Earth's Bow Shock Research Articles

Test kinetic modelling of collisionless perpendicular shocks

AbstractTest kinetic simulation results are presented for perpendicular collisionless shocks in magnetized plasmas that are representative of the Earth's bow shock. In this approach, particle kinetics are described by tracing particle trajectories in prescribed electromagnetic fields obtained in the MHD approximation, and applying Liouville's theorem. This provides a first-order description of particle dynamics in complex systems, given approximate fields obtained with a low-level description of the plasma. The method also provides a useful consistency check in assessing the validity of approximate solutions such as those obtained in the ideal MHD approximation. Compared with the more familiar test particle approach, in which trajectories of randomly injected particles are followed in time, the present approach has the advantage of being numerically more efficient, and producing results without statistical errors.

COSTEP/SOHO observations of energetic electrons far upstream of the Earth's bow-shock

Abstract. We have analyzed 124 electron bursts at energies above 0.25 MeV observed with the EPHIN/COSTEP instrument onboard the SOHO spacecraft far upstream of the Earth's bow-shock at the libration point L1 from 1996 through 2005. Most of the bursts were observed during low solar activity (in 1996–1997 and in 2005) and all 124 bursts were not associated with solar particle events. It is shown that some upstream events are detected at energies above 0.7 MeV. We find that the event occurrence number shows a distinct seasonal variation with maxima around equinoxes and minima near solstices. This together with a close correspondence between the event occurrence number with maxima in solar wind speed (Vsw), geomagnetic activity index (Ap) and in the southward interplanetary magnetic field (IMF) component (Bz) indicates that the observed events can be explained in terms of leakage of magnetospheric particles during enhanced geoactivity rather than by acceleration at the Earth's bow-shock.

Cluster observations of electrostatic solitary waves near the Earth's bow shock

Using a period of internal burst mode data from the Cluster Electric Field and Wave instrument a number of electrostatic solitary structures have been identified in the foot region of Earth's quasi‐perpendicular bow shock. The four individual probe potential measurements are utilized to investigate the fundamental characteristics of the solitary wave structures such as wave propagation vector, propagation velocity, scale‐size and potential amplitude. Two classes of waves are observed. Bipolar solitary waves typically propagate in the solar wind direction toward the shock but at a significant angle from the ambient magnetic field. Unipolar/tripolar solitary waves tend to propagate along the ambient magnetic field. The wave amplitude‐scale size relation is similar to that obtained for similar structures observed in the auroral zone. The structures lie in the theoretically allowed region in width‐amplitude space to be consistent with the BGK ion holes. Using a period of internal burst mode data from the Cluster Electric Field and Wave instrument a number of electrostatic solitary structures have been identified in the foot region of Earth's quasi‐perpendicular bow shock. The four individual probe potential measurements are utilized to investigate the fundamental characteristics of the solitary wave structures such as wave propagation vector, propagation velocity, scale‐size and potential amplitude. Two classes of waves are observed. Bipolar solitary waves typically propagate in the solar wind direction toward the shock but at a significant angle to the ambient magnetic field in contrast to most previous studies which assume parallel propagation to the ambient magnetic field. In contrast, unipolar/tripolar solitary waves tend to propagate along the ambient magnetic field. The wave amplitude‐scale size relation is similar to that obtained for structures observed in the auroral zone. The structures lie in the theoretically allowed region in width‐amplitude space to be consistent with the BGK (Bernstein‐Greene‐Kruskal) ion holes. The two classes of observed solitary waves may greatly influence the ambient plasma dynamics around the shock. The bipolar solitary waves do not exhibit a large net potential difference but may still play an important role in plasma thermalisation by particle scattering. Unipolar/tripolar solitary waves exhibit a remarkable net potential difference that may be responsible for the plasma energisation along the ambient magnetic field.

Distribution of escaping ions produced by non‐specular reflection at the stationary quasi‐perpendicular shock front

Field‐aligned and gyrophase bunched ion beams are observed in the foreshock of the Earth bow shock. One of the mechanisms proposed for their production is non‐specular reflection at the shock front. We study the distributions which are formed at the stationary quasi‐perpendicular shock front within the same process which is responsible for the generation of reflected ions and transmitted gyrating ions. The test particle motion analysis in a model shock allows one to identify the parameters which control the efficiency of the process and the features of the escaping ion distribution. These parameters are: the angle between the shock normal and the upstream magnetic field, the ratio of the ion thermal velocity to the flow velocity upstream, and the cross‐shock potential. A typical distribution of escaping ions exhibits a bimodal pitch angle distribution (in the plasma rest frame).

The Quasi-Perpendicular Bow Shock as a Temporal Trapping Barrier and Accelerator of Magnetospheric Particles

The bow shock has been studied so far, mostly as a boundary that influences the particles that are incident from the upstream region (of solar origin). In this paper, we provide, for the first time, observational evidence from the energetic-particle-experiment and the charged-particle-measurement-experiment instruments onboard the IMP-8 spacecraft, showing that ions leaking from the magnetosphere, during storms or substorms, are affected by the quasi-perpendicular (Q-P) bow shock and can be temporally trapped just downstream from the shock in a magnetic configuration opposite to the magnetic mirror. The observations from three representative event periods examined in this paper suggest that magnetospheric energetic ( keV) ions show general flows along the field lines in the direction from the magnetosheath toward the interplanetary space, in both sides of the shock (up- and downstream), and characteristic cross-field anisotropic distributions just downstream from the shock, consistent with a ldquotrapped population.rdquo In a series of successive bow-shock crossings within several hours, the IMP-8 spacecraft observed intensity gradients toward the magnetosheath, which strongly suggest a spatial modulation of magnetospheric ion fluxes at the Q-P bow shock. Highest peaks of ion intensities and a very hard spectrum in the energy range between 100 and 400 keV were observed just at the shock front, which suggest acceleration of magnetospheric particles during their temporal trapping at the bow shock. The observations near the Earth's bow shock examined in this paper are well explained in terms of the shock drift acceleration (SDA) theory for magnetospheric particles reaching the bow shock. The phenomenon discussed here, an apparent temporal trapping-and acceleration-of escaped magnetospheric ions at the Earth's bow shock, appears to be an important mechanism that influences the particle distributions near the Earth's bow shock and may have important applications to other shocks in our solar system (planetary, heliospheric, interplanetary, and corotating shock waves) and the interstellar medium (supernova shocks).

Influence of the Ionospheric Conductance on the Size of the Rarth's Magnetopause and Bow Shock

AbstractThis paper studies the influence of the ionospheric conductance on the size of the Earth's magnetopause and bow shock under the following assumptions: (1) the ionosphere, treated as a spherical shell, has a uniform Pedersen conductance ΣP and a zero Hall conductance, and (2) the Earth's dipole moment is due southward and the interplanetary magnetic field (IMF) has only south component (Bz < 0). The size of the magnetopause and bow shock is characterized by the geocentric distances of their intersection points with the three axes of the GSE frame, i.e., the subsolar point, the dawn‐dusk flank point, and the north‐south top point. Given the solar wind conditions, and the values of Bz and ΣP, a quasi‐steady state of the system is obtained by 3‐D global MHD simulations. It is shown that the influence of ΣP on the size of the magnetopause and bow shock is significant in the range of about 1~5 S but negligible otherwise. As ΣP increases, the magnetopause and bow shock expand outward as a whole, and the former expands less than the latter so that the magnetosheath widens. The variation of the flank point position of the magnetopause with ΣP depends on the magnitude of Bz: the flank point shifts inward with increasing ΣP for weak southward IMF cases and outward otherwise. The above‐mentioned results indicate that the effect of the ionospheric conductance should be incorporated in constructing empirical models of the magnetopause and bow shock.

Simulation of Energetic Electron Bursts Upstream of Re‐Forming Shocks

Energetic electrons are widely observed in vicinity of planetary bow shocks, interplanetary shocks, and coronal mass ejection driven shocks. In this paper the electron energization is numerically studied by tracing exact test particle electron trajectories in the time-dependent electromagnetic fields typical for the Earth's bow shock. The time-dependent re-forming shock profiles are self-consistently generated by one-dimensional multiscale hybrid simulations. It is shown that energetic electron bursts occur cyclically at the shock re-formation period. The upstream electron distributions show time-varying loss-cone, beam, and ring-beam features in velocity space. The beam density, beam speed, average beam kinetic energy, velocity spread, and associated wave growth rate in the upstream region of the shock cyclically change with time by a factor of ~2-4. These characteristics are qualitatively very different from the continuous beam expected for a time-stationary shock and are important for the plasma instabilities/radio emission phenomena near the shocks.

On the physics of collisionless shocks: Cluster investigations and simulations

Collisionless shocks can be found in many astrophysical settings but the Earth's environment is easiest to access. The foreshock region of the Earth's bow shock is populated by a variety of waves and particle populations allowing us to study wave–particle interactions. In the parallel and quasi-parallel regime short large amplitude magnetic structures (SLAMS) and their properties have been investigated. At the perpendicular and quasi-perpendicular shocks, advances have been made in ion reflection, thermalization and ion acceleration using Cluster data. Interplanetary disturbances cause temporal and spatial variations at the Earth's bow shock that in turn trigger a variety of processes. Magnetic reconnection in the tail region is one of them. In reconnection, heating and acceleration occur mainly in the slow-mode shocks, which bound the reconnection wedge. The Cluster mission, related simulation and theoretical considerations provided many new insights into the above-mentioned topics.

Electron dynamics and cross‐shock potential at the quasi‐perpendicular Earth's bow shock

The evolution of the electron distribution function through quasi‐perpendicular collisionless shocks is believed to be dominated by the electron dynamics in the large‐scale coherent and quasi‐stationary magnetic and electric fields. We investigate the electron distributions measured on board Cluster by the Plasma Electron and Current Experiment (PEACE) instrument during three quasi‐perpendicular bow shock crossings. Observed distributions are compared with those predicted by electron dynamics resulting from conservation of the first adiabatic invariant and energy in the de Hoffmann‐Teller frame, for all pitch angles and all types of trajectories (passing and, for the first time, reflected or trapped). The predicted downstream velocity distributions are mapped from upstream measurements using an improved Liouville mapping technique taking into account the overshoots. Furthermore, for one of these crossings we could take advantage of the configuration of the Cluster quartet to compare mapped upstream velocity distributions with those simultaneously measured at a relatively well magnetically connected downstream location. Consequences of energy and adiabatic invariant conservation are found to be compatible with the observed electron distributions, confirming the validity of electron “heating” theories based on DC fields as zeroth‐order approximations, but some systematic deviations are found between the dynamics of low‐ and high‐adiabatic invariant electrons. Our approach also provides a way to estimate the cross‐shock electric potential profile making full use of the electron measurements, and the results are compared to other estimates relying on the steady state dissipationless electron fluid equations. At the temporal resolution of the instruments, the scales associated to the change of the potential generally appear to be comparable to those of the magnetic field, but some differences between the methods appear within the shock transition. It is argued that potentials evaluated from Liouville mapping rely on less restrictive hypotheses and are therefore more reliable. Finally, we show how, in contrast to methods using electron velocity moments, the technique can be used to produce high‐time‐resolution electric potentials and discuss the electric potential profiles through the shock.

Trajectories of ions specularly reflected from non-planar collisionless shocks

An important contribution to the thermalization of the solar wind ions at the Earth's bow shock for high Mach numbers comes from the reflection of a fraction of these ions from the shock. Previous studies have examined the trajectories of the reflected ions assuming the shock to be an infinite plane. In this paper a model is developed to describe the trajectories of particles after reflection for a variety of shock geometries. Of particular interest are the initial conditions which allow the particle to return to the shock with a greater normal velocity than at first encounter, or to return to the shock at all. The effects of the magnetic field direction and the curvature of the shock on particle trajectories are discussed for cylindrical and spherical shock geometries and compared to those for a planar shock.

Ion thermalization and wave excitation downstream of Earth's bow shock: A theory for Cluster observations of He2+ acceleration

It has been well documented that the plasma immediately downstream of Earth's quasi‐perpendicular bow shock, which consists of reflected protons and directly transmitted ions with large temperature anisotropies (T⊥/Tz), is unstable to the excitation of ion cyclotron waves. These waves in turn scatter the protons and ions to marginal stability. Using Cluster data following the inbound shock crossing at 1717:48 UT on 31 March 2001, we investigate the joint evolution of the proton and helium distribution functions. Within a short distance downstream of the shock the perpendicular heating of helium is faster than the parallel heating, so that the temperature anisotropy of helium first increases near the shock before decreasing farther downstream. The observed spectra of magnetic fluctuations, which are dominated by left‐hand circularly polarized waves, display one peak at < gα (He2+ gyrofrequency), just downstream of the shock, and two peaks with a slot near ≈ gα, farther downstream, where is wave frequency in hertz. We present a quasi‐linear theory that accounts for the observed long‐time decrease of the He2+ temperature anisotropy and the excited wave spectrum. The predicted temperature anisotropy and the general shape of the excited wave spectrum match the observations remarkably well. Nevertheless, certain features of the observations, such as the large amplitude of the lower‐frequency peak and very low amplitude of the higher‐frequency peak just downstream of the shock, require further work.

Modeling of the Temperature‐Anisotropy Relaxation Time of the Earth's Magnetosheath

AbstractIn the present paper, a short review of plasma waves and turbulence in the Earth's bow shock and magnetosheath is given. Magnetohydrodynamic models which are recently applied for the magnetosheath are presented. Further, results for the relaxation of the proton temperature‐anisotropy in the magnetosheath by proton pitch‐angle diffusion obtained for two different magnetohydrodynamic models are discussed. It is pointed out that the relaxation time is determined by the varying strength of the excitation of ion‐cyclotron and mirror waves in the different magnetosheath regions. Besides, there seems to be a background wave transfer from the solar wind into the magnetosheath. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

Measurement of Large Parallel and Perpendicular Electric Fields on Electron Spatial Scales in the Terrestrial Bow Shock

Large parallel (<or=100 mV/m) and perpendicular (<or=600 mV/m) electric fields were measured in the Earth's bow shock by the vector electric field experiment on the Polar satellite. These are the first reported direct measurements of parallel electric fields in a collisionless shock. These fields exist on spatial scales comparable to or less than the electron skin depth (a few kilometers) and correspond to magnetic-field-aligned potentials of tens of volts and perpendicular potentials up to a kilovolt. The perpendicular fields are amongst the largest ever measured in space, with energy densities of epsilon0E2/nkBTe of the order of 10%. The measured parallel electric field implies that the electrons are demagnetized, which may result in stochastic (rather than coherent) electron heating.

Intermittent nature of solar wind turbulence near the Earth’s bow shock: Phase coherence and non-Gaussianity

The link between phase coherence and non-Gaussian statistics is investigated using magnetic field data observed in the solar wind turbulence near the Earth's bow shock. The phase coherence index Cphi, which characterizes the degree of phase correlation (i.e., nonlinear wave-wave interactions) among scales, displays a behavior similar to kurtosis and reflects a departure from Gaussianity in the probability density functions of magnetic field fluctuations. This demonstrates that nonlinear interactions among scales are the origin of intermittency in the magnetic field turbulence.

Scattering of field-aligned beam ions upstream of Earth's bow shock

Abstract. Field-aligned beams are known to originate from the quasi-perpendicular side of the Earth's bow shock, while the diffuse ion population consists of accelerated ions at the quasi-parallel side of the bow shock. The two distinct ion populations show typical characteristics in their velocity space distributions. By using particle and magnetic field measurements from one Cluster spacecraft we present a case study when the two ion populations are observed simultaneously in the foreshock region during a high Mach number, high solar wind velocity event. We present the spatial-temporal evolution of the field-aligned beam ion distribution in front of the Earth's bow shock, focusing on the processes in the deep foreshock region, i.e. on the quasi-parallel side. Our analysis demonstrates that the scattering of field-aligned beam (FAB) ions combined with convection by the solar wind results in the presence of lower-energy, toroidal gyrating ions at positions deeper in the foreshock region which are magnetically connected to the quasi-parallel bow shock. The gyrating ions are superposed onto a higher energy diffuse ion population. It is suggested that the toroidal gyrating ion population observed deep in the foreshock region has its origins in the FAB and that its characteristics are correlated with its distance from the FAB, but is independent on distance to the bow shock along the magnetic field.

Whistler critical Mach number and electron acceleration at the bow shock: Geotail observation

The ‘whistler critical Mach number’, Mcritw, is one of the dimensionless parameters that characterizes collisionless shocks. Originally, it was introduced to indicate the critical point above which whistler waves do not propagate upstream. Indeed our analysis of Geotail data at the Earth's bow shock shows intense whistler waves in the sub‐critical regime, MA &lt; Mcritw, but not in the super‐critical regime. In this paper, we further report that Mcritw seems to regulate the electron acceleration efficiency at the shocks. At the shock transition layer it is found that the spectral index Γ of electron energy spectra defined by f(E) ∝ E−Γ is distributed between 3.5 and 5.0 in the sub‐critical regime, while the hardest energy spectra with Γ = 3–3.5 are detected in the super‐critical regime. We discuss a possible relationship between Mcritw and the electron acceleration.

Interpreting multipoint observations of substructure at the quasi‐perpendicular bow shock: Simulations

Two‐dimensional hybrid simulations of high Mach number quasi‐perpendicular collisionless shocks, as relevant to the Earth's bow shock, show strong fluctuations of density and magnetic field within the average shock profile. In particular, there are rapid variations moving across the shock surface, in terms of local changes in its position and the shock gradient normal direction on scales of order of the ion inertial length. Using virtual probes, we simulate the magnetic field time series that would be observed by a multipoint observation at a high Mach number, moderate plasma beta, quasi‐perpendicular shock as a function of shock crossing speed. For crossing speeds greater than twice the upstream Alfvén speed, the time series profiles are similar to the spatially averaged profile. As the crossing speed decreases, more structure becomes visible in the time series so that oscillations and major differences of amplitude and gradient are evident even between closely spaced probes. These signatures are directly linked to the spatiotemporal variability of the shock front. Even at slow crossing speeds sharp gradients can sometimes be seen in the time series owing to propagation of fluctuations across the shock surface. On the basis of the simulations, oscillatory substructure becomes increasingly significant when the crossing speed becomes less than the Alfvén speed. We suggest some signatures that may then be used observationally to infer the presence of the associated surface fluctuations.

Origin of heavy ions in upstream events near the Earth's bow shock

We have surveyed the ∼20–160 keV/nucleon heavy ion composition of 2102 upstream events observed by the Wind/STEP instrument near the Earth's bow shock over a complete solar cycle from day 325, 1994 through day 90, 2006. Our main results are: (1) During solar minimum conditions, both the C/O and Fe/O ratios are similar to the corresponding values measured in the solar wind and/or CIRs. (2) During solar maximum conditions, the C/O ratio is similar to that measured in SEP and CME‐driven IP shock events, while the Fe/O ratio lies between the values measured in IP shock and SEP events. We conclude that the source material for upstream events near the Earth's bow shock originates from a dynamic suprathermal ion population that is dominated by ions accelerated in SEP events during solar maximum conditions and by suprathermal solar wind ions and/or those accelerated in CIRs during solar minimum conditions.

Ripples observed on the surface of the Earth's quasi‐perpendicular bow shock

Multipoint measurements from Cluster of a particularly slow encounter with the Earth's bow shock are presented. The shock is classified as high Mach number, quasi‐perpendicular, and high plasma beta. Coherent oscillations of the plasma density and the magnetic field amplitude are seen in the foot and ramp of the shock with period approximately 15 s; the traversal of the shock layer lasts 2 min. The oscillation amplitude decreases upstream from a maximum value at the location of the shock overshoot so that it is confined within the shock layer. Phase differences in the oscillations as seen on the four Cluster spacecraft indicate that the oscillations are propagating, and cannot be explained by a one‐dimensional shock profile fluctuating in position. Four‐point timing shows that the oscillations correspond to ripples traveling across the surface of the shock, with wavelength 1000–2000 km and propagation direction roughly parallel to the magnetic field. The presence of these oscillations could have major implications for the analysis of crossings observed at higher relative shock‐spacecraft speeds or where the interspacecraft spacing is larger and the shock velocity is changing.