A mathematical magnetospheric field model with independent physical parameters

A quantitative magnetospheric magnetic field model has been calculated in three dimensions. The model is based on an analytical solution of the Chapman-Ferraro problem. For this solution, the magnetopause was assumed to be an infinitesimally thin discontinuity with given geometry. The shape of the dayside magnetopause is in agreement with measurements derived from spacecraft boundary crossings.The magnetic field of the magnetopause currents can be derived from scalar potentials. The scalar potentials result from solutions of Laplace's equation with Neumann's boundary conditions. The boundary values and the magnetic flux through the magnetopause are determined by all magnetic sources which are located inside and outside the magnetospheric cavity. They include the Earth's dipole field, the fields of the equatorial ring current and tail current systems, and the homogeneous interplanetary magnetic field. In addition, the flux through the magnetopause depends on two constants of interconnection which provide the possibility of calculating static interconnection between magnetospheric and interplanetary field lines. Realistic numerical values for both constants have been derived empirically from observed displacements of the polar cusps which are due to changes in the orientation of the interplanetary field. The transition from a closed to an open magnetosphere and vice versa can be computed in terms of a change of the magnetic boundary conditions on the magnetopause. The magnetic field configuration of the closed magnetosphere is independent of the amount and orientation of the interplanetary field. In contrast, the configuration of the open magnetosphere confirms the observational finding that field line interconnection occurs primarily in the polar cusp and high latitude tail regions.The tail current system reflects explicitly the effect of dayside magnetospheric compression which is caused by the solar wind. In addition, the position of the plasma sheet relative to the ecliptic plane depends explicitly on the tilt angle of the Earth's dipole. Near the tail axis, the tail field is approximately in a self-consistent equilibrium with the tail currents and the isotropic thermal plasma.The models for the equatorial ring current depend on the D_st-parameter. They are self-consistent with respect to measured energy distributions of ring current protons and the axially symmetric part of the magnetospheric field.     

The structure of the magnetopause

The solar wind is a magnetized flowing plasma that intersects the Earth's magnetosphere at a velocity much greater than that of the compressional fast mode wave that is required to deflect that flow. A bow shock forms that alters the properties of the plasma and slows the flow, enabling continued evolution of the properties of the flow on route to its intersection with the magnetopause. Thus the plasma conditions at the magnetopause can be quite unlike those in the solar wind. The boundary between this “magnetosheath” plasma and the magnetospheric plasma is many gyroradii thick and is surrounded by several boundary layers. A very important process occurring at the magnetopause is reconnection whereby there is a topological change in magnetic flux lines so that field lines can connect the solar wind plasma to the terrestrial plasma, enabling the two to mix. This connection has important consequences for momentum transfer from the solar wind to the magnetosphere. The initiation of reconnection appears to be at locations where the magnetic fields on either side of the magnetopause are antiparallel. This condition is equivalent to there being no guide field in the reconnection region, so at the reconnection point there is truly a magnetic neutral or null point. Lastly reconnection can be spatially and temporally varying, causing the region of the magnetopause to be quite dynamic.     

Effect of finite parallel conductivity on the magnetospheric convection

The magnetospheric plasma convection is studied, taking into account the finite conductivity along magnetic field lines. Field-aligned currents flowing at the inner boundary of the magnetospheric plasma sheet give rise to parallel electric fields which insignificantly affect the convection on the ionospheric level but change drastically the convection system in the magnetosphere. Intense azimuthal convective streams arise along both sides of the plasma sheet boundary. A part of convection lines appears to be completely closed in the inner magnetosphere.     

Solar wind energy transfer regions inside the dayside magnetopause—I. Evidence for magnetosheath plasma penetration

PROGNOZ-7 high temporal resolution measurements of the ion composition and hot plasma distribution in the dayside high latitude boundary layer near noon have revealed that magnetosheath plasma may penetrate the dayside magnetopause and form high density, high β, magnetosheath-like regions inside the magnetopause. We will from these measurements demonstrate that the magnetosheath injection regions most probably play an important role in transferring solar wind energy into the magnetosphere. The transfer regions are characterized by a strong perpendicular flow towards dawn or dusk (depending on local time) but are also observed to expand rapidly along the boundary layer field lines. This increased flow component transverse to the local magnetic field corresponds to a predominantly radial electric field of up to several mV m^?1, which indicates that the injected magnetosheath plasma causes an enhanced polarization of the boundary layer. Polarization of the boundary layer can therefore be considered a result of a local MHD-process where magnetosheath plasma excess momentum is converted into electromagnetic energy (electric field), i.e. we have primarily an MHD-generator there. We state primarily because we also observe acceleration of “cold” ions inside the magnetopause as a result of this radial electric field. A few cases of polarity reversals suggest that the polarization is sometimes quite localized.The perhaps most significant finding is that the boundary layer is observed to be charged up to tens of kilovolts, a potential which may be highly variable depending on e.g. the presence of a momentum exchange by the energy transfer regions.     

Differences between solar wind plasmoids and ideal magnetohydrodynamic filaments

Plasma irregularities present in the solar wind are plasmoids, i.e. plasma-magnetic field entities. These actual plasmoids differ from ideal magnetohydrodynamic (MHD) filaments. Indeed, (1) their “skin” is not infinitely thin but has a physical thickness which is determined by the gyromotion of the thermal ions and electrons, (2) they are of finite extent and their magnetic flux is interconnected with the interplanetary magnetic flux, (3) when they penetrate into the magnetosphere their magnetic field lines become rooted in the ionosphere (i.e. in a medium with finite transverse conductivity), (4) the external Lorentz force acting on their boundary surface depends on the orientation of their magnetic moment with respect to the external magnetic field, (5) when their mechanical equilibrium is disturbed, hydromagnetic oscillations can be generated. It is also suggested that the front side of all solar wind plasmoids which have penetrated into the magnetosphere is the inner edge of the magnetospheric boundary layer while the magnetopause is considered to be the surface where the magnetospheric plasma ceases to have a trapped pitch angle distribution.     

HEOS-2 observations of the boundary layer from the magnetopause to the ionosphere

HEOS-2 low energy electron data (10 eV–3.7 keV) from the LPS Frascati plasma experiment have been used to identify three different magnetospheric electron populations. Magnetosheathlike electron energy spectra (35–50 eV) are characteristic of the plasma mantle, entry layer and cusps from the magnetopause down to 2–3 R_E Plasma sheet electrons (energy > 1 keV) are found at all local times, with strong intensities in the early morning quadrant and weaker intensities in the afternoon quadrant. The plasma sheet shows a well defined inner edge at all local times and latitudes, the inner edge coinciding probably with the plasmapause. The plasma sheet does not reach the magnetopause, but it is separated from it by a boundary layer electron population that is very distinct from the other two electron populations, most electrons having energies 100–300 eV.We map these three electron populations from the magnetopause down to the high latitude near earth regions, by making use of the HEOS-2 low latitude inbound passes and the high latitude outbound passes (in Solar Magnetic (SM) coordinates). The boundary layer extends along the magnetopause up to 5–7 R_E above the equator; at higher latitudes it follows the magnetic lines of force and it is found closer and closer to the earth, so that it has the same invariant latitudes of the system 1 currents observed by Iijima and Potemra (1976) in their region 1. The plasma sheet can be mapped into their region 2 and the cusp-entry layer-plasma mantle can be mapped into their cusp currents region. The boundary layer is observed for any Interplanetary Magnetic Field (IMF) direction. We speculate that magnetosheath particles penetrate into the magnetosphere everywhere along the magnetopause. The electron energization, however, is observed only in the boundary layer, on both dawn and dusk side and could be due to the polarization electric field at magnetopause generated by the magnetosheath plasma bulk motion in the region where such motion is roughly perpendicular to the magnetospheric magnetic field. The electron energization is absent in the regions (entry layer and plasma mantle) where the sheath plasma motion is roughly parallel or antiparallel to the magnetospheric magnetic field.     

Interpretation of magnetic field perturbations in the earth's magnetopause boundary layers

Studies of the boundary layers in the vicinity of the Earth's dayside magnetopause are important in determining the nature of the processes which couple the magnetosphere to the flowing solar wind, thereby driving magnetospheric convection. In this paper we examine theoretically the magnetic field and plasma properties expected in the boundary regions for various models involving either diffusion or reconnection at the boundary. For diffusion models the transport of magnetosheath momentum across the magnetopause will result in field shears on either side of the boundary, the field rotations being in opposite senses on either side relative to the undisturbed fields. The directions of these rotations depend upon location at the magnetopause relative to the momentum transfer region and to the noon meridian. In reconnection models the effect of the tension of the open boundary layer field lines must be taken into account in addition to the magnetosheath flow, but on the super-Alfvénic flanks of the magnetosphere the latter still dominates, so that qualitatively similar effects will occur in the two models. More detailed, quantitative or statistical studies are then required to distinguish the two models in this regime. In the sub-Alfvénic dayside region, however, open field tension effects will dominate in reconnection models such that boundary layer field and plasma properties will then be determined mainly by the magnetosheath magnetic field configuration. In particular the East-West flow in the magnetospheric boundary layer will be controlled largely by the East-West field in the magnetosheath, leading to flow reversals across the magnetopause in some quadrants of the magnetopause. This behaviour is directly related to the Svalgaard-Mansurov effect and is a signature unique to reconnection models. The boundary layer fields are also expected to tilt towards the field on the opposite side of the boundary in these models on the dayside. “Toward” tilting can also occur in this regime in diffusion models, but “away” tilting, a signature unique to dayside diffusion, should also occur equally frequently. Finally, we briefly discuss previously published high-resolution ISEE 1 and 2 data from the boundary regions in the light of our results. We find that “toward” tilting generally occurs in boundary region crossings previously identified as being reconnection-associated and we present some examples in which the above unique reconnection signature has been observed. During impulsive FTE-like events, however, the field may tilt in either direction, possibly as a result of field line twists, thus complicating our simple picture in this case. We also show that the “reverse draping” observations presented by Hones et al. (1982) approximately satisfy the open magnetopause stress balance conditions.     

Peculiarities of solar-wind flow around the magnetosphere and the magnetopause position

MHD problems of solar wind interaction with the Earth's magnetosphere on the day-side are investigated. These ideas are used for the analysis of satellite data on the day-side magnetopause crossing. It is shown that the observed regularities may be adequately explained within the bounds of MHD-flow theory which includes the stagnation line at the nose of the magnetosphere. The ratio k of the magnetic field pressure to the plasma pressure in the vicinity of the subsolar point of the magnetosphere, which determines the magnitude of the interplanetary magnetic field penetrating into the magnetosphere, was estimated.     

The effect of the atmosphere and ionosphere on long period magnetospheric micropulsations

A study is made of the screening effect of the atmosphere and ionosphere which lets only part of a magnetospheric micropulsation signal reach the ground. We obtain analytical expressions relating the magnetic field in the magnetosphere to that on the ground, which are confirmed by computing a full solution. Only the part of the signal with no vertical current will be seen on the ground; this agrees with previous work. Using this result, we find that the reflection condition of a transverse hydromagnetic wave incident on the top of the ionosphere indicates a ‘fixed-end’ boundary condition for the field line. To a first approximation, micropulsation polarisations observed on the ground must be rotated through a right angle to obtain those in the magnetosphere. The strength of the electric field predicted in the ionosphere agrees with radio aurorae observations.     

Auroral-polar currents during periods of moderate magnetospheric activity

Data from a meridian line of three component magnetometers were used to investigate the character of the equivalent overhead current flow at high latitudes during periods of moderately strong magnetospheric activity. The polar cap equivalent current flow is inexplicable in terms of our knowledge of the polar cap electric field configuration and probably represents the combined effect of several real current systems seated in the auroral oval and the polar cap. An important contributing factor is the current system associated with the interaction of the magnetosphere with the azimuthal component of the interplanetary magnetic field. The region of the Harang discontinuity is identifiable through the intrusion of polar cap equivalent current flow into the latitudinal regime normally occupied by the eastward and westward electrojets. The Harang discontinuity exhibits marked changes in scale size in association with substorm activity.     

Interaction of interplanetary MHD shock waves with the magnetopause

The interaction between a shock-wave and the magnetopause is formulated on the basis of one-dimensional magnetohydrodynamics. The magnetopause is assumed to be a tangential discontinuity, and the magnetic field is limited to the case of perpendicularity. Both the forward and reverse shocks' impact on the magnetopause are considered and analyzed separately. The forward shock-magnetopause interaction results in a transmitted shock, a tangential discontinuity, and a simple rarefaction wave. The reverse shock-magnetopause interaction creates a transmitted shock, a tangential discontinuity, and a reflected wave. The propagation of an SSC signal which is related to an interplanetary shock-induced geomagnetic storm's onset-time on Earth is discussed in general terms. It was found in earlier work (Shen and Dryer, 1972) that the propagation velocity of an inter-planetary shock is decreased by about 1015% following its impact with the earth's bow shock; the present study shows that its velocity is then suddenly increased by a factor of two to three after impact with the magnetopause. The fast propagating shock-wave inside the magnetosphere degenerates into a hydromagnetic wave as it advances into an increasing intensity of the distorted dipole geomagnetic field.     

A theoretically derived energy coupling function for the magnetosphere

The energy coupling function between the solar wind and the magnetosphere can be obtained for two extreme situations, in which the magnetospheric geometry is determined primarily by either (i) the interplanetary magnetic field, or (ii) the solar wind pressure. In this paper, we obtained an expression for the energy coupling function by assuming a simple interpermeation of the interplanetary and geomagnetic fields. Two important quantities in this case are the potential difference between the two neutral points and the amount of open flux. From these two overall quantities, the voltage and the current of the magnetospheric dynamo are calculated. The dynamo power output represents the rate at which energy is transferred from the solar wind to the magnetosphere. The derived functional dependence on the interplanetary conditions provides a theoretical basis for the energy coupling function previously deduced from observations.     

Analysis of energetic electron drop-outs in the upper atmosphere of Titan during flybys in the dayside magnetosphere of Saturn

We discuss the high energy electron absorption signatures at Titan during the Cassini dayside magnetospheric encounters. We use the electron measurements of the Low Energy Measurement System of the Magnetospheric Imaging Instrument. We also examine the mass loading boundary based on the ion data of the Ion Mass Spectrometer sensor of the Cassini Plasma Spectrometer. The dynamic motion of the Kronian magnetopause and the periodic charged particle flux and magnetic field variations – associated with the magnetodisk of Saturn – of the subcorotating magnetospheric plasma creates a unique and complex environment at Titan. Most of the analysed flybys (like T25–T33 and T35–T51) cluster at similar Saturn Local Time positions. However the instantaneous direction of the incoming magnetospheric particles may change significantly from flyby to flyby due to the very different magnetospheric field conditions which are found upstream of Titan within the sets of encounters.The energetic magnetospheric electrons gyrate along the magnetic field lines of Saturn, and at the same time bounce between the mirror points of the magnetosphere. This motion is combined with the drift of the magnetic field lines. When these flux tubes interact with the upper atmosphere of Titan, their content is depleted over approximately an electron bounce period. These depletion signatures are observed as sudden drop-outs of the electron fluxes. We examined the altitude distribution of these drop-outs and concluded that these mostly detected in the exo-ionosphere of Titan and sometimes within the ionosphere.However there is a relatively significant scatter in the orbit to orbit data, which can be attributed to the which can be attributed to the variability of the plasma environment and as a consequence, the induced magnetosphere of Titan. A weak trend between the incoming electron fluxes and the measured drop-out altitudes has also been observed.     

Effect of parallel electric field on charged particle precipitation

Considering the presence of electric field parallel to geomagnetic field in the magnetosphere, the problem of wave-particle interaction has been considered. Dispersion equation of whistler mode wave in presence of parallel electric field has been derived. Using the effective dispersion equation, the wave-particle interaction has been reformulated to account for the effect of parallel electric field. Using charged particle energy spectrum and magnetospheric field and plasma models, the flux of electron precipitation has been computed. It is shown that the parallel electric field plays an important role and may work in simultaneity with other processes known for enhancement of electron precipitation.     

Thermal protons in the morning magnetosphere: Filling and heating near the equatorial plasmapause

Thermal H⁺ distributions have been measured as the European Space Agency GEOS-1 satellite passed through the late morning equatorial magnetosphere, plasmapause and plasmasphere. The unique capabilities of the on-board Supralhermal Plasma Analysers (SPA) have been used to overcome the retarding floating potential of the satellite and measure the velocity distribution of the cold protons. In the magnetosphere an enhanced source cone of such ions with a temperature of ~ 0.5 eV is a signature of the filling process occurring outside the plasmapause where flux tubes are relatively empty. In the plasmasphere the thermal H⁺ is essentially isotropic with a temperature less than 0.5 eV but the motion of the satellite introduces apparent drift.These measurements of cold proton velocity distribution now permit a reappraisal of the definition of the “plasmapause”. It becomes inappropriate to use an arbitrary empirical density, e.g. the conventional 10 cm ^?3, in order to establish a boundary. It is now possible to identify a plasmapause interaction region where the two cold proton populations co-exist. This region generally lies Earthward of the 10 cm ^?3 density level, has a width which is strongly dependent on magnetic activity and the temperature is typically between 0.5 and 1.5 eV. The change from “filled” to “unfilled” flux tubes relates to the physical processes which are occurring and the controlling electric field configuration; in particular, the last closed equipotential. Throughout this region, in going from the plasmasphere to the magnetosphere, the plasma drift motion is expected to change from corotation to a convection which is controlled by E ×B, and is predominantly Sunward due to the dawn-dusk electric field. Crossing the plasmapause on the morning side, little change in drift direction should occur but subtle variations in the ionic velocity distribution do reflect the change in the degree of flux tube density equilibrium.Our first direct measurement of the magnetospheric E × B drift has been reported previously but here measurements from a selected six day period show how the plasma in the plasmapause region responds to changing magnetospheric activity. The drift velocities cannot he derived with high accuracy but the analysis shows that the technique can provide a valid mapping of the magnelospheric electric field. In addition, since the magnetospheric cold plasma distribution is observed after it has come from the ionosphere, a distance of many Earth radii, the scattering and accelerating mechanisms along the flux tube can be studied. For this particular data-set taken in the late morning, the maximum potential drops along the flux tubes were less than a volt. The ionospheric proton source cone is observed to be broad, pitch angle scattering persists up to 40 or even 70°.Although these results throw new light on the plasmaspheric filling process one must recognise that, however the plasmapause is defined, it is not a simple matter to map this boundary from the equatorial plane down to low altitudes and the mid-latitude trough.     

Reflection and refraction of hydromagnetk waves at the magnetopause

Reflection and transmission coefficients of MHD waves are obtained at a stable, plane interface which separates two compressible, perfectly conducting media in relative motion to each other. The coefficients are evaluated for representative conditions of the quiettime, near-Earth magnetopause. The transmission coefficient averaged over a hemispherical distribution of incident waves is found to be 1–2 per cent. Yet the magnitude of the energy flux deposited into the magnetosphere in a day averaged over a hemispherical distribution of waves having amplitudes of say 2–3 gamma, is estimated to be of the order 10²² erg. Therefore the energy input of MHD waves must contribute significantly to the energy budget of the magnetosphere. The assumption that the boundary surface is a tangential discontinuity with no curvature limits the present theory to hydromagnetic frequencies higher than about 10⁻¹ Hz. The ion gyrofrequencies for the models assumed here lie above 2 × 10⁻¹ Hz. Therefore the present treatment applies to MHD waves near 10⁻¹ Hz.     

The Kelvin-Helmholtz instability on the magnetopause

Conditions for the development of Kelvin-Helmholtz (K-H) waves on the magnetopause have been known for more than 15 years; more recently, spacecraft observations have stimulated further examination of the properties of K-H waves. For amagnetopause with no boundary layer, two different modes of surface waves have been identified and their properties have been investigated for various assumed orientations of magnetic field and flow velocity vectors. The power radiated into the magnetosphere from the velocity shear at the boundary has been estimated. Other calculations have focused on the consequences of finite thickness boundary layers, both uniform and non-uniform. The boundary layer is found to modify the wave modes present at the magnetopause and to yield a criterion for the wavelength of the fastest growing surface waves. The paper concludes by questioning the extent to which the inferences from boundary layer models are model dependent and identifies areas where further work is needed or anticipated.     

A three-ring circuit model of the magnetosphere

We have modeled the magnetosphere by superimposing a dipole field, a uniform field and a perturbation field due to a simple current system. This current system consists of a ring current in the neutral line of the dipole plus uniform fields, together with vertical currents representing field-aligned currents to the neutral line. The current circuit is closed by two additional ring currents above and below the equatorial plane representing distributed adiabatic perpendicular currents. This system produces many magnetospheric features including a magnetopause, bending of magnetic field lines in the anti-solar direction, a magnetotail, and cusps on the day-side of the Earth. Our aim is to demonstrate that it is not necessary to think of the magnetic field topology as being caused by the flowing plasma carrying field lines. The fundamental physical problem is to derive the current system from the self-consistent interaction of the solar-wind and magnetospheric plasmas and fields.     

Reconstruction of propagating Kelvin–Helmholtz vortices at Mercury's magnetopause

A series of quasi-periodic magnetopause crossings were recorded by the MESSENGER spacecraft during its third flyby of Mercury on 29 September 2009, likely caused by a train of propagating Kelvin–Helmholtz (KH) vortices. We here revisit the observations to study the internal structure of the waves. Exploiting MESSENGER's rapid traversal of the magnetopause, we show that the observations permit a reconstruction of the structure of a rolled-up KH vortex directly from the spacecraft's magnetic field measurements. The derived geometry is consistent with all large-scale fluctuations in the magnetic field data, establishes the non-linear nature of the waves, and shows their vortex-like structure. In several of the wave passages, a reduction in magnetic field strength is observed in the middle of the wave, which is characteristic of rolled-up vortices and is related to the increase in magnetic pressure required to balance the centrifugal force on the plasma in the outer regions of a vortex, previously reported in computer simulations. As the KH wave starts to roll up, the reconstructed geometry suggests that the vortices develop two gradual transition regions in the magnetic field, possibly related to the mixing of magnetosheath and magnetospheric plasma, situated at the leading edges from the perspectives of both the magnetosphere and the magnetosheath.     

Magnetospheric plasma interactions

The Earth's magnetosphere (including the ionosphere) is our nearest cosmical plasma system and the only one accessible to mankind for extensive empirical study by in situ measurements. As virtually all matter in the universe is in the plasma state, the magnetosphere provides an invaluable sample of cosmical plasma from which we can learn to better understand the behaviour of matter in this state, which is so much more complex than that of unionized matter.It is therefore fortunate that the magnetosphere contains a wide range of different plasma populations, which vary in density over more than six powers of ten and even more in equivalent temperature. Still more important is the fact that its dual interaction with the solar wind above and the atmosphere below make the magnetosphere the site of a large number of plasma phenomena that are of fundamental interest in plasma physics as well as in astrophysics and cosmology.The interaction of the rapidly streaming solar wind plasma with the magnetosphere feeds energy and momentum, as well as matter, into the magnetosphere. Injection from the solar wind is a source of plasma populations in the outer magnetosphere, although much less dominating than previously thought. We now know that the Earth's own atmosphere is the ultimate source of much of the plasma in large regions of the magnetosphere. The input of energy and momentum drives large scale convection of magnetospheric plasma and establishes a magnetospheric electric field and large scale electric current systems that carry millions of ampère between the ionosphere and outer space. These electric fields and currents play a crucial role in generating one of the most spectacular among natural phenomena, the aurora, as well as magnetic storms that can disturb man-made systems on ground and in orbit. The remarkable capability of accelerating charged particles, which is so typical of cosmical plasmas, is well represented in the magnetosphere, where mechanisms of such acceleration can be studied in detail. In situ measurements in the magnetosphere have revealed an unexpected tendency of cosmical plasmas to form cellular structure, and shown that the magnetospheric plasma sustains previously unexpected, and still not fully explained, chemical separation mechanisms, which are likely to operate in other cosmical plasmas as well.Presented at the 2nd UN/ESA Workshop, held in Bogotá, Colombia, 9–13 November, 1992.