On solar wind interaction with the earth's magnetosphere

Hydrodynamic and electrodynamic problems of solar wind interaction with the Earth's magnetosphere on the day-side are investigated.The initial fact, well established, is that the density of the magnetic field energy in the solar wind is rather small. Magnetic field intensity and orientation are shown to determine the character of the solar wind flow around the magnetosphere. For mean parameters of the wind, if the tangential component of the magnetic field is more or equal 5γ, the flow in the magneto-sheath will be laminar. For other cases the flow is of a turbulent type.For turbulent flow, typical plasma parameters are estimated: mean free path, internal scale of inhomogeneities and dissipated energy. The results obtained are compared with experimental data.For the case of laminar flow, special attention is paid to the situation when magnetic fields of the solar wind and Earth are antiparallel. It is suggested, on the basis of solid arguments, that the southward interplanetary field diffuses from the magnetosheath into the Earth's magnetosphere. These ideas are used for the estimation of the distance to the magnetopause subsolar point. A detailed comparison with results of observation is made. The coincidence is satisfactory. Theoretical investigation has been made to a great extent for thin magnetopause with thickness δ ～ R_He-gyroradius of an electron.It is shown that during magnetospheric substorms relaxation oscillations with the period τ = 100–300 sec must appear. A theorem is proved about the appearance of a westward electrical field during the substorm development, when the magnetosphere's day-side boundary moves Earthward and about the recovery phase, when the magnetopause motion is away from the Earth, when there is an eastward electrical field.In the Appendix, plasma wave exitation in the magnetopause is considered and conductivity magnitudes are calculated, including the reduction due to the scattering by plasma turbulence.     

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.     

Theory of the plasma sheet in the jovian magnetosphere

The magnetic field in the middle magnetosphere of Jupiter was suggested to be the planetary dipole field plus a perturbation field due to a current sheet (Smith et al, 1974). Since no data of the low energy plasma are available the existence of a plasma sheet could not be confirmed directly. In this paper we show how the plasma pressure and density-can be derived from the magnetic field in the framework of a self-consistent theory. For the magnetic field model proposed by Goertz et al. (1976c) we compute the isobars and isodensity lines and confirm the existence of a thin plasma sheet.     

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.     

Correlations between magnetic field and electron density observations during the inbound Ulysses Jupiter flyby

The spacecraft Ulysses flew through the Jovian magnetosphere during February 1992. This paper compares the magnetic field observations recorded during the inbound pass of the flyby with the electron density as derived from the URAP instrument. In general, it is expected that the density variations will anti-correlate with the magnetic field strength in order to maintain pressure balance, although there may be instances when a temperature or energy rise alone could balance the static stress. Furthermore, there is the possibility that a dynamic process could occur which would cause both the density and field magnitude to rise in unison. In the middle magnetosphere, anti-correlation is found to exist between the two data sets; however, in the outer magnetosphere (which was characterized by very disturbed fields) and in the transition region between the outer and middle magnetospheres, there is no simple relationship between the density and field. Examples of anti-correlation, temperature or energy increases and dynamic processes are found.     

Projection of auroral intensity contours into the magnetosphere

Isointensity contours of 630 nm auroral emission are traced into the magnetosphere, using two different empirical magnetic field models, the Mead-Fairfield model, and the Hedgecock-Thomas model. The auroral data are for a specific ISIS-II satellite pass, and so the starting points are expressed in geographic latitude and longitude coordinates, at a specific universal time. The magnetic field models are constructed from satellite magnetometer measurements, and those used correspond to magnetically quiet times. The projections are found to agree reasonably well with direct plasma measurements of the plasma sheet. The projections of the dayside contour connect to widely different regions of the magnetosphere, providing an interpretation that is consistent with observations of the dayside aurora. It is concluded that field line projections of the aurora into the magnetosphere using these models is a valid procedure, but only under quiet-time conditions.     

Low energy electrons and protons in the magnetosphere

Observations made by HEOS-2 of low energy electrons and protons in the high latitude magnetosphere are presented. Plasma in the magnetosphere is observed in the cusp (which extend down to low altitudes) and over large areas adjacent to the high latitude magnetopause both on the dayside and on the nightside (the entry layer and the plasma mantle respectively).A comparative study of the plasma properties in the various parts of the magnetosphere is performed. An ion bulk motion directed tailward along the geomagnetic field lines is observed both in the entry layer and in the plasma mantle; in the cusp, on the contrary, the bulk motion is practically absent. Moreover the electron thermal anisotropy is parallel to the magnetic field in the magnetosheath, and perpendicular to it in the plasma mantle. One possible explanation (suggested by Rosenbauer et al., 1975) of the origin of these populations is that plasma, penetrated from the magnetosheath in the entry layer, flows tailward along the field lines, is then reflected in the cusp region and convected in the plasma mantle.     

Magnetic field variations of the SI in the magnetosphere and correlated effects in interplanetary space

Explorer 26 magnetic field data in the magnetospheric region of L=3?6 and LT 1100–1500 hr with geomagnetic latitude range ?6° to 27° have been analyzed for studying nineteen SI and SC events. Most of the SI events observed in the magnetosphere at less than 15° geomagnetic latitude are compressional with magnetic perturbations along the ambient field. Elliptic polarizations with magnetic field variations in all three components have been observed between 10° and 27° geomagnetic latitude. Polarization directions have been shown to have similar patterns to those observed in the surface magnetic field data. Afternoon LT zone data in the magnetosphere indicate polarization patterns in general agreement with the results of Wilson and Sugiura (1961) obtained earlier from surface observations. The SI/SC perturbations are also qualitatively shown to be related to changes in the interplanetary magnetic field observed beyond 1 a.u.     

A calculation of auroral hiss with improved models for geoplasma and magnetic field

Intensities of auroral hiss generated by the Cerenkov radiation process by electrons in the lower magnetosphere are calculated with respect to a realistic model of the Earth's magnetosphere. In this calculation, the magnetic field is expressed by the “Mead-Fairfield Model” (1975), and a static model of the iono-magnetospheric plasma distribution is constructed with data accumulated by recent satellites (Alouette-I, -II, ISIS-I, OGO-4, -6 and Explorer 22). The energy range of hiss producing electrons and the frequency range of the calculated VLF are 100–200 keV, and 2–200 kHz, respectively. Intensities with a maximum around 20 kHz, of the order of 10^?14 W/m²/Hz¹ at the ground seem to be ascribable to the incoherent Cerenkov emission from soft electrons with a differential energy spectrum E^?2 having an intensity of the order of 10⁸cm^?2/sec/sr/eV at 100 eV. It is shown that the frequency of the maximum hiss spectral density at geomagnetic latitudes 80° on the day-side and 70° on the night-side is around 20 kHz for the soft spectrum (～E^?2) electrons, which shifts toward lower frequency (～10 kHz) for a hard spectrum (～E^?1·2) electrons. The maximum hiss intensity produced by soft electrons is more than one order higher than that of hard electron produced hiss. The higher rate of hiss occurrence in the daytime side, particularly in the soft electron precipitation zone in the morning sector, and the lesser occurrence of auroral hiss in night-time sectors must be, therefore, due to the local time dependence of the energy spectra of precipiating electrons rather than the difference in the geomagnetic field and in the geoplasma distributions.     

Some properties of geomagnetic field pulsations in the 0.1–1.0-Hz frequency range: A quantitative description and comparison with the satellite and ground-based observations

By using an image-dipole magnetic field model for a variety of plasma density profiles we have studied the latitude effect of the 0.1–1.0-Hz hydromagnetic wave propagation in the Earth's magnetosphere. On comparing the results of signal group delay time calculations for dipole and model magnetic fields with ground and satellite observations we obtain some propagation characteristics of Pc1s and localize the regions of their generation. Our results show that most high-latitude Pc1 events are generated in the outer magnetosphere in accordance with ground and satellite observations and theoretical considerations. The non-dipole geometry of the geomagnetic field in the outer magnetosphere (at geomagnetic latitudes φ₀ > 66°, L > 6) has a significant effect on the hydromagnetic wave propagation.     

Relations between turbulent regions of interplanetary magnetic field and Jovian decametric radio wave emissions from the main source

Jovian decametric radio wave emissions that were observed at Goddard Space Flight Center, U.S.A. for a period from 1 October to 31 December, 1974 and data obtained at Mt Zao observatory, Tohoku University, Japan, for a period from 14 July to 6 December, 1975 have been used to investigate the relationship of the occurrence of the Jovian decametric radio waves (JDW), from the main source, to the geomagnetic disturbance index, ΣK_p. The dynamic cross-correlation between JDW and ΣK_p indicates an enhanced correlation for certain values of delay time. The delay time is consistent with predicted values based on a model of rotating turbulent regions in interplanetary space associated with two sector boundaries of the interplanetary magnetic field, i.e. the rotating sector boundaries of the interplanetary magnetic field first encounter the Earth's magnetosphere producing the geomagnetic field disturbances, and after a certain period, they encounter the Jovian magnetosphere. There are also cases where the order of the encounter is opposite, i.e. the sector boundaries encounter first Jovian magnetosphere and encounter the Earth's magnetosphere after a certain period.     

A modeling of the magnetospheric substorm

This paper reports some results of an attempt to simulate the large-scale changes of the internal structure of the magnetosphere during the magnetospheric substorm by assuming the growth of two current systems, one in the nightside and the other in the day-side.     

A self-consistent model of the magnetosphere with centrifugal wind,I

Under the purely centrifugal approximation (gravity and pressure force are neglected), stellar magnetospheres are classified into three main types of different physical properties in the two-dimensional parameter space. They are characterized essentially by the strength of the magnetic field and the plasma density, at the base of the magnetosphere. Among the three types, the type II magnetosphere has moderate surface densities for a given field strength, and is expected to possess a centrifugal wind blowing across the magnetic field lines without affecting them appreciably. Such a situation may be realized through a modification of the electric field from that under the ideal-MHD condition, owing to the inertia of a plasma. In order to illustrate this mechanism, the type II magnetosphere is taken up for a numerical simulation. The effect of artificial viscosity is avoided by integrating the characteristic equations for both components of the plasma, instead of solving the fluid equations directly. Our model reproduces a disk-like outflow of the centrifugal wind across the magnetic field lines which are closed through the equatorial plane.     

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.     

On some problems concerning the calculation of the form of the magnetopause and the electric field on the magnetopause in the framework of the continuum medium model

In order to understand the reason of the existence of the electric field in the magnetosphere, and for the theoretical evaluation of its value, it is necessary to find the solution of the problem of determination of the magnetosphere boundary form in the frameworks of the continuum medium model which takes into account part of the magnetospheric plasma movement in supporting the magnetospheric boundary equilibrium. A number of problems for finding the distribution of the pressure, the density, the magnetic field and the electric field on the particular tangential discontinuity is considered in the case when the form of discontinuity is set (the direct problem) and a number of problems for finding the form of the discontinuity and the distribution of the above-mentioned physical quantities on the discontinuity is considered when the law of the change of the external pressure along the boundary is set (for example, with the help of the approximate Newton equation). The problem which is considered here, which deals with the calculation of the boundary form and with the calculation of the distribution of the corresponding physical quantities on the discontinuity of the 1st kind for the compressible fluid with the magnetic field with field lines which are perpendicular to the plane of the flow in question, concerns the last sort of problems. The comparison of the results of the calculation with the data in the equatorial cross-section of the magnetosphere demonstrates that the calculated form of the boundary, the value of the velocity of the return flow and the value of the electric field on the magnetopause, agree satisfactorily with the observational data.     

Instability near proton-cyclotron harmonics due to anti-loss cone proton distributions

Waves with frequencies near the harmonics of the proton-cyclotron frequency, and propagating almost transverse to the ambient magnetic field, can become unstable by hot protons having an anti-loss cone (ALC) distribution function. The maximum growth rates increase with an increase in anti-loss cone index, ratio of the temperatures of trapped to missing protons, and with a decrease in _H ( _H being the ratio of transverse thermal pressure of protons to magnetic field pressure). The growth rates are typically in the range 0.01–1.0 , where is the proton-cyclotron frequency. This instability may be relevant to the observations of EHC waves on auroral field lines (Kintner, 1979), ULF waves in the day-side magnetosphere (Perrautet al., 1978) and the lowfrequency part of the electric field spectrum (from 5 Hz to 20 Hz) in the region upstream of the bow-shock (Gurnettet al., 1979).     

Variations of the magnetic field near Mars caused by magnetic crustal anomalies

The possible avenues for photoelectron transport were determined during southern hemisphere winter at Mars by using a mapping analysis of the theoretical magnetic field. Magnetic field line tracing was performed by superposing two magnetic field models: (1) magnetic field derived from a three-dimensional (3D) self-consistent quasi-neutral hybrid model which does not contain the Martian crustal magnetic anomalies and (2) a 3D map of the magnetic field associated with the magnetic anomalies based on Mars Global Surveyor magnetic field measurements. It was found that magnetic field lines connected to the nightside of the planet are mainly channeled within the optical shadow of the magnetotail whereas magnetic field lines connected to the dayside of the planet are observed to form the remainder of the magnetosphere. The simulation suggests that the crustal anomalies create “a magnetic shield” by decreasing the region near Mars which is magnetically connected to the Martian magnetosphere. The rotation of Mars causes periodic changes in magnetic connectivity, but not to qualitative changes in the overall magnetic field draping around Mars.     

Dependence of the amount of open magnetic flux on the direction of the interplanetary magnetic field

The power generated by the solar wind—magnetosphere dynamo is proportional to the amount of the open magnetic flux Φ. It is difficult to use this fact in determining observationally the dependence of Φ on the orientation of the interplanetary magnetic field vector. It is shown that, for a simple vacuum superposition of the earth's dipole field and a uniform magnetic field, Φ is very closely proportional to sin θ/2) for a wide range of the intensity of the uniform field, where θ denotes the polar angle of the interplanetary magnetic field vector in the Y-Z plane of solar-magnetospheric coordinates.     

Initial Venus Express magnetic field observations of the magnetic barrier at solar minimum

Although there is no intrinsic magnetic field at Venus, the convected interplanetary magnetic field piles up to form a magnetic barrier in the dayside inner magnetosheath. In analogy to the Earth's magnetosphere, the magnetic barrier acts as an induced magnetosphere on the dayside and hence as the obstacle to the solar wind. It consists of regions near the planet and its wake for which the magnetic pressure dominates all other pressure contributions. The initial survey performed with the Venus Express magnetic field data indicates a well-defined boundary at the top of the magnetic barrier region. It is clearly identified by a sudden drop in magnetosheath wave activity, and an abrupt and pronounced field draping. It marks the outer boundary of the induced magnetosphere at Venus, and we adopt the name “magnetopause” to address it. The magnitude of the draped field in the inner magnetosheath gradually increases and the magnetopause appears to show no signature in the field strength. This is consistent with PVO observations at solar maximum. A preliminary survey of the 2006 magnetic field data confirms the early PVO radio occultation observations that the ionopause stands at ∼250 km altitude across the entire dayside at solar minimum. The altitude of the magnetopause is much lower than at solar maximum, due to the reduced altitude of the ionopause at large solar zenith angles and the magnetization of the ionosphere. The position of the magnetopause at solar minimum is coincident with the ionopause in the subsolar region. This indicates a sinking of the magnetic barrier into the ionosphere. Nevertheless, it appears that the thickness of the magnetic barrier remains the same at both solar minimum and maximum. We have found that the ionosphere is magnetized ∼95% of the time at solar minimum, compared with 15% at solar maximum. For the 5% when the ionosphere is un-magnetized at solar minimum, the ionopause occurs at a higher location typically only seen during solar maximum conditions. These have all occurred during extreme solar conditions.