Terrestrial Magnetosheath Research Articles

Magnetosheath – Interplanetary medium reference frame: Application for a statistical study of mirror type waves in the terrestrial plasma environment

A Magnetosheath – interplanetary medium (MIPM) reference frame is introduced to study various dynamical processes in the region between the planetary bow shock and the magnetosphere. The MIPM reference frame uses recently developed analytical models to determine the bounding magnetopause and bow shock surfaces, and a fractional distance across the magnetosheath. The inputs of the model are the magnetic field and solar wind plasma parameters measured in the interplanetary medium. Angular coordinates of the MIPM reference frame (zenith and clock angles) correspond to those used in the geocentric interplanetary medium (GIPM) frame. The MIPM reference frame is applied then for a statistical study of the frequency of mirror type magnetic field depressions (linearly polarized, relatively large amplitude and symmetric shape) in the terrestrial magnetosheath based on the 10 years long 4 s resolution ISEE-1 magnetic field observations. It was found that these events most frequently occurred in the inner regions of the magnetosheath: close to the magnetopause at larger zenith angles and closer to the middle of the sheath in the subsolar region. Mirror type depressions were least frequently observed in the ‘dawn’ magnetosheath of the MIPM reference frame (downstream of the quasiparallel part of the bow shock), but their relative intensity was the largest in this region. The relative intensity of mirror type depressions was smaller in magnetosheath regions located closer to the bow shock and farther away from the subsolar point. These results suggest that pressure anisotropy raising downstream of quasiperpendicular bow shocks is favorable for the generation of mirror mode waves in addition to magnetic field draping at the magnetopause.

Measuring and understanding space turbulence

For many physical issues including reconnection, the role of waves and turbulence is likely to be predominant in space physics. This role can be viewed as a natural consequence of the general properties of turbulence, but these properties, although widely recognized in hydrodynamics, are much less familiar in plasmas. The connections between the different media, neutral or ionized, are presented first, in order to set up the décor and introduce what has been done recently to improve our knowledge about this topic and what can be done in the future. For the experimental point of view, the main emphasis is put on the new results brought by the Cluster mission: when variations are observed from mono-spacecraft measurements, it is impossible to determine to what extent they are due to intrinsic temporal variations or to crossing of spatial gradients, and in the second case, what are the size, the velocity, and the 3-D shape of the gradient sheets. The Cluster mission, with its four spacecraft, has been designed to disentangle as much as possible this spatio-temporal ambiguity, which is actually mandatory for characterizing the space turbulence, especially whenever the spectrum involves an unknown Doppler effect and when it cannot be assumed to be isotropic. Taking the example of the plasma turbulence in the terrestrial magnetosheath, we show how the k-filtering technique constitutes the appropriate tool to make the best use of the 4-point measurements for this objective. For the theoretical point of view, the main emphasis is put on the “weak turbulence” conditions, which seem to be frequently met, and which allow developing the theory beyond the usual heuristic and dimensional approaches. Because of the natural complexity of the calculations implied by this approach, it has not been possible to apply it up to now beyond the simple frame of incompressible ideal MHD, which proves to be quite insufficient for interpreting the observations. We show how recent results, using the Hamiltonian formalism of continuous media, constitute the first important step for overcoming these difficulties.

Motion and orientation of magnetic field dips and peaks in the terrestrial magnetosheath

Using data from the four Cluster spacecraft, estimates of the motion of isolated magnetic field dips and peaks in the magnetosheath are presented. Their motion and orientation are deduced using four‐spacecraft timing, with typical spacecraft separations of ∼100 km. A set of 39 clear isolated dips and 12 peaks, spread over 4 days, is considered. The calculated velocities in the plasma frame are scattered around zero, with a width of ∼30 km/s and an average absolute value of 21 km/s. This places an upper limit on the speed of these structures, and within timing errors these values are consistent with the structures being stationary in the plasma frame. Two events had estimated speeds of over half the local Alfvén speed; it is shown that these two estimates were unreliable as a result of uncertainties in timings. The inferred propagation speeds were typically slower than local wave speeds (95% less than half the local Alfvén speed), even allowing for their orientations (85% less than the slow mode speed and 56% less than half of it). These results are consistent with the structures being stationary in the plasma frame, as expected for mirror modes, rather than being propagating waves or solitons. In addition, they are not consistent with structures standing in the flow. However, it is not possible to eliminate the possibility that a small number of the structures may have been slowly propagating. The normals of the structures deduced from the timings suggest that they are cylinders rather than sheets and that the maximum variance direction is a reliable estimate of their axis orientation, with a precision of ∼20° for maximum/intermediate eigenvalue ratios of 10 or more.

Steady state slow shock inside the Earth's magnetosheath: To be or not to be? 2. Numerical three‐dimensional MHD modeling

Large‐scale structures in the dayside terrestrial magnetosheath are studied in this paper. The question about existence of the steady state slow MHD shock in the inner magnetosheath is one of the principal theoretical and experimental problems which has not been solved yet. In part 1, the original observations have been revisited. In this part, the numerical results of the three‐dimensional MHD model are presented and discussed. It is shown that for the given observations the density enhancement identified previously as a slow mode transition region is explained by temporal variations of the magnetic field and density observed in the supersonic solar wind. There are three factors resulting in the density increase in the slow mode transition region: A density increase in the upstreamflow, a decrease of the IMF modulus, and a new IMF orientation which forms a quasi‐parallel bow shock in the subsolar region. We show that numerical solutions obtained by non‐stationary and stationary MHD models are significantly different for the same solar wind conditions. We discuss how the magnetopause motion may enlarge the observed variations of the magnetosheath density. Also we answer the question why the existed numerical MHD models do not predict the slow shock in the steady state solution and show how the magnetosheath flow may be organized without such shock.

Modelling the solar wind interaction with Mercury by a quasi-neutral hybrid model

Abstract. Quasi-neutral hybrid model is a self-consistent modelling approach that includes positively charged particles and an electron fluid. The approach has received an increasing interest in space plasma physics research because it makes it possible to study several plasma physical processes that are difficult or impossible to model by self-consistent fluid models, such as the effects associated with the ions’ finite gyroradius, the velocity difference between different ion species, or the non-Maxwellian velocity distribution function. By now quasi-neutral hybrid models have been used to study the solar wind interaction with the non-magnetised Solar System bodies of Mars, Venus, Titan and comets. Localized, two-dimensional hybrid model runs have also been made to study terrestrial dayside magnetosheath. However, the Hermean plasma environment has not yet been analysed by a global quasi-neutral hybrid model. In this paper we present a new quasi-neutral hybrid model developed to study various processes associated with the Mercury-solar wind interaction. Emphasis is placed on addressing advantages and disadvantages of the approach to study different plasma physical processes near the planet. The basic assumptions of the approach and the algorithms used in the new model are thoroughly presented. Finally, some of the first three-dimensional hybrid model runs made for Mercury are presented. The resulting macroscopic plasma parameters and the morphology of the magnetic field demonstrate the applicability of the new approach to study the Mercury-solar wind interaction globally. In addition, the real advantage of the kinetic hybrid model approach is to study the property of individual ions, and the study clearly demonstrates the large potential of the approach to address these more detailed issues by a quasi-neutral hybrid model in the future.Key words. Magnetospheric physics (planetary magnetospheres; solar wind-magnetosphere interactions) – Space plasma physics (numerical simulation studies)

Spatial maps of heliospheric and geocoronal X‐ray intensities due to the charge exchange of the solar wind with neutrals

X‐rays are generated throughout the heliosphere and the terrestrial magnetosheath as a consequence of charge transfer collisions between heavy solar wind ions and interstellar and geocoronal neutrals, respectively. Simple models of this X‐ray emission have been presented in the past, but results from a more sophisticated model are described in this paper. In particular, to obtain the densities of interstellar neutrals our X‐ray model uses to determine X‐ray intensities, we use the Fahr [1971] hot model although with recently determined input parameters. The geocoronal X‐ray model we use in this paper has also been improved, as described in a recent paper by Robertson and Cravens [2003]. In previous papers we demonstrated that there is significant correlation between the “long‐term enhancement” part of the soft X‐ray background measured by the Röntgen Satellite (ROSAT) and the solar wind proton flux. In the current paper we determine the steady‐state X‐ray intensities due to the interaction between the solar wind and both interstellar neutrals and the geocoronal neutrals as a function of look direction and time of year. X‐ray intensity maps are shown for both a spherically symmetric solar wind and for a latitude‐dependent solar wind (i.e., fast and slow solar wind regions). In all cases, the X‐ray intensity is highest when the view direction is towards the Sun, but the intensity is also relatively high for view directions intersecting the gravitational focusing cone of interstellar helium. We also show a heliospheric/geocoronal X‐ray intensity map for the conditions used by Snowden et al. [1995] in producing the 1/4 keV channel soft X‐ray background map in galactic coordinates. Our preliminary conclusion is that very roughly 50% of the total background soft X‐ray intensity in the galactic plane and 25% at high galactic latitudes can be attributed to the charge transfer process operating within the solar system, with the remaining emission coming from outside our heliosphere.

Identification of low frequency waves in the vicinity of the terrestrial bow shock

In this paper, methods for the determination of the wave mode for low frequency waves based on observed differences in phase are reviewed. Examples, using measurements made in the terrestrial foreshock and magnetosheath, are used to illustrate the application of these methods. The use of advance methods such as NARMAX modelling or genetic algorithms to identify the plasma wave mode is also discussed.

X‐ray emission from the terrestrial magnetosheath

X‐rays are generated throughout the terrestrial magnetosheath as a consequence of charge transfer collisions between heavy solar wind ions and geocoronal neutrals. The solar wind ions resulting from these collisions are left in highly excited states and emit extreme ultraviolet or soft X‐ray photons. A model has been created to simulate this X‐ray radiation. Published terrestrial exospheric hydrogen distributions and solar wind speed, density and temperature distributions were used in this model. Simulated images were created as seen from an observation point outside the geocorona. The locations of the bow shock and magnetopause are evident in these images. Perhaps this X‐ray emission can be used to remotely sense the solar wind flow around the magnetosphere. Since similar X‐rays are produced in the heliosphere, the challenge will be, however, to eliminate this background emission.

On the magnetosheath thicknesses of interplanetary coronal mass ejections

Interplanetary coronal mass ejections (ICMEs) often move relative to the ambient solar wind plasma at a speed that exceeds the fast magnetosonic velocity, producing a standing shock wave in the frame of the ICME and a magnetosheath whose plasma flows around the obstacle much as the terrestrial magnetosheath flows around the Earth's magnetosphere. The half-thickness of an ICME is typically 0.1 AU at 1 AU . If this dimension represented the characteristic scale size of the obstacle, then the thickness of the magnetosheath should be about 0.025 AU but it is typically closer to 0.1 AU . In order to treat this problem we convert the original Spreiter et al. (Planet. Space Sci. 14 (1966) 223) formula for the terrestrial magnetosheath thickness to one that is appropriate for the ICME magnetosheath. This treatment allows us to conclude that the characteristic radius of curvature of an ICME at 1 AU is about 0.4 AU . This radius of curvature is provided by both the bend of the axis of the rope and by an elongation of the ICME in the direction perpendicular to both the rope axis and the solar wind flow. Thus near 1 AU ICMEs have a radial thickness that is smaller than their other two characteristic dimensions.

The evolution of mirror mode fluctuations in the terrestrial magnetosheath

Mirror type fluctuations were identified in magnetic field data measured aboard the ISEE-1/2 spacecraft in different regions of the magnetosheath. Minimum variance analysis was applied to find the mirror type fluctuations, and the amplitude of the fluctuations was determined individually. Assuming that the source of the mirror mode instability is at the bow shock, the growth rate of the field strength perturbations was determined for four selected magnetosheath passes when mirror type fluctuations were observed in the outer, middle, and inner region of the sheath. The obtained growth rate values are in the range 0.002 s −1<γ<0.0035 s −1 being almost an order of magnitude smaller than the maximum growth rate values calculated by Gary et al. (J. Geophys. Res. 98 (1993) 1481) based on a numerical evaluation of the full kinetic dispersion relation. The significant difference between the observed and calculated growth rate values can be explained if the mirror type fluctuations observed in different regions of the magnetosheath do not always originate from the bow shock, but the source may be somewhere else (e.g. at the magnetopause, inside the magnetosheath, or in localized regions of the bow shock). Also, the linear approximation applied in the above-mentioned calculations may be inappropriate for describing the growth of the observed fluctuations.

Cluster as a wave telescope – first results from the fluxgate magnetometer

Abstract. The four Cluster spacecraft provide an excellent opportunity to study spatial structures in the magnetosphere and adjacent regions. Propagating waves are amongst the interesting structures and for the first time, Cluster will allow one to measure the wave vector of low-frequency fluctuations in a space plasma. Based on a generalized minimum variance analysis wave vector estimates will be determined in the terrestrial magnetosheath and the near-Earth solar wind. The virtue and weakness of the wave telescope technique used is discussed in detail.Key words. Electromagnetics (wave propagation) – Magnetospheric physics (MHD waves and instabilities; plasma waves and instabilities)

On the effects of solar wind dynamic pressure on the anisotropic terrestrial magnetosheath

We apply our recent three‐dimensional anisotropic MHD model of magnetosheath flow [Erkaev et al., 1999] to study quantitatively effects of solar wind dynamic pressure (Pd∞ ) and Alfvén Mach number (Ma∞) on the anisotropic magnetosheath and the plasma depletion layer (PDL) in the subsolar region. Given the wide range over which these two parameters vary, their influence on the magnetosheath structure may be significant. Our analysis is applicable to quasi‐steady changes in the interplanetary medium. Following our earlier work, and in general agreement with the data, we define the sunward edge of the PDL by β‖ = 1, where β‖ is the proton beta parallel to the magnetic field. We first discuss changes in Pd∞ occurring under constant Ma∞. In this case, a rescaling of the parameters yields the effects on the magnetosheath. We then study quantitatively a changing dynamic pressure through a varying Alfvén Mach number. We obtain profiles of key magnetosheath parameters and the width of the PDL for Alfvén Mach numbers representative of the solar wind at Earth orbit. Gradients in parameter profiles become steeper and shift toward the magnetopause as Ma∞ increases. We find that PDL width varies as even in the anisotropic magnetosheath. Using our model to study the magnetosheath location where the electromagnetic ion cyclotron wave (EICW) instability dominates over the mirror instability, we find that this location occurs well inside the PDL. In addition, we estimated the fraction of the PDL width occupied by the EICWs as a function of solar wind Alfvén Mach number. We conclude that the EICW regime is contained in, but is not co‐extensive with, the PDL. Examining critically this issue by changing the PDL identification criterion to others based on a density decrease relative to the bow shock value and a systematic drop toward the magnetopause, we find that this result still holds, but the region where EICWs are destabilized occupies a different fraction of the PDL thus defined. Some model results are compared with documented data from an inbound crossing of the magnetosheath made on December 24, 1994. Good agreement with model predictions are obtained.

On the processes in the terrestrial magnetosheath: 1. Scheme development

We propose a new method to study the structure of the magnetosheath and thereby determine the underlying processes that create this structure. This method provides a systematic means of separating perturbations due to the solar wind variations from those generated within the magnetosheath. As a result, we are able to study the magnetosheath processes as well as the dynamic solar wind‐magnetopause interaction. We use the solar wind measurements from an upstream monitor as the input to the gasdynamic convected field model and then compare the model output with the in situ magnetosheath observations. We introduce three parameters to scale the model prediction to match the timings of the magnetopause crossing, bow shock crossing, and upstream variations. With this procedure the relationship between the upstream measurements and the magnetosheath observations and the location of the magnetosheath satellite relative to the magnetopause and bow shock boundaries are highly constrained. We then introduce a series of normalization procedures that provide the means to remove the effects of the solar wind variations. The systematic differences between the model prediction and observation indicate physical processes that are not included in the gasdynamic model. An application of this approach is presented in a companion paper.

On the processes in the terrestrial magnetosheath: 2. Case study

We test a new scheme to study the magnetosheath. The scheme uses the solar wind measurements as the input into the gasdynamic convected field model, and the model output is compared with magnetosheath observations. In our four test cases there is a significant overall success in the model prediction. This scheme works better than other methods in magnetosheath studies and is potentially useful for space weather forecasts and nowcasts. The direction of the magnetic field is modeled most accurately. The prediction of the size of the magnetosphere is accurate within a few percent. The predicted thickness of the magnetosheath is accurate up to 90%. With a double‐normalization procedure developed in this study, we are able to separate the processes intrinsic in the magnetosheath from those due to large‐scale upstream temporal variations. The test cases confirm the existence of a compressional front one third of the distance from the magnetopause to the bow shock near the stagnation streamline. The magnetosheath density profile near the stagnation streamline is consistent with the models that add a compressional front between the two depletion processes described by the plasma depletion model. A major unexpected feature is that the magnetosheath flow pattern is very different from that described by the model and maybe by most other models, including MHD models. The magnetosheath flow near the stagnation streamline does not slow down gradually toward the stagnation point. It moves rapidly until reaching a very small region near the magnetopause.

Proton temperature anisotropy upper bound

The electromagnetic proton cyclotron instability and the mirror instability are driven by the proton temperature anisotropy T⊥p/T‖p &gt; 1, where ⊥ and ‖ denote directions relative to the background magnetic field. Linear theory and one‐dimensional hybrid simulations imply that the former mode grows more rapidly over 0.05 ≤ β‖p ≤ 5 and that wave‐particle scattering by its enhanced fluctuations imposes an upper bound on the temperature anisotropy of the form urn:x-wiley:01480227:media:jgra13669:jgra13669-math-0001 where and B0 is the background magnetic field. Here Sp and αp are fitting parameters, and . This paper describes results from more general two‐dimensional hybrid simulations, which permit both instabilities to grow simultaneously. These simulations confirm the one‐dimensional results on the initial domain ; enhanced fluctuations display the properties of the proton cyclotron instability and αp ≃ 0.4. On this domain the two‐dimensional simulations also yield an upper bound for the fluctuating field energy density of the form urn:x-wiley:01480227:media:jgra13669:jgra13669-math-0005 with fitting parameter . The simulations on the initial domain 10 ≤ β‖p≤100 show spectral characteristics of both instabilities and exhibit a more stringent bound on the proton anisotropy, in agreement with observations in the terrestrial magnetosheath.

Possible plasma depletion layer ahead of an interplanetary ejecta

We present observations of a plasma depletion layer in front of an interplanetary magnetic cloud and analyze them quantitatively using a recent magnetohydrodynamic (MHD) theory of flow around magnetic clouds driving shocks. The magnetic field and plasma measurements were made by the ISEE 3 and IMP 8 on September 28–29, 1978. The magnetic cloud is expanding, and with a frontside boundary speed of ≈ 900 km s−1 it is one of the fastest ever seen at Earth orbit. We find a simple variation of field and plasma parameters in the sheath region behind the shock. Along the spacecraft trajectory the sum of the gas and plasma pressures is approximately constant, with a plasma beta less than unity. As the frontside boundary of the magnetic cloud is approached, the magnetic field strength increases while the density and temperature simultaneously decrease. These are defining characteristics of a plasma depletion layer, similar to that often seen in the terrestrial magnetosheath adjacent to the magnetopause. This suggests that the underlying cause is the same: the stretching of interplanetary magnetic field lines around the ejecta. The plasma depletion layer extends throughout the sheath region for which data are available, that is, for approximately 3 out of 5.7 hours. The sheath terminates at a clear discontinuity at the cloud's surface. To compare the observations with MHD theory, we model the ejecta as a magnetic flux rope of locally straight cylindrical geometry. We consider two limiting cases separately: (1) bulk motion relative to the surrounding medium but without expansion and (2) expansion into the ambient medium but without bulk motion. The predictions of both these limiting theories yield good agreement with observed variations of plasma parameters and magnetic field strength across the sheath. This paper is intended as a first attempt at modeling plasma depletion layers associated with interplanetary magnetic clouds.

Low-frequency waves in the Earth's magnetosheath: present status

Abstract. The terrestrial magnetosheath contains a rich variety of low-frequency (≲ proton gyrofrequency) fluctuations. Kinetic and fluid-like processes at the bow shock, within the magnetosheath plasma, and at the magnetopause all provide sources of wave energy. The dominance of kinetic features such as temperature anisotropies, coupled with the high-β conditions, complicates the wave dispersion and variety of instabilities to the point where mode identification is difficult. We review here the observed fluctuations and attempts to identify the dominant modes, along with the identification tools. Alfvén/ion-cyclotron and mirror modes are generated by T^/T∥&gt;1 temperature anisotropies and dominate when the plasma β is low or high, respectively. Slow modes may also be present within a transition layer close to the subsolar magnetopause, although they are expected to suffer strong damping. All mode identifications are based on linearized theory in a homogeneous plasma and there are clear indications, in both the data and in numerical simulations, that nonlinearity and/or inhomogeneity modify even the most basic aspects of some modes. Additionally, the determination of the wave vector remains an outstanding observational issue which, perhaps, the Cluster mission will overcome.

Anomalous magnetosheath properties during Earth passage of an interplanetary magnetic cloud

The aim of this paper is to model for the first time the variation of field and flow parameters in the magnetosheath during Earth passage of an interplanetary magnetic cloud. Under typical Solar wind conditions, magnetohydrodynamic (MHD) effects on the flow of plasma in the terrestrial magnetosheath are important only in a layer adjacent to the magnetopause which is a few thousand kilometers thick (“depletion layer” or “magnetic barrier”). During the passage of an interplanetary magnetic cloud, however, conditions upstream of the bow shock depart strongly from the norm. In this case, interplanetary parameters vary slowly over a wide range of values. Values of the upstream Alfvén Mach number are much lower than those otherwise sampled (∼3 versus 8–10). Together with the magnetic shear across the magnetopause, this parameter plays a central role in determining the structure of the magnetosheath close to the magnetopause. As a consequence of sustained low values of the upstream Alfvén Mach number, the magnetic field exerts a strong influence on the flow over a very substantial fraction of the magnetosheath throughout the duration of cloud passage, i.e., for a time period of the order of 1–2 days. We apply an algorithm to integrate the ideal MHD equations, using a boundary layer technique, and compute the variations of field and flow parameters along the stagnation streamline. We choose as our example the magnetic cloud which passed Earth on January 14–15, 1988. The interaction of this cloud with the magnetosphere, as regards the resulting ionospheric flow patterns and the substorm activity, has been the subject of various investigations. Using information from these studies, we obtain results on the magnetosheath when the magnetopause is modeled, first as a tangential discontinuity and then as a rotational discontinuity. Our results are in good general agreement with recent observations on the behavior of field and flow quantities in the magnetosheath region adjacent to the magnetopause. In addition, we predict the existence of a magnetic barrier when the upstream Alfvén Mach number is low, irrespective of the magnetic shear across the magnetopause.

Low‐frequency fluctuations in the magnetosheath near the magnetopause

There are four low‐frequency modes which may propagate in a high‐beta nearly bi‐Maxwellian plasma. These are the magnetosonic, Alfvén, ion acoustic, and mirror modes. This manuscript defines a procedure based on linear Vlasov theory for the unique identification of these modes by use of transport ratios, dimensionless ratios of the fluctuating field and plasma quantities. A single parameter, the mode deviation, is defined which characterizes the difference between the theoretical transport ratios of a particular mode and the observed ratios. The mode deviation is calculated using the plasma and magnetic field data gathered by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module spacecraft to identify the modes observed in the terrestrial magnetosheath near the magnetopause. As well as determining the mode which best describes the observed fluctuations, it gives us a measure of whether or not the resulting identification is unique. Using 17 time periods temporally close to a magnetopause crossing, and confining our study to the frequency range from 0.01 to 0.04 Hz, we find that the only clearly identified mode in this frequency range is the mirror mode. Most commonly, the quasi‐perpendicular mirror mode (with wave vector k roughly perpendicular to the background magnetic field B0) is observed. In two events the quasi‐parallel mirror mode (k ∥ B0) was identified.

Observations in the sheath region ahead of a magnetic cloud and in the dayside magnetosheath during magnetic cloud passage

We present magnetic field and particle (protons and electrons) observations in the sheath region behind an interplanetary shock driven by a magnetic cloud, and in the magnetic cloud itself. We also discuss observations in the dayside terrestrial magnetosheath during cloud passage. We find that the region ahead of the cloud is in pressure balance. Further, throughout its extent (>0.06 AU), the magnetic field strength is anticorrelated with the plasma density, with the latter decreasing steadily as the cloud is approached. This behaviour is indicative of magnetic forces influencing the flow topology and highlights a large-scale breakdown of predictions based solely on gas dynamical considerations. We also study density structures inside the cloud which result in an undulating dynamic pressure being applied to the magnetopause causing it to oscillate with amplitudes of ∼1–3 Re and period ∼2h.