Solar wind access to the plasma sheet along the flanks of the magnetotail

Low-energy particle trajectories in an idealized magnetotail magnetic field are investigated to determine the accessibility of magnetosheath protons and electrons to the plasma sheet along the flanks of the tail magnetopause. The drift motion of the positively (negatively) charged particles incident on the dawn (dusk) magnetotail flank causes such particles to penetrate deeper into the magnetotail. For certain combinations of particle energy, incident velocity vector and initial penetration point on the tail magnetopause, the incident particles can become trapped in the plasma sheet, after which their net drift motion then provides a current capable of supporting the entire observed magnetotail field. The results further indicate that the bulk of the solar wind plasma just outside the distant tail boundary, which streams preferentially in a direction along the magnetopause away from the Earth at velocities around 400 km s^?1, can be caught up in the tail if the initial penetration point is within about 2R_E, of the quasi-neutral sheet. It is suggested that a large fraction of the magnetotail plasma is composed of former solar wind particles which have penetrated the magnetospheric boundary at the tail flanks.     

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 effect of a normal magnetic field component on current sheet stability

A $\text{2}\text{2}\text{5}\text{-}\text{dimensional}$ particle-mesh computer model for the simulation of the current-sheet region of the geomagnetic tail is described. Important features are (a) the use of Fast Fourier techniques for the efficient solution of Ampere's equation, (b) the incorporation of sources and sinks of particles, (c) facilities for simulating finite width effects and (d) the option of including a normal magnetic field component linking through the sheet.Simulations carried out using this model indicate that current sheets with a non-zero normal magnetic field component and an infinite width are stable. The particles trace out Speiser-like orbits in such a case. Sheets with B_normal = 0 and a finite width are unstable with respect to the ion tearing-mode instability. However the presence of a normal magnetic field stabilises the system provided ρ₀<2L_y where ρ₀ is the characteristic length associated with the normal field and where L_y is the width of the sheet.On the basis of these results it is suggested that a geomagnetic substorm occurs when the normal magnetic field drops below the critical value needed for stability.     

Two spacecraft observation of particle bursts at the distant magnetopause and in the magnetotail boundary layer

Bursts of energetic particles have been observed simultaneously by IMP-6 (≈ 24 R_E, R_p ? 0.21 MeV) and IMP-8 (≈ 29.7 R_E, E_p ? 0.29 MeV, E_e ? 0.22 MeV) in the distant magnetotail on Nov. 26, 1973 at a time when the auroral electrojet showed significant intensification. During one of the bursts IMP-6 was briefly in the duskside plasma sheet and IMP-8 was only a few R_E away at the magnetopause/boundary layer, as revealed from magnetic field and plasma measurements. The time behaviour of the proton intensities and anisotropies indicate that the particles have their origin in the plasma sheet. Measurements of the energy spectra during one of the bursts in the boundary layer/magnetosheath show significant variation of the differential exponent and suggest a rigidity-dependent escape of energetic particles from the plasma sheet into the magnetosheath. With the high temporal resolution of IMP-8 data intensity peaks of relativistic electrons and/or energetic protons could be detected at the magnetopause when Bx ≈ 0 γ. They appear superimposed on the general intensity time profile of the burst and last 2–3 min. It is concluded that some of the relativistic electrons can escape from the plasma sheet very fast and form a temporally-varying layer at the magnetopause.     

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.     

The warm current sheet model, and its implications on the temporal behaviour of the geomagnetic tail

A simple model current sheet is studied numerically. Consistent fields and particle trajectories, and their dependence on electron and proton temperature, convection velocity and normal field, B_z, linking through the current sheet, are presented and discussed. It is shown that the protons, which are the major current carriers, largely retain the decoupling of the motion in the x-y plane from the normal oscillations as in the ‘cold’ current sheet. The positive potential of the current sheet is shown to be sufficient to trap some energetic electrons, the motion of which enables the predominance of energetic electrons towards the dawn side of the tail to be understood. Semi-empirical relationships for the thickness and the potential of the current sheet are obtained.

The consequences of such a current sheet on the behaviour of the geomagnetic tail are investigated. Using Faraday's law and the consistent cross tail electric field it is shown that the effect of a southward turning of the interplanetary field is to lead to a decrease in B_z,an increase of the current sheet conductivity, and a growth of stored field energy, i.e. the current sheet blocks merging. The decrease of the resistance of the current sheet is limited by the finite width of the tail. Finally, it is pointed out that if the conditions which bring about the growth of field energy persist, then the collapse of the field lines characteristic of substorms may occur.     

Time-dependent configuration changes of the magnetotail and plasma sheet thinning

The configuration of the magnetotail magnetic field has been calculated for a situation where a disruption of a portion of the tail current system develops. The decrease of the current in a localized region of the magnetotail leads to a collapse of the magnetic field in that vicinity. The calculated configuration of the field resembles what is predicted by reconnection models with the field lines moving toward the neutral sheet and then connecting and either moving toward or away from the earth. Associated with this changing magnetic field there is an induced electric field which will then influence the motion of the plasma in the magnetotail via E × B drifts.When the current from X_sm = ?20 to ?40 R_E in the tail is decreasing with a tune-constant of 0.5 h the electric field produced, which is primarily westward, has a maximum value of 0.83 mV m^?1 and produces plasma sheet thinning velocities of 0.3 km s^?1. Higher velocities result for more rapid rates of current decrease, and they agree well with experimental observations. The plasma flows in the sunward direction are, however, much smaller than what has been observed. This is due in part to the inability of the magnetic field model to adequately represent the magnetic field in the immediate vicinity of the neutral sheet. Use of an improved model would give better agreement with the observations.The calculations show that the induced electric field of a time-dependent magnetic field is able to explain certain observed features of the plasma sheet motions. Also, this agreement suggests that the assumption that there is no charge separation contribution to the electric field may be reasonable during situations of large scale and rapid current disruptions in the magnetotail.     

Response of the polar cap boundary and the current system to changes in IMF observed from the Magsat satellite in the southern hemisphere during summer

The magnetic field vector residuals observed from the Magsat satellite have been used to obtain the dependence of the polar cap boundary and the current system on IMF for quiet and mildly disturbed conditions (K_p ⩽ 3 +). The study has been carried out for the summer months in the Southern Hemisphere. “Shear reversals” (SRs) in vector residuals indicative of the infinite current sheet approximation of the field-aligned currents (FACs) indicate roughly the polar cap boundary or the poleward boundary of the plasma sheet. This is also the poleward edge of the region 1 FACs. The SR is defined to occur at the latitude where the vector goes to minimum and changes direction by approximately 180°.It is found that SRs mainly occur when the interplanetary magnetic field (IMF) has a southward-directed B_z- component and in the latitude range of about 70°–80°. SRs in the dusk sector occur predominantly when the azimuthal component B_y is positive and in the dawn sector when B_y is negative, irrespective of the sign of B_z These results agree with the known merging process of IMF with magnetopause field lines. When SRs occur on both dawn and dusk sectors, the residuals over the entire polar cap are nearly uniform in direction and magnitude, indicating negligible polar currents. Similar behaviour is observed during highly disturbed conditions usually associated with large negative values of B_z.Forty-one Magsat orbits with such SRs are quantitatively modelled for preliminary case studies of the resulting current distribution. It is found that SRs, in the plane perpendicular to the geomagnetic field, for the current vectors and the magnetic vector residuals (perturbations relative to the unperturbed field) occur at almost the same latitudes. The electrojet intensities range from 1.2 × 10⁴ to 6.5 × 10⁵ A (amperes). A preliminary classification of polar cap boundary crossings characterized by vector rotations rather than SRs also shows that they tend to occur mainly for negative B_z.     

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 asymmetries associated with the y-component of the IMF

Observed magnetospheric asymmetries which occur in response to the y-component of the IMF are discussed in terms of the open model of the magnetosphere. The torque which the IMF exerts on the magnetosphere about the Earth-Sun axis results in asymmetric addition of open flux tubes to the tail lobes about the noon-midnight meridian. In response an IMF-associated B_y field appears across the tail lobes. The ratio between internal and external B_y fields will generally be same as the ratio between internal and external electric fields. If the tail flux asymmetry is related to an asymmetric distribution of the field normal to the tail magnetopause then an asymmetry in tail lobe electric field and plasma populations will immediately result, as observed. If the flux asymmetry is associated with a twist in the tail then the B_y field will appear but not necessary the electric field and plasma asymmetries. Generally both effects may occur together. Simple open tail lobe models are derived which demonstrate the asymmetry effects. These represent more physically satisfactory models of the tail and its plasma populations than available hitherto, but they remain somewhat unrealistic in a number of respects. Finally, it is shown that the observed asymmetry effects on closed (auroral zone) field lines may be at least qualitatively accounted for if the cross-magnetosphere IMF-associated B_y field pervades not only the open but also the closed field line regime, as may be generally expected.     

The near earth magnetic field of the magnetotail current

In the forward part of the magnetosphere the distant tail current system approximates a magnetic quadrupole composed of two distorted adjacent solenoids. The current in the neutral sheet at this distance is accurately approximated as an infinitesimally thin current sheet. We have calculated the magnetic field near the Earth by integrating over the entire tail current system assuming the magnetotail is a cylinder of constant radius and that the tail current decreases with distance into the tail as $\text{|x|}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$. The field is then represented by a scalar potential expanded into spherical harmonics which may be conveniently added to the spherical harmonic expansion of the scalar potential representing the magnetopause current system.     

A short wavelength instability in the neutral sheet of the earth's geomagnetic tail

In an earlier paper, Bowers (1973), ion plasma oscillations were found to be unstable in the steady state developed by Cowley (1972) for the neutral sheet in the Earth's geomagnetic tail. In this paper a similar stability analysis is carried out but for a different steady state, suggested by Dungey, with the result that unstable waves with frequencies near the electron plasma frequency are found. In the Dungey steady state the current necessary for magnetic field reversal is carried by plasma originating from both the magnetosheath and the lobes of the tail. This modifies the steady state proposed by Alfvén and subsequently developed by Cowley in which all the current is carried by plasma from the lobes of the tail thereby fixing the cross-tail potential Φ. With magnetosheath plasma present the value of Φ is no longer fixed solely by parameters in the lobes of the tail but the cross-tail electric field is still assumed localised in the dusk region of the sheet as in the Cowley model due to the balance of charge required in the neutral sheet. The value of Φ can be expected to increase as magnetic flux is transported to the tail which inflates and causes flux annihilation because the magneto-sheath plasma in the neutral sheet has insufficient pressure to keep the two lobes of the tail apart. The Vlasov-Maxwell set of equations is perturbed and linearised enabling a critical condition for instability to be found for modes propagating across the tail. Typically, this condition requireseΦ≳KT _m whereT _m is the temperature of magnetosheath electrons. The instability occurs in the presence of cold plasma which hasE×B drifted into the neutral sheet from the lobes of the tail. This contrasts with the usual two stream instability which is stabilised by the cold plasma. Once precipitated the instability may be explosive provided current disruption occurs, for then a further increase in Φ will result which drives a greater range of wave numbers unstable thereby causing even more turbulence and an even larger cross-tail electric field. Because of this behaviour the instability may be a trigger for a substorm.     

A mechanism for the growth phase of magnetospheric substorms

A mechanism is presented whereby the rate of energy dissipation in the magnetosphere is controlled by the particle density in the plasma sheet in the near geomagnetic tail. The mechanism is based on a model in which the plasma sheet is sustained by injection of solar-wind particles into the dayside magnetosphere. The efficiency of the injection is controlled by solarwind parameters, in particular, the north-south component of the interplanetary magnetic field; the maximum injection rate occurs when the interplanetary field is northward. During geomagnetically quiet times, this source balances the loss of particles from the edges of the tail current sheet. If the dayside source rate is reduced (e.g. by a southward-turning interplanetary magnetic field), then the plasma sheet is depleted and the rate of magnetic merging is enhanced in the earthward portion of the tail current sheet. This period of steadily-enhanced merging is associated with the growth phase, i.e. the period of enhanced magnetospheric convection for about one hour preceding the breakup of a polar magnetic or auroral substorm. The breakup can be understood as the result of the collapse of a portion of the tail current sheet following the local depletion of the plasma sheet.     

The effect of pressure anisotropy on the equilibrium structure of magnetic current sheets

The equilibrium structure of two-dimensional magnetic current sheets is investigated for systems in which the plasma pressure dominates the bulk flow energy, as appears appropriate for the quiet time plasmasheet in the geomagnetic tail. A simple model is studied in which the field is contained between plane parallel boundaries and varies exponentially along the system, while the plasma pressure is anisotropic, the anisotropy being arbitrary but constant along the centre plane. When the field is highly inflated by the plasma current it is found that adiabatic solutions exist only when the plasma pressure is close to isotropic. For the case P_∥ > P_⊥ it is argued that a thin, non-adiabatic current layer will in general form at the sheet centre, usually embedded within a much broader adiabatic current distribution. When P_⊥ > P_∥, a broad region of very depressed fields develops about the centre of the current sheet, terminated at its outer boundary by a spike in the current density. This central region becomes unstable to the mirror mode well before the limiting adiabatic solution is reached.     

The three-dimensional shape of the magnetopause

Nearly 1000 magnetopause crossings from HEOS-2, HEOS-1, OGO-5 and 5 IMP space-craft covering most of the northern and part of the southern dayside and near-Earth tail magnetopause (X >?15 R_E) have been used to perform a detailed study of the three-dimensional shape and location of the magnetopause. The long-term influence of the solar wind conditions on the average magnetopause geometry has been reduced by normalising the radial distances of the observed magnetopause crossings to an average dynamical solar wind pressure. Best-fit ellipsoids have been obtained to represent the average magnetopause surface in geocentric solar ecliptic (GSE) and (as a function of tilt angle) in solar magnetic (SM) coordinates. Average geocentric distances to the magnetopause for the 1972–1973 solar wind conditions (density 9.4 cm^?3, velocity 450 km s^?1) are 8.8 R_E in the sunward direction, 14.7 R_E in the dusk direction, 13.4 R_E in the dawn direction and 13.7 R_E in the direction normal to the ecliptic plane. The magnetopause surface is tilted by 6.6° ± 2° in a direction consistent with that expected from the aberration effect of the radial solar wind. Our data suggest that the solar wind plasma density and the interplanetary magnetic field (IMF) orientation affect the distance to the polar magnetopause, larger distances corresponding to higher plasma density and southward fields. Our best-fit magnetopause surface shows larger geocentric distances than predicted by the model of Choe et al. [Planet Space Sci. 21, 485 (1973).] normalised to the same solar wind pressure.     

The estimate of the Venus magnetotail length

We consider the process of flux tubes straightening in the Venus magnetotail on the basis of MHD model. We estimate the distance x _t, where flux tubes are fully straightened due to the magnetic tension and the magnetotail with the characteristic geometry of field lines (“slingshot” geometry) ends. We investigate the influence of the transversal current sheet scale on the process of flux tubes straightening. The assumption of a thin current sheet allows to obtain a lower estimate of the magnetotail length, x _t > 31R _V (R _V is the Venus radius), while the assumption of a broad current sheet allows to obtain an upper estimate, x _t < 44R _V. We show that kinetic effects associated with the losses of particles with small pitch angles from the flux tube and the influx of magnetosheath plasma into the flux tube do not significantly affect the estimate of the magnetotail length. The model predicts the existence of energetic fluxes of protons H⁺ (2–5 keV) and oxygen ions O⁺ (35–80 keV) in the distant tail. We discuss the magnetotail structure at x > x _t.     

Dependence of the magnetopause position on the southward interplanetary magnetic field

The distance to the dayside magnetopause is statistically analyzed in order to detect the possible dependence of the dayside magnetic flux on the polarity of the interplanetary magnetic field. The effect of changing solar wind pressure is eliminated by normalizing the observed magnetopause distances by the simultaneous solar wind pressure data. It is confirmed that the normalized size of the dayside magnetosphere at the time of southward interplanetary magnetic field is smaller than that at the time of northward interplanetary magnetic field. The difference in the magnetopause position between the two interplanetary field polarity conditions ranges from 0 to 2R_E. Statistics of the relation between the magnetopause distance and the magnetic field intensity just inside the magnetopause testifies that the difference in the magnetopause position is not due to a difference in the magnetosheath plasma pressure. The effect of the southward interplanetary magnetic field is seen for all longitudes and latitudes investigated (|λ_GM|? 45°, |φ_SM|? 90°). These results strongly suggest that a part of the dayside magnetic flux is removed from the dayside at the time of southward interplanetary magnetic field.     

On the distribution of By in the geomagnetic tail

The distribution of B_y in the geomagnetic tail associated with a net cross-tail magnetic flux, recently experimentally discovered, is here investigated within the framework of two-dimensional but non-planar field adiabatic time-independent equilbria. It is found that the flux distribution is controlled by the pressure anisotropy of the plasma, B_y being enhanced at the current sheet centre relative to that in the lobes for P_∥>P_⊥ and vice-versa for P_⊥>P_∥. For P_⊥>P_∥ a broad region of depressed field strength is found across the centre plane of the current sheet, terminated at its outer boundaries by spikes in the perpendicular current, across which B_y and B_x are “switched on” and rapidly increase towards their values in the low-β lobes. For P_∥>P_⊥ a thin high-current density layer forms at the sheet centre if the marginal firehose condition is approached, across which the B_x field reverses by rotation at nearly constant magnitude about the z-axis. The field magnitude in this thin layer depends upon the pressure anisotropy, such that the plasma remains just firehose stable within it, and may approach an appreciable fraction of the lobe field strength even for moderate anisotropies. Such structures have been observed in the geomagnetic tail, but do not appear to be a common feature of the quiet-time plasmasheet, where the field strength at the centre plane can reach small values with little obvious enhancement of B_y. In terms of the present model these observations require that either P_⊥>P_∥ in the quiet-time tail or that the plasma is within one or two per cent of isotropy if P_∥>P_⊥. These results then indicate that the production of plasma pressure anisotropy during adiabatic inward transport towards the Earth, which is generally expected to lead to P_∥>P_⊥ and its destruction by either macroscopic or microscopic processes, requires further study.     

A magnetospheric field model incorporating the OGO 3 and 5 magnetic field observations

A magnetospheric field model is presented in which the usually assumed toroidal ring current is replaced by a circular disk current of finite thickness that extends from the tail to geocentric distances less than 3R _E. The drastic departure of this model from the concept of the conventional ring current lies in that the current is continuous from the tail to the inner magnetosphere. This conceptual change was required to account for the recent results of analysis of the OGO 3 and 5 magnetic field observations. In the present model the cross-tail current flows along circular arcs concentric with the Earth and completes circuit via surface currents on the magnetopause. Apart from these return currents in the tail magnetopause, Mead's (1964) model is used for the field from the magnetopause current. The difference scalar field, ΔB, defined as the difference between the scalar field calculated from the present model and the magnitude of the dipole field is found to be in gross agreement with the observed ΔB (i.e. the observed scalar field minus a scalar reference geomagnetic field). An updated version of the ΔB contours from the OGO 3 and 5 observations, which is used for the comparison, is presented in this paper. Significant differences in details exist, however, between the model and the observed results. These differences will provide a guide for making modifications in the equatorial current system in future models.