth bow shock: Cluster observations

Abstract. A new method for remote sensing of the quasiperpendicular part of the bow shock surface is presented. The method is based on analysis of high frequency electric field fluctuations corresponding to Langmuir, upshifted, and downshifted oscillations in the electron foreshock. Langmuir waves usually have maximum intensity at the upstream boundary of this region. All these waves are generated by energetic electrons accelerated by quasiperpendicular zone of the shock front. Nonstationary behavior of the shock, in particular due to rippling, should result in modulation of energetic electron fluxes, thereby giving rise to variations of Langmuir waves intensity. For upshifted and downshifted oscillations, the variations of both intensity and central frequency can be observed. For the present study, WHISPER measurements of electric field spectra obtained aboard Cluster spacecraft are used to choose 48 crossings of the electron foreshock boundary with dominating Langmuir waves and to perform for the first time a statistical analysis of nonstationary behavior of quasiperpendicular zone of the Earth's bow shock. Analysis of hidden periodicities in plasma wave energy reveals shock front nonstationarity in the frequency range 0.33 fBi<f<fBi, where fBi is the proton gyrofrequency upstream of the shock, and shows that the probability to observe such a nonstationarity increases with Mach number. The profiles observed aboard different spacecraft and the dominating frequencies of the periodicities are usually different. Hence nonstationarity and/or rippling seem to be rather irregular both in space and time rather than resembling a quasiregular wave propagating on the shock surface.

Particle acceleration at coronal mass ejection–driven interplanetary shocks and the Earth's bow shock

Particle acceleration in space plasmas, particularly at collisionless shocks, remains a fundamental yet poorly understood problem in space physics. The most important questions that need to be addressed include (1) where are the particles accelerated, (2) what source material is available for acceleration, (3) what mechanisms are responsible for injecting and accelerating the particles, and (4) how are the particle properties modified during their propagation from the acceleration sites to the observation point? Answering these questions will enable further development of the theoretical framework and models that will facilitate quantitative predictions of key properties of the accelerated particles. In this paper, we review recent observations associated with two distinct but widely studied energetic ion populations: (1) solar energetic particles associated with coronal mass ejection–driven interplanetary shocks and (2) energetic ions observed upstream of the Earth's bow shock. We review the common theoretical concepts and physical processes that are believed to be responsible for accelerating particles at these two types of collisionless shocks, emphasizing the commonalities between these distinct structures and their associated particle populations.

Wave activity inside hot flow anomaly cavities

Low‐frequency wave properties inside two hot flow anomalies (HFAs) at different stages of evolution are, for the first time, studied applying the k‐filtering technique on multipoint measurements from the Cluster satellites. The observed wave activity in an HFA cavity in an early stage of its evolution was interpreted as the combination of inherent fluctuation in the solar wind and those of a plasma component specularly reflected at the Earth's bow shock, where the amplitude of the fluctuations had been enhanced by a plasma beam instability. The wave field of a more evolved HFA was found to be less complex but contained a periodicity in the wave number distribution with a period that is suggested to come from the geometry of the HFA cavity.

The spatial distribution of upstream ion events from the Earth's bow shock measured by ACE, Wind, and STEREO

Using simultaneous measurements of >40 keV upstream ions observed at ACE, Wind, and STEREO‐A during the solar minimum period of 2007, day 1 through 2007, day 181, we investigate their spatial distributions by calculating their occurrence probabilities as a function of lateral and radial separation between L1 and STEREO‐A. Our main results are given as follows: (1) STEREO‐A observed upstream events even when it was separated from Earth by ∼1750 RE and ∼3800 RE in the radial and lateral directions, respectively. (2) The occurrence probability (∼20–30%) for measuring simultaneous upstream events at L1 and STEREO‐A was far greater than that expected from accidental coincidences. (3) The occurrence rate of simultaneous upstream events at L1 and STEREO‐A is significantly higher inside rarefaction regions of high‐speed solar wind flows (>500 km s−1) that follow corotating compression regions and when there exist antisunward propagating Alfvén waves. These new results confirm the global nature of the source region and place limits on the spatial size of the interplanetary structures that could either accelerate the ions in the first place or at the very least provide them with easier access by facilitating their scatter‐free transport from the Earth's foreshock into the far upstream regions traversed by STEREO‐A. We suggest that the existence of large amplitude Alfvén waves with spatial scales of the order of 0.03 AU that are embedded in and get convected past the Earth by high‐speed solar wind streams plays a critical and necessary role in the occurrence of upstream ion events near the Earth.

Numerical simulation of electron distributions upstream and downstream of high Mach number quasi‐perpendicular collisionless shocks

Test particle calculations are performed to investigate the effects of different shock parameters on electron distributions upstream and downstream of quasi‐perpendicular model shocks. The electron trajectories are followed exactly, and the model shock profiles are carefully prescribed as typical internal structures relevant to Earth's bow shock. Kuncic et al.'s [2002] model is employed to calculate the net cross‐shock potential jump. A detailed argument for neglecting the noncoplanar magnetic field component is given. The results show that the primary effects on the upstream and downstream electron distributions are determined by (1) variation of the angle θbn between the upstream magnetic field and shock normal, (2) the existence or not of overshoots in magnetic field and cross‐shock potential, (3) the spatial profile of the cross‐shock potential relative to the magnetic field, and (4) the spatial scale of the shock. Changes in the scale and amplification factors of the shock foot (providing the foot remains small compared with the overall shock), and in the spatial scale of a non‐self‐consistent Gaussian model for the cross‐shock potential, have little effect. The electron distributions, both upstream and downstream, agree very well with the predictions of adiabatic theory. Realistic shocks with self‐consistent magnetic and potential profiles have well‐defined loss cones, ring beam, and beam features in the upstream and downstream distributions. Leakage of downstream electrons into the upstream region significantly affects the upstream distributions and should not be neglected. Remote extraction of shock structure and parameters appears possible using upstream or downstream electron distributions. Calculations of the wave growth, and resulting particle heating and acceleration, from these distributions should be pursued for time‐stationary or reforming shocks with realistic shock profiles.

Coherent electric structures: Vlasov‐Ampère simulations and observational consequences

Coherent electrostatic structures, like bipolar electric pulses (also called electrostatic solitary waves) or Langmuir waves, are frequently observed in many astrophysical plasma of the Earth environment (plasma sheet boundary layer, Earth bow shock, auroral regions etc.) or in the solar wind. They are thought to play a crucial role in the energy transfer from small to large scale and to reconnection processes. Numerous simulations have studied their emergence and evolution. Most of them are based on the development of two stream instabilities. Another mechanism is investigated here: the plasma is excited by a localized, time dependent modulation of the electron distribution function (heating of the electrons). The investigation is performed through a 1D Vlasov‐Ampere code, in open boundary conditions. We explore the response of the plasma to several heating conditions, mass ratio and density gradient. We find that the heating leads to the development of an extended turbulent domain. We also show that the history of the electrostatic solitary waves (ESW) strongly depends on the presence of a density gradient and the mass ratio between species. If the positive charged neutralizing background is composed of heavy ions, the ESW turns back to the entrance domain when a density gradient is included. From the observational point of view, this means that the electric field shows a polarity reversal with time.

Consistency check of a global MHD simulation using the test-kinetic approach

The test-kinetic approach is used to study first order particle kinetic effects in the vicinity of the Earth bow shock, and check consistency with a solution obtained in the MHD approximation. The method, also referred to as reverse particle tracing, consists of integrating particle trajectories backward in time, using electromagnetic fields as obtained from an MHD simulation model. By following particles back to a region where the plasma distribution function is known, and using Liouville's theorem, it is possible to compute the distribution function at arbitrary points in space. Compared with the more familiar test-particle approach, where large numbers of particles are followed forward in time, the present method has the advantage of producing distribution functions without statistical errors. The test-kinetic method is applied here in combination with magnetospheric fields obtained with the global MHD code BATS-R-US. Consistency between the MHD solution and the first order kinetic solution is checked by comparing moments of the computed ion distribution function directly with corresponding physical parameters obtained in the MHD approximation. From there, the validity and limitations of both the MHD solution and the inferred particle kinetic solution can be assessed.