Global MHD modeling of Mercury's magnetosphere with applications to the MESSENGER mission and dynamo theory

We use a global magnetohydrodynamic (MHD) model to simulate Mercury's space environment for several solar wind and interplanetary magnetic field (IMF) conditions in anticipation of the magnetic field measurements by the MESSENGER spacecraft. The main goal of our study is to assess what characteristics of the internally generated field of Mercury can be inferred from the MESSENGER observations, and to what extent they will be able to constrain various models of Mercury's magnetic field generation. Based on the results of our simulations, we argue that it should be possible to infer not only the dipole component, but also the quadrupole and possibly even higher harmonics of the Mercury's planetary magnetic field. We furthermore expect that some of the crucial measurements for specifying the Hermean internal field will be acquired during the initial fly-bys of the planet, before MESSENGER goes into orbit around Mercury.     

Origin of Mercury’s double magnetopause: 3D hybrid simulation study with A.I.K.E.F.

During the first and second Mercury flyby the MESSENGER spacecraft detected a dawn side double-current sheet inside the Hermean magnetosphere that was labeled the “double magnetopause” (Slavin, J.A. et al. [2008]. Science 321, 85). This double current sheet confines a region of decreased magnetic field that is referred to as Mercury’s “dayside boundary layer” (Anderson, M., Slavin, J., Horth, H. [2011]. Planet. Space Sci.). Up to the present day the double current sheet, the boundary layer and the key processes leading to their formation are not well understood. In order to advance the understanding of this region we have carried out self-consistent plasma simulations of the Hermean magnetosphere by means of the hybrid simulation code A.I.K.E.F. (Müller, J., Simon, S., Motschmann, U., Schüle, J., Glassmeier, K., Pringle, G.J. [2011]. Comput. Phys. Commun. 182, 946–966). Magnetic field and plasma results are in excellent agreement with the MESSENGER observations. In contrast to former speculations our results prove this double current sheet may exist in a pure solar wind hydrogen plasma, i.e. in the absence of any exospheric ions like sodium. Both currents are similar in orientation but the outer is stronger in intensity. While the outer current sheet can be considered the “classical” magnetopause, the inner current sheet between the magnetopause and Mercury’s surface reveals to be sustained by a diamagnetic current that originates from proton pressure gradients at Mercury’s inner magnetosphere. The pressure gradients in turn exist due to protons that are trapped on closed magnetic field lines and mirrored between north and south pole. Both, the dayside and nightside diamagnetic decreases that have been observed during the MESSENGER mission show to be direct consequences of this diamagnetic current that we label Mercury’s “boundary-layer-current“.     

Observations of suprathermal electrons in Mercury's magnetosphere during the three MESSENGER flybys

In 2008 the MESSENGER spacecraft made the first direct observation of Mercury's magnetosphere in the more than 30 years since the Mariner 10 encounters. During MESSENGER's first flyby on 14 January 2008, the interplanetary magnetic field (IMF) was northward immediately prior to and following MESSENGER's equatorial passage through this small magnetosphere. The Energetic Particle Spectrometer (EPS), one of two sensors on the Energetic Particle and Plasma Spectrometer instrument that responds to electrons from ∼35 keV to 1 MeV and ions from ∼35 keV to 2.75 MeV, saw no increases in particle intensity above instrumental background (∼5 particles/cm²/sr/s/keV at 45 keV) at any time during the probe's magnetospheric passage. During MESSENGER's second flyby on 6 October 2008, there was a steady southward IMF, and intense reconnection was observed between the planet's magnetic field and the IMF. However, once again EPS did not observe bursts of energetic particles similar to those reported by Mariner 10 from its March 1974 encounter. On 29 September 2009, MESSENGER flew by Mercury for the third and final time before orbit insertion in March 2011. Although a spacecraft safe-hold event stopped science measurements prior to the outbound portion of the flyby, all instruments recorded full observations until a few minutes before the closest approach. In particular, the MESSENGER Magnetometer documented several substorm-like signatures of extreme loading of Mercury's magnetotail, but again EPS measured no energetic ions or electrons above instrument background during the inbound portion of the flyby. MESSENGER's X-Ray Spectrometer (XRS) nonetheless observed photons resulting from low-energy (∼10 keV) electrons impinging on its detectors during each of the three flybys. We infer that suprathermal plasma electrons below the EPS energy threshold caused the bremsstrahlung seen by XRS. In this paper, we summarize the energetic particle observations made by EPS and XRS during MESSENGER's three Mercury flybys, and we revisit the observations reported by Mariner 10 in the context of these new results.     

Electron transport and precipitation at Mercury during the MESSENGER flybys: Implications for electron-stimulated desorption

To examine electron transport, energization, and precipitation in Mercury's magnetosphere, a hybrid simulation study has been carried out that follows electron trajectories within the global magnetospheric electric and magnetic field configuration of Mercury. We report analysis for two solar-wind parameter conditions corresponding to the first two MESSENGER Mercury flybys on January 14, 2008, and October 6, 2008, which occurred for similar solar wind speed and density but contrasting interplanetary magnetic field (IMF) directions. During the first flyby the IMF had a northward component, while during the second flyby the IMF was southward. Electron trajectories are traced in the fields of global hybrid simulations for the two flybys. Some solar wind electrons follow complex trajectories at or near where dayside reconnection occurs and enter the magnetosphere at these locations. The entry locations depend on the IMF orientation (north or south). As the electrons move through the entry regions they can be energized as they execute non-adiabatic (demagnetized) motion. Some electrons become magnetically trapped and drift around the planet with energies on the order of 1–10 keV. The highest energy of electrons anywhere in the magnetosphere is about 25 keV, consistent with the absence of high-energy (>35 keV) electrons observed during either MESSENGER flyby. Once within the magnetosphere, a fraction of the electrons precipitates at the planetary surface with fluxes on the order of 10⁹ cm⁻² s⁻¹ and with energies of hundreds of eV. This finding has important implications for the viability of electron-stimulated desorption (ESD) as a mechanism for contributing to the formation of the exosphere and heavy ion cloud around Mercury. From laboratory estimates of ESD ion yields, a calculated ion production rate due to ESD at Mercury is found to be on par with ion sputtering yields.     

An assessment of the length and variability of Mercury's magnetotail

We employ Mariner 10 measurements of the interplanetary magnetic field in the vicinity of Mercury to estimate the rate of magnetic reconnection between the interplanetary magnetic field and the Hermean magnetosphere. We derive a time-series of the open magnetic flux in Mercury's magnetosphere, from which we can deduce the length of the magnetotail. The length of the magnetotail is shown to be highly variable, with open field lines stretching between 15R_H and 850R_H downstream of the planet (median 150R_H). Scaling laws allow the tail length at perihelion to be deduced from the aphelion Mariner 10 observations.     

The space environment of Mercury at the times of the second and third MESSENGER flybys

The second and third flybys of Mercury by the MESSENGER spacecraft occurred, respectively, on 6 October 2008 and on 29 September 2009. In order to provide contextual information about the solar wind properties and the interplanetary magnetic field (IMF) near the planet at those times, we have used an empirical modeling technique combined with a numerical physics-based solar wind model. The Wang–Sheeley–Arge (WSA) method uses solar photospheric magnetic field observations (from Earth-based instruments) in order to estimate the inner heliospheric radial flow speed and radial magnetic field out to 21.5 solar radii from the Sun. This information is then used as input to the global numerical magnetohydrodynamic model, ENLIL, which calculates solar wind velocity, density, temperature, and magnetic field strength and polarity throughout the inner heliosphere. WSA-ENLIL calculations are presented for the several-week period encompassing the second and third flybys. This information, in conjunction with available MESSENGER data, aid in understanding the Mercury flyby observations and provide a basis for global magnetospheric modeling. We find that during both flybys, the solar wind conditions were very quiescent and would have provided only modest dynamic driving forces for Mercury's magnetospheric system.     

The dayside magnetospheric boundary layer at Mercury

Magnetic field and plasma data from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft on the outbound portions of the first (M1) and second (M2) flybys of Mercury reveal a region of depressed magnetic field magnitude and enhanced proton fluxes adjacent to but within the magnetopause, which we denote as a dayside boundary layer. The layer was present during both encounters despite the contrasting dayside magnetic reconnection, which was minimal during M1 and strong during M2. The overall width of the layer is estimated to be between 1000 and 1400 km, spanning most of the distance from the dayside planetary surface to the magnetopause in the mid-morning. During both flybys the magnetic pressure decrease was ∼1.6 nPa, and the width of the inner edge was comparable to proton gyro-kinetic scales. The maximum variance in the magnetic field across the inner edge was aligned with the magnetic field vector, and the magnetic field direction did not change markedly, indicating that the change in field intensity was consistent with an outward plasma-pressure gradient perpendicular to the magnetic field. Proton pressures in the layer inferred from reduced distribution observations were 0.4 nPa during M1 and 1.0 nPa during M2, indicating either that the proton pressure estimates are low or that heavy ions contribute substantially to the boundary-layer plasma pressure. If the layer is formed by protons drifting westward from the cusp, there should be a strong morning–afternoon asymmetry that is independent of the interplanetary magnetic field (IMF) direction. Conversely, if heavy ions play a major role, the layer should be strong in the morning (afternoon) for northward (southward) IMF. Future MESSENGER observations from orbit about Mercury should distinguish between these two possibilities.     

Mercury’s magnetosphere-solar wind interaction for northward and southward interplanetary magnetic field: Hybrid simulation results

Analysis of global hybrid simulations of Mercury’s magnetosphere-solar wind interaction is presented for northward and southward interplanetary magnetic field (IMF) orientations in the context of MESSENGER’s first two encounters with Mercury. The global kinetic simulations reveal the basic structure of this interaction, including a bow shock, ion foreshock, magnetosheath, cusp regions, magnetopause, and a closed ion ring belt formed around the planet within the magnetosphere. The two different IMF orientations induce different locations of ion foreshock and different magnetospheric properties: the dayside magnetosphere is smaller and cusps are at lower latitudes for southward IMF compared to northward IMF whereas for southward IMF the nightside magnetosphere is larger and exhibits a thin current sheet with signatures of magnetic reconnection and plasmoid formation. For the two IMF orientations the ion foreshock and quasi-parallel magnetosheath manifest ion-beam-driven large-amplitude oscillations, whereas the quasi-perpendicular magnetosheath shows ion-temperature-anisotropy-driven wave activity. The ions in Mercury’s belt remain quasi-trapped for a limited time before they are either absorbed by Mercury’s surface or escape from the magnetosphere. The simulation results are compared with MESSENGER’s observations.     

Magnetic fields and plasmas in the inner heliosphere: Helios results

The magnetic field of Mercury and the structure and dynamics of Mercury's magnetosphere, which will be studied by the spacecraft orbiting Mercury, are strongly influenced by the interaction of the solar wind with Mercury. In order to understand the internal magnetic field, it will be necessary to correct the observations of the external field for the distortions produced by the solar wind. Understanding of the solar wind interaction with Mercury is essential for understanding the structure and dynamics of the magnetosphere and phenomena such as magnetic storms. Helios 1 and 2 made a number of passes in the region traversed by the orbit of Mercury, and each pass provided a sample of the solar wind environment of Mercury. This paper reviews the plasma and magnetic field observations from Helios that provide a general basis for interpreting the observations of Mercury that will be made by orbiting spacecraft. The variables that govern the structure and dynamics of the magnetospheres of Mercury and Earth are approximately 5–10 times larger at Mercury than at Earth. Thus, the solar wind interaction with Mercury will be much stronger than the interaction with Earth. Moreover, the solar wind at Mercury is probably more variable than that at Earth. There is a clear need for measurements of the solar wind during the approach of spacecraft to Mercury and while they are in orbit around Mercury.     

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.     

The Kelvin-Helmholtz instability at Mercury: An assessment

The Kelvin-Helmholtz instability is believed to be an important means for the transfer of energy, plasma, and momentum from the solar wind into planetary magnetospheres, with in situ measurements reported from Earth, Saturn, and Venus. During the first MESSENGER flyby of Mercury, three periodic rotations were observed in the magnetic field data possibly related to a Kelvin-Helmholtz wave on the dusk side magnetopause. We present an analysis of the event, along with comparisons to previous Kelvin-Helmholtz observations and an investigation of what influence finite ion gyro radius effects, believed to be of importance in the Hermean magnetosphere, may have on the instability. The wave signature does not correspond to that of typical Kelvin-Helmholtz events, and the magnetopause direction does not show any signs of major deviation from the unperturbed case. There is thus no indication of any high amplitude surface waves. On the other hand, the wave period corresponds to that expected for a Kelvin-Helmholtz wave, and as the dusk side is shown to be more stable than the dawn side, we judge the observed waves not to be fully developed Kelvin-Helmholtz waves, but they may be an initial perturbation that could cause Kelvin-Helmholtz waves further down the tail.     

The MESSENGER mission to Mercury: scientific objectives and implementation

Mercury holds answers to several critical questions regarding the formation and evolution of the terrestrial planets. These questions include the origin of Mercury's anomalously high ratio of metal to silicate and its implications for planetary accretion processes, the nature of Mercury's geological evolution and interior cooling history, the mechanism of global magnetic field generation, the state of Mercury's core, and the processes controlling volatile species in Mercury's polar deposits, exosphere, and magnetosphere. The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission has been designed to fly by and orbit Mercury to address all of these key questions. After launch by a Delta 2925H-9.5, two flybys of Venus, and two flybys of Mercury, orbit insertion is accomplished at the third Mercury encounter. The instrument payload includes a dual imaging system for wide and narrow fields-of-view, monochrome and color imaging, and stereo; X-ray and combined gamma-ray and neutron spectrometers for surface chemical mapping; a magnetometer; a laser altimeter; a combined ultraviolet–visible and visible-near-infrared spectrometer to survey both exospheric species and surface mineralogy; and an energetic particle and plasma spectrometer to sample charged species in the magnetosphere. During the flybys of Mercury, regions unexplored by Mariner 10 will be seen for the first time, and new data will be gathered on Mercury's exosphere, magnetosphere, and surface composition. During the orbital phase of the mission, one Earth year in duration, MESSENGER will complete global mapping and the detailed characterization of the exosphere, magnetosphere, surface, and interior.     

Induced magnetic field effects at planet Mercury

At Mercury's surface external magnetic field contributions caused by magnetospheric current systems play a much more important role than at Earth. They are subjected to temporal variations and therefore will induce currents in the large conductive iron core. These currents give rise to an additional magnetic field superposing the planetary field. We present a model to estimate the size of the induced fields using a magnetospheric magnetic field model with time-varying magnetopause position. For the Hermean interior we assume a two-layer conductivity distribution. We found out that about half of the surface magnetic field is due to magnetospheric or induced currents. The induced fields achieve 7-12% of the mean surface magnetic intensity of the internal planetary field, depending on the core size. The magnetic field was also modeled for a satellite moving along a polar orbit in the Hermean magnetosphere, showing the importance of a careful separation of the magnetic field measurements.     

The interplanetary magnetic field environment at Mercury's orbit

Mercury is exposed to the most dynamic heliospheric space environment of any planet in the solar system. The magnetosphere is particularly sensitive to variations in the interplanetary magnetic field (IMF), which control the intensity and geometry of the magnetospheric current systems that are the dominant source of uncertainty in determinations of the internal planetary magnetic field structure. The Magnetometer on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft has made extensive magnetic field observations in the inner heliosphere over the heliocentric distances of Mercury's orbit, between 0.31 and 0.47 AU. In this paper, Magnetometer data from MESSENGER, obtained at rates of 2 and 20 vector samples per second, are used together with previous observations in the inner heliosphere by Helios and at Earth by the Advanced Composition Explorer, to study the characteristics of IMF variability at Mercury's orbit. Although the average IMF geometry and magnitude depend on heliocentric distance as predicted by Parker, the variability is large, comparable to the total field magnitude. Using models for the external current systems we evaluate the impact of the variability on the field near the planet and find that the large IMF fluctuations should produce variations of the magnetospheric field of up to 30% of the dipole field at 200 km altitude, corresponding to the planned periapsis of MESSENGER's orbit at Mercury. The IMF fluctuations in the frequency range are consistent with turbulence, whereas evidence for dissipation was observed for . The transition between the turbulent and dissipative regimes is indicated by a break in the power spectrum, and the frequency of this break point is proportional to the IMF magnitude.     

Asymmetry of plasma fluxes at Mars. ASPERA-3 observations and hybrid simulations

The asymmetry of fluxes of solar wind and planetary ions is studied by using the ASPERA-3 observations onboard the Mars Express spacecraft in February 2004 to March 2006. Due to the small scale of the Martian magnetosphere and its induced origin, the flow pattern near Mars is sensitive to the directions of the interplanetary magnetic and electric (-V×B) fields. Asymmetry of the magnetic field draping produces an asymmetry in plasma flows in the plane containing the IMF. The crustal magnetic fields on Mars also influence the flow pattern. Scavenging of planetary ions is less efficient in the regions of strong crustal magnetization and therefore the escape fluxes of planetary ions in the southern hemisphere are smaller. The results of the observations are compared to simulations based on a 3D hybrid model with several ion species.     

Influence of the magnetosheath on solar proton penetration into the magnetosphere

The observation of solar protons (1–9 MeV) aboard HEOS-2 in the high-latitude magnetotail and magnetosheath on 9 June 1972, and their comparison with simultaneous measurements on Explorers 41 and 43, both in interplanetary space, indicate the existence of a distinct region of the inner magnetosheath (about 3 Earth radii thick) near the high-latitude magnetopause in which the solar particle flow is almost reversed with respect to the flow observed in interplanetary space. The region can also be seen by comparing magnetic field measurements on the three spacecraft. The observations in the outer layer of the magnetotail show solar protons predominantly entering the magnetosphere somewhere near the Earth, perhaps the cusp region.     

Mercury’s magnetospheric magnetic field after the first two MESSENGER flybys

The “paraboloid” model of Mercury’s magnetospheric magnetic field is used to determine the best-fit magnetospheric current system and internal dipole parameters from magnetic field measurements taken during the first and second MESSENGER flybys of Mercury on 14 January and 6 October 2008. Together with magnetic field measurements taken during the Mariner 10 flybys on 29 March 1974 and 16 March 1975, there exist three low-latitude traversals separated in longitude and one high-latitude encounter. From our model formulation and fitting procedure a Mercury dipole moment of 196 nT ·  (where R_M is Mercury’s radius) was determined. The dipole is offset from Mercury’s center by 405 km in the northward direction. The dipole inclination to Mercury’s rotation axis is relatively small, ∼4°, with an eastern longitude of 193° for the dipole northern pole. Our model is based on the a priori assumption that the dipole position and the moment orientation and strength do not change in time. The root mean square (rms) deviation between the Mariner 10 and MESSENGER magnetic field measurements and the predictions of our model for all four flybys is 10.7 nT. For each magnetic field component the rms residual is ∼6 nT or about 1.5% of the maximum measured magnetic field, ∼400 nT. This level of agreement is possible only because the magnetospheric current system parameters have been determined separately for each flyby. The magnetospheric stand-off distance, the distance from the planet’s center to the inner edge of the tail current sheet, the tail lobe magnetic flux, and the displacement of the tail current sheet relative to the Mercury solar-magnetospheric equatorial plane have been determined independently for each flyby. The magnetic flux in the tail lobes varied from 3.8 to 5.9 MWb; the subsolar magnetopause stand-off distance from 1.28 to 1.43 R_M; and the distance to the inner edge of the current sheet from 1.23 to 1.32 R_M. The differences in the current systems between the first and second MESSENGER flybys are attributed to the effects of strong magnetic reconnection driven by southward interplanetary magnetic field during the latter flyby.     

Magnetospheric Cusps under Extreme Conditions: Cluster Observations and MHD Simulations Compared

MHD simulations are here applied to aid in the interpretation of three apparent cusp encounters by the Cluster 4 spacecraft in unusual places when the magnetosphere was under extreme solar wind and interplanetary magnetic field (IMF) conditions associated with the passage of magnetic clouds imbedded within fast ICMEs. At the time of each cusp encounter the IMF was very strong, generally northward in one case, generally equatorial in a second case, and generally southward in the third case. In the southward IMF case, the MHD models locate the origin of the cusp-like plasma by showing that the position of the spacecraft at the time of encounter was engulfed in a tongue of high-pressure plasma extending from the magnetopause into the magnetosphere. This tongue points to the northern-hemisphere cusp as the source of the feature. In the equatorial IMF case an elevated-pressure feature that apparently marked a cusp encounter in the computations coincided, however, with a passage in the solar wind of a dynamic pressure pulse, thus giving an alternative interpretation of the feature. However, Cluster data unambiguously identified the event as an encounter with magnetosheath-like plasma. Given that the Cluster observations classify the event as a true encounter with a cusp-like plasma feature (and not a compression event), the model simulations can be interpreted as identifying the origin of the feature to have been the northern-hemisphere cusp even though?—?and this is the interesting point?—?the observation point was in the southern hemisphere. In the northward IMF case, neither cusp (defined as a magnetic funnel linking the magnetopause to the Earth) was directly connected to the observation point. Instead, this encounter of magnetosheath-like plasma appears to be an instance of boundary-layer formation by means of the Song?–?Russell mechanism in which two-point magnetic reconnection entrains magnetosheath plasma on closed field lines when the IMF is northward.     

The MESSENGER mission to Mercury: scientific payload

The MErcury, Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission will send the first spacecraft to orbit the planet Mercury. A miniaturized set of seven instruments, along with the spacecraft telecommunications system, provide the means of achieving the scientific objectives that motivate the mission. The payload includes a combined wide- and narrow-angle imaging system; γ-ray, neutron, and X-ray spectrometers for remote geochemical sensing; a vector magnetometer; a laser altimeter; a combined ultraviolet-visible and visible-infrared spectrometer to detect atmospheric species and map mineralogical absorption features; and an energetic particle and plasma spectrometer to characterize ionized species in the magnetosphere.     

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.