Energy transfer by magnetopause reconnection and the substorm parameter ϵ

An expression for the magnetopause reconnection power based on the dawn-dusk component of the reconnection electric field, that reduces to the substorm parameter ? for the limit that involves equal geomagnetic (B_G) and magnetosheath (B_M) magnetic field amplitudes at the magnetopause, is contrasted with the expression based on the whole reeonnection electric field vector (Gonzalez, 1973). The correlation examples of this report show that this (more general) expression for the reconnection power seems to correlate with the empirical dissipation parameter U_T (Akasofu, 1981), with slightly better correlation coefficients than those obtained from similar correlations between the parameter ? and U_T Thus, these (better) correlations show up for the more familiar values of the ratio B_G/B_M > 1. Nevertheless, the (expected) relatively small difference that seems to exist between these correlation coefficients suggests that, for practical purposes, the parameter ? could be used as well (instead of the more general expression) in similar correlation studies due to its simpler format. On the other hand, studies that refer mainly to the difference in the magnitudes of ? and of the more general expression are expected to give results with less negligible differences.     

Radiative transfer across a magnetic flux tube

In the coming years, some solar telescopes will be able to yield the Stokes' parameters of polarized light with a resolution better than 1 arc sec (0.3 arc sec for THEMIS). We have simulated the Stokes' parameters of a solar magnetic flux tube as seen with such a resolution. We have shown that, observing with a line-of-sight not parallel to the axis of the flux tube (assumed vertical and axisymmetric), it is possible to see differences between different configurations of the magnetic field inside the flux tube (presence, and in what direction, of an azimuthal component of the field). Furthermore, along such a line-of-sight, the polarization profiles of any atomic line are strongly absorbed at the line center. We then suggest a strategy to infer the structure of the magnetic field from observations at high spatial resolution.     

Stability of the magnetopause

The Magnetosphere-Solar Wind boundary is treated as a tangential discontinuity between collisionless plasma described by C.G.L. equations. An estimate is made, analytically, of the minimum shear speed required to render the interface unstable for propagation in any arbitrary direction. It is found that even systems, which are, for all shear speeds, stable towards propagation parallel to the field, are rendered unstable by propagation away from the field, in some velocity domain. Numerical evaluations for parameters characteristic of the Solar wind-Magnetosphere boundary show that the interface could be unstable even under relatively quiet conditions.     

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.     

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.     

Observations of soft electron flux during SAR arc event

Attempts to test the validity of the soft electron flux hypothesis for the excitation of SAR arcs have heretofore met with no apparent success. However, observations of other emissions during the times of some SAR arcs repeatedly favour the presence of the soft electron flux in the topside ionosphere.Although no new cases of coincident measurements of SAR arc intensities and the corresponding soft electron flux values are available, an instance has been analyzed in which an SAR arc was examined shortly after an OGO 6 measurement of the soft electron flux. The SAR arc observations were then interrupted by the weather, but in view of the behaviour of the electron flux during the arc development it is believed that this event lends strong observational support to the hypothesis that soft electrons can be an excitation source for SAR arcs.In the case considered, the precipitation of soft electron flux peaks at about the same location and time of occurrence as the SAR arc. The peak value is found to be 5.2 × 10⁸ cm^?2 sec^?1, which is more than adequate to excite the observed arc.     

The stability of the pristine magnetopause

A MHD theory of combined Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) instabilities for a transition layer with two different scale lengths (Δ and δ for the variation of velocity/magnetic fields and density, respectively) is presented. The study is motivated by reports of magnetopauses with no low latitude boundary layer, in which a sharp density drop over a distance δ?Δ is observed (“pristine” magnetopauses (J. Geophys. Res. 101 (1996) 49). The theory ignores compressibility effects and applies to subsonic regions of the dayside magnetopause. The RT effect is included to account for temporary periods of acceleration of the magnetopause, caused by sudden changes of the solar wind dynamic pressure. For small wavelengths λ, such that δ?λ?Δ, a WKB solution shows that the velocity gradient operates, together with magnetic tensions, to attenuate or even stabilize the Rayleigh-Taylor instability within a certain wavelength range. An exact dispersion relation for flute modes, valid for all λ, in the form of a fourth order polynomial for the complex frequency ω, is obtained from a model with a constant velocity gradient, dV/dy within Δ, and with δ→0. Flute modes are possible because of the existence of bands of very small magnetic shear on the dayside magnetopause (J. Geophys. Res. 103 (1998) 6703). The exact solution allows for a study of the change of the action of the velocity gradient with λ from the long-λ range where dV/dy is KH destabilizing to the short-λ range where dV/dy produces a stabilizing effect. Both, the WKB approximation and the well known tangential discontinuity model (Δ→0) are recovered as limiting cases of the exact solution. Properties of the KH and RT instabilities, for different density ratios on either side of the magnetopause, are described. For flute modes, at very small λ the RT instability grows faster and becomes the dominant effect. However, it is shown that the growth rate remains bounded at a finite value as λ→0, when a theory with a finite δ model is considered. To study configurations with finite, arbitrary, δ/Δ ratios, the MHD perturbation equations are solved numerically, using hyperbolic tangent functions for both the density and velocity transitions across the magnetopause. To examine the influence of different δ/Δ ratios on the growth rates of KH and RT, calculations are performed for different δ/Δ, with and without acceleration, and for two different density ratios. It is found that the general features exhibited by the constant dV/dy model, are confirmed by these numerical solutions. The stability of pristine magnetopauses, and the possibility of observing some theoretical predictions during magnetopause crossings in ongoing missions, are discussed.     

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.     

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.     

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.     

Turbulence generation in the magnetopause on account of magnetic islands

The present model is proposed to study the effect of thickness of Harris sheet and strength of guide field on the evolution of magnetic islands and generation of turbulence in magnetic reconnection sites. The governing model equation has been derived using EMHD model in the presence of the equilibrium magnetic field, consisting of guide field and shear field in the Harris sheet. We have carried out a numerical simulation of the dynamical equation for magnetopause region parameters. Simulation results reveal that as the thickness of Harris sheet increases, the intensity of evolution of magnetic islands decreases, but with increasing strength of guide field, intensity gradually increases and at later times irregular structures are formed. These structures give the indication of turbulence in magnetic reconnection site. Further, we have calculated power spectrum, which follows power index \({\sim}\,{-}1.5\) in the inertial range.     

Long-term effects of an interplanetary shock on the flux and anisotropy profiles of the associated low-energy particle event

A large energetic storm particle event associated with an interplanetary shock was detected by ISEE-3 on 24 April, 1979. We have studied the effects of this shock on the flux and anisotropy profiles in the upstream region of the particle event, and we have developed a propagation model that permits to reproduce the observations. This model includes particle injection, both at the Sun and at the shock, therefore it allows to study the parameters for the interplanetary propagation of low-energy particles, the particle injection rates, and to relate them to the conditions at the shock front.Paper presented at the 11 th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Steady state charge neutral models of the magnetopause

Plane models of the magnetopause are investigated under the assumption that ionospheric electrons are able to short-circuit electric fields (exact charge neutrality). Using the Vlasov theory a general method is presented for constructing distribution functions that lead to given magnetic field and tangential bulk velocity profiles. As an example we describe the magnetic field transition in terms of error functions and obtain particle distributions in explicit form, including bulk velocities.It is thus shown that bulk velocities in the direction of the magnetic field do not necessarily lead to a non-equilibrium magnetopause which investigations by Parker and Lerche seem to suggest.Of the European Space Research Organisation (ESRO).     

Solar wind energy transfer regions inside the dayside magnetopause—II. Evidence for an MHD generator process

In this paper a quantitative analysis of magnetosheath injection regions observed by PROGNOZ-7 in the dayside high latitude boundary layer is performed. Particular emphasis is laid on describing the consequences of the observed excess transverse momentum of solar wind ions (H⁺ and He²⁺) as compared to the magnetospheric ions (e.g. He⁺ and O⁺) in the magnetosheath injection regions, hereafter referred to as energy transfer regions.An important result of this study is that the observed excess drift velocity of the solar wind ions as compared to the magnetospheric ions can be interpreted as a negative inertia current being present in the boundary layer. This means that the inertia current goes against the local electric field and that particle kinetic energy is converted into electric energy there. The dayside high-latitude boundary layer therefore constitutes a voltage generator (at least with respect to the injected magnetosheath plasma).The MHD-theory predicts a strong coupling of the energy transfer process in the boundary layer and the ionosphere, both regions being connected by field aligned currents. The rate of decay of the inertia current in the injected plasma element is in the range of a few minutes, a value which is directly proportional to the ionospheric resistance. By taking into account both the Hall and the Pedersen conductivities in the ionosphere, the theory also predicts a strong coupling between ionospheric East/West and North/South currents. A considerable part of the inertia current may actually flow in the tangential (East/West) direction due to this coupling. Thus, a consequence of the boundary layer energy transfer process is that it may generate currents, powering other magnetospheric plasma processes, down to ionospheric heights.     

The formation of asymmetric Stokes V profiles in the presence of a magnetopause

A magnetopause that separates two regimes of different flow, additional to the separation of a magnetic field from a field-free plasma, gives rise to the formation of asymmetric Stokes profiles. Using a simple two-layer model atmosphere, where one layer comprises a magnetic field, the other being field-free, it is shown by analytical derivation that a wide variety of Stokes V profiles can be produced, having amplitude asymmetries a in the range –a. These include two-humped V profiles, which have two lobes of equal sign. For the most simple models, the asymmetry depends on the ratio of continuum intensity to the Planck radiation intensity of the magnetic layer at the wavelength of the spectral line under consideration, and on the line depth. Two-humped profiles (|a|>1) require the temperature of the magnetic layer to surpass the temperature of the line-core forming region, implying a temperature inversion, so that the V profile is partially in emission. The confrontation of this formation scenario with properties of observed one-lobe profiles of quiet-Sun network regions is inconclusive due to insufficient spatial resolution and lack of a sufficient sample of simultaneously recorded Stokes spectral lines of varying line depths. It seems, however, to be in good agreement with the observed frequent occurrence of abnormal V profiles of the very strong Nai D ₂ and D ₂ spectral line. A possible observational verification for the present formation scenario of abnormal Stokes V profiles and a novel method of Stokes inversion are discussed.     

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.     

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.     

On the equilibrium of an exact charge neutral magnetopause

The way is discussed by which microinstabilities of an exact charge neutral magnetopause could lead to a trapped particle flow, the absence of which causes the non-existence of an equilibrium magnetospheric boundary layer in the Parker-Lerche model. Furthermore, it is argued that instead of the non-equilibrium effect of Parker and Lerche, microinstabilities of an exact charge neutral magnetopause might be the underlying physical process of an Axford and Hines' type viscous interaction.     

A quasi-self-consistent axially symmetric model for the growth of a ring current through earthward motion from a pre-storm configuration

A quasi-self-consistent axially symmetric model of a storm-time ring current that has evolved quasi-adiabatically through inward motion from a prestorm state is presented in which the disturbance field as a function of geocentric distance, r, in the equatorial plane (including the value, H, at r = 0 from which Dst can be found), the beta of the plasma as a function of r, and the ring current magnetic moment are all given in terms of analytic expressions, having only two independent ring current parameters: the geocentric distance to the inner edge of the ring current, R, and the distance at which the beta of the plasma is unity, k—a constant of the model. The model is used to find H as a function of R at constant k, which corresponds to the growth of Dst as the ring current moves earthward, and to illustrate how the radial profile of the disturbance field varies also as the ring current moves earthward. Comparison with published S³-A storm-time, particle and field data shows reasonable agreement. The model is also able to fit the empirically determined relationship between Dst and the equatorward extension of quiet auroral arcs. This result applied to the great magnetic storm of September 1859 predicts a Dst of the order of 2000 nT, a value for which the sparse magnetometer data for that storm offer some support. Because the model (quasi) self-consistently determines the particle distribution function by allowing it to (quasi) adiabatically evolve in a field of its own making, the model avoids difficulties encountered by previous ring current models in which the particle distribution function had to be assumed. For example, the ring current magnetic moment is not limited to values less than the geomagnetic dipole moment, and null points in the field do not develop even in very high beta situations.