Plasma populations in a simple open model magnetosphere

The acceleration of charged particles in the magnetic current sheets downstream from magnetic neutral lines is discussed and related to the plasma populations expected to be formed in a simple open model magnetosphere. A simple model of plasma acceleration in the dayside current sheet is set up, and it is shown that magnetospheric particles may take up a considerable fraction of the electromagnetic energy dissipated in the sheet even though they may represent only a small fraction of the total particle influx. The process should result in energetic ring current and ionospheric particles being found in boundary layers on either side of the magnetopause, and accelerated ionospheric particles in the plasma mantle. Acceleration of magnetosheath plasma in the dayside current sheet should result in enhanced flow speeds in these boundary layers, but the process may amount to little more than a return to the sheath plasma of energy previously extracted from it during its inflow on the dayside and stored in the compressed sheath field, due to the appreciable energy take-up from the current sheet by magnetospheric particles. The energy separation between ionospheric plasma and magnetosheath plasma on cusp field lines is shown to result in a spatial separation of polar wind and plasma mantle populations in the tail, the polar wind ions usually reaching out to only a few tens of R _E down-tail such that they usually remain on closed field lines, forming a wedge-shaped region within the mantle shadow-zone. Polar wind ions are then convected back towards the Earth and thus their major sink is via the dayside current sheet rather than outflow into the tail. The major source for the plasmasheet depends upon the location of the neutral line, but mantle ions may usually be dominant. However, with a near-Earth neutral line during disturbed periods ionospheric plasma will be the sole ring-current source. Under usual conditions with a more distant neutral line the spatial separation of the two plasma sources in the tail may result in an energy separation in the inner ring current, with ionospheric particles dominant up to 2 to 20 keV and mantle ions dominant at higher energies. Formation of the plasmasheet is discussed, and it is shown that a layer of ions unidirectionally streaming towards the Earth should be formed on its outer boundary, due to current sheet acceleration of lobe particles and inward convection of the field lines. A similar process leads to earthward flows on the inner layer of the dayside cusp. Finally, the region tailward of the nightside neutral line is discussed and it is shown that a thin tailward flowing two-stream plasma band should be formed across the centre plane of the tail. The slow-speed stream corresponds to incoming lobe ions, the faster stream to the current sheet accelerated ions.     

The magnetogram inversion technique: Applications to the problem of magnetospheric substorms

The magnetogram inversion technique (MIT) is based upon recordings of geomagnetic variations at the worldwide network of ground-based magnetometers. MIT ensures a calculation of a global spatial distribution of the electric field, currents and Joule heating in the ionosphere. Variant MIT-2 provides, additionally, continuous monitoring of the following parameters: Poynting vector flux from the solar wind into the magnetosphere (); power, both dissipated and accumulated in the magnetosphere; magnetic flux in the open tail; and the magnetotail length (l _T) (distance between the dayside and nightside neutral points in the Dungey model). Using MIT-2 and data of direct measurements in the solar wind, an analysis is made of a number of substorms, and a new scenario of substorms is suggested. The scenario includes the convection model, the model with a neutral line and the model of magnetosphere-ionosphere coupling (outside the current sheet), i.e., the three known models. A brief review is given of these and some other substorms models. A new element in the scenario is the strong positive feedback in the primary generator circuit, which ensures growth of the ratio = / _Aby an order of magnitude or more during the substorms. Here _Ais the Pointing vector flux in the Akasofu-Perrault approximation, i.e., without the feedback taken into account. The growth of during the substorm is caused only by the feedback effect. It is assumed that the feedback arises due to an elongation of the magnetotail, i.e., a growth of l _Tby a factor of (23) during the substorm.In the active phase of substorm, a part (the first active phase) has been identified, where the principal role in the energetics is played by the feedback mechanism and the external energy source (although the internal source plus reconnection inside the plasma sheet make a marked contribution). In the second active phase (expansion) the external generator (solar wind) is switched off, and the main role is now played by the internal energy source (the tail magnetic field and ionospheric wind energy).Models of DP-2 DP-1 transitions are also considered, as well as the magnetospheric substorm-solar flare analogy.     

Near Earth Current Meander (Necm) Model of Substorms

We propose that the appropriate instability to trigger a substorm is a tailward meander (in the equatorial plane) of the strong current filament that develops during the growth phase. From this single assumption follows the entire sequence of events for a substorm. The main particle acceleration mechanism in the plasma sheet is curvature drift with a dawn-dusk electric field, leading to the production of auroral arcs. Eventually the curvature becomes so high that the ions cannot negotiate the sharp turn at the field-reversal region, locally, at a certain time. The particle motion becomes chaotic, causing a local outward meander of the cross-tail current. An induction electric field is produced by Lenz's law, E ^ind=–A/t. An outward meander with B _z>0 will cause E×B flow everywhere out from the disturbance; this reaction is a macroscopic instability which we designate the electromotive instability. The response of the plasma is through charge separation and a scalar potential, E ^es=–. Both types of electric fields have components parallel to B in a realistic magnetic field. For MHD theory to hold the net E must be small; this usually seems to happen (because MHD often does hold), but not always. Part of the response is the formation of field-aligned currents producing the well-known substorm current diversion. This is a direct result of a strong E ^ind (the cause) needed to overcome the mirror force of the current carriers; this enables charge separation to produce an opposing electrostatic field E ^es (the effect). Satellite data confirm the reality of a strong E in the plasma sheet by counter-streaming of electrons and ions, and by the inverse ion time dispersion, up to several 100 keV. The electron precipitation is associated with the westward traveling surge (WTS) and the ion with omega () bands, respectively. However, with zero curl, E ^es cannot modify the emf =Edl=–d^M/dt of the inductive electric field E ^ind (a property of vector fields); the charge separation that produces a reduction of E must enhance the transverse component E . The new plasma flow becomes a switch for access to the free energy of the stressed magnetotail. On the tailward side the dusk-dawn electric field with EJ<0 will cause tailward motion of the plasma and a plasmoid may be created; it will move in the direction of least magnetic pressure, tailward. On the earthward side the enhanced dawn-dusk induction electric field with EJ>0 will cause injection into the inner plasma sheet, repeatedly observed at moderate energies of 1–50 keV. This same electric field near the emerging X-line will accelerate particles non-adiabatically to moderate energies. With high magnetic moments in a weak magnetic field, electrons (ions) can benefit from gradient and curvature drift to attain high energies (by the ratio of the magnetic field magnitude) in seconds (minutes).     

The near-Earth plasma sheet: An AMPTE/IRM perspective

During the last five years, statistical studies using plasma measurements made by the AMPTE/IRM satellite have lead to a better understanding of the structure and dynamics of the near-Earth plasma sheet between about 10 and 20R _E. The most notable new findings are: (1) the adiabatic non-isentropic behavior of the tail plasma during quiet times; (2) the strong non-adiabatic heating of ions and electrons during substorms and the strong coupling of the ion and electron temperature withT _i/T_i7; and (3) the high-speed flow bursts which carry most of the tail plasma transport. Moreover, it became clear that it is the central plasma sheet, and not the plasma sheet boundary layer, which is most affected by substorm activity.     

Substorm Trigger Processes in the Magnetotail: Recent Observations and Outstanding Issues

The present article reviews recent studies about near-Earth substorm processes. A focus is placed on the relationship between two fundamental processes, that is, tail current disruption (TCD) and the formation of a near-Earth neutral line (NENL). The former is inferred to cause dipolarization, and the latter is often associated with the fast plasma flow in the plasma sheet. Whereas it is inferred from the directions of fast plasma flows that the NENL is formed at 20–30 R _E from the Earth, dipolarization is most manifest in the near-Earth (6.6–12 R _E) region. The observation of the fast plasma flow prior to substorm (Pi2) onsets favors the idea that the NENL is formed first and dipolarization is the effect of the pile-up of magnetic flux convected earthward from the NENL, which is called the pile-up model. The present paper addresses several outstanding issues regarding this model, including (1) the interpretation of plasma flow deceleration in terms of the flux pile up, (2) highly irregular magnetic fluctuations observed in the near- Earth region, (3) the spatial coherency of the fast plasma flow, (4) the spatial structure and expansion of dipolarization region, and (5) the explosive growth phase. The paper also proposes the possibility that TCD is an independent process, but the formation of the NENL sets a favorable condition for it.     

Tearing instability of reconnecting current sheets in space plasmas

Magnetic reconnection provides an efficient conversion of the so-called free magnetic energy to kinetic and thermal energies of cosmic plasmas, hard electromagnetic radiation, and accelerated particles. This phenomenon was found in laboratory and space, but it is especially well studied in the solar atmosphere where it manifests itself as flares and flare-like events. We review the works devoted to the tearing instability — the inalienable part of the reconnection process — in current sheets which have, inside of them, a transverse (perpendicular to the sheet plain) component of the magnetic field and a longitudinal (parallel to the electric current) component of the field. Such non-neutral current sheets are well known as the energy sources for flare-like processes in the solar corona. In particular, quasi-steady high-temperature turbulent current sheets are the energy sources during the main or hot phase of solar flares. These sheets are stabilized with respect to the collisionless tearing instability by a small transverse component of magnetic fiel, normally existing in the reconnecting and reconnected magnetic fluxes. The collision tearing mode plays, however, an important and perhaps dominant role for non-neutral current sheets in solar flares. In the MHD approximation, the theory shows that the tearing instability can be completely stabilized by the transverse fieldB _n if its value satisfies the conditionB _n /BS ^–3/4 B is the reconnecting component of the magnetic field just near the current sheet,S is the magnetic Reynolds number for the sheet. In this case, stable current sheets become sources of temporal spatial oscillations and usual MHD waves. The application of the theory to the solar atmosphere shows that the effect of the transverse field explains high stability of high-temperature turbulent current sheets in the solar corona. The stable current sheets can be sources of radiation in the radio band. If the sheet is destabilized (atB _n /BS ^–3/4) the compressibility of plasma leads to the arizing of the tearing instability in a long wave region, in which for an incompressible plasma the instability is absent. When a longitudinal magnetic field exists in the current sheet, the compressibility-induces instability can be dumped by the longitudinal field. These effects are significant in destabilization of reconnecting current sheets in solar flares: in particular, the instability with respect to disturbances comparable with the width of the sheet is determined by the effect of compressibility.     

Role of ionospheric effects and plasma sheet dynamics in the formation of auroral arcs

At the ionospheric level, the substorm onset (expansion phase) is marked by the initial brightening and subsequent breakup of a pre-existing auroral arc. According to the field line resonance (FLR) wave model, the substorm-related auroral arc is caused by the field-aligned current carried by FLRs. The FLRs are standing shear Alfvén wave structures that are excited along the dipole/quasi-dipole lines of the geomagnetic field. The FLRs (that can cause auroral arc) thread from the Earthward edge of the plasma sheet and link the auroral arc to the plasma sheet region of 6–15 R _E. The region is associated with magnetic fluctuations that result from the nonlinear wave-wave interactions of the cross-field current-instability. The instability (excited at the substorm onset) disrupts the cross-tail current which is built up during the growth phase of the substorms and results in magnetic fluctuations. The diversion of the current to polar regions can lead to auroral arc intensification. The current FLR model is based on the amplitude equations that describe the nonlinear space-time evolution of FLRs in the presence of ponderomotive forces exerted by large amplitude FLRs (excited during substorms). The present work will modify the FLR wave model to include the effects arising from magnetic fluctuations that result from current disruption near the plasma sheet (6–15 R _E). The nonlinear evolution of FLRs is coupled with the dynamics of plasma sheet through a momentum exchange term (resulting from magnetic fluctuations due to current disruption) in the generalized Ohm's law. The resulting amplitude equations including the effects arising from magnetic fluctuations can be used to study the structure of the auroral arcs formed during substorms. We have also studied the role of feedback mechanism (in a dipole geometry of the geomagnetic field) in the formation of the discrete auroral arc observed on the nightside magnetosphere. The present nonlinear dispersive model (NDM) is extended to include effects arising from the low energy electrons originating from the plasma sheet boundary layer. These electrons increase the ionospheric conductivity in a localized patch and enhance the field-aligned current through a feedback mechanism. The feedback effects were studied numerically in a dipole geometry using the the NDM. The numerical studies yield the magnitude of the field-aligned current that is large enough to form a discrete auroral arc. Our studies provide theoretical support to the observational work of Newell et al. that the feedback instability plays a major role in the formation of the discrete auroral arcs observed on the nightside magnetosphere.     

The Jovian magnetodisk

Magnetic field measurements made by the vector helium magnetometers on board Pioneers-10 and 11 reveal the existence of a current sheet (thickness 2R _J) carrying an eastward current. Self-consistent studies of the current sheet show that the magnitude of the current is of the order of 10⁺² Am⁺¹ and that the current is carried by a hot (T>1 keV) plasma, the density of which varies between 1 cm⁺³ at 30R _J to 10⁺² cm⁺³ at 80R _J. The current sheet is warped azimuthally and parallel to the magnetic dipole equator.The existence of an azimuthal field component indicates a poloidal plasma flow transporting some 10²⁹ ions per second from Jupiter into the outer magnetosphere. It is shown that, if the outer magnetosphere is in a steady state, this plasma must be transported outward within the current sheet by a diffusion process which is faster than the one responsible for particle transport in the inner magnetosphere but slower than Bohm diffusion. It is suggested that the diffusion is due to the observed mhd turbulence in the current sheet. Such a model requires the existence of open field lines along which particles can escape freely into interplanetary space.Proceedings of the Symposium on Solar Terrestrial Physics held in Innsbruck, May–June 1978.     

Physics of Substorm Growth Phase,Onset, and Dipolarization

A new scenario of substorm growth phase, onset and dipolarization during expansion phase and the corresponding physical processes are presented. During the growth phase, as a result of enhanced plasma convection, the plasma pressure and its gradient continue to be enhanced over the quiet-time values in the plasma sheet. Toward the late growth phase, a strong cross-tail current sheet is formed in the near-Earth plasma sheet region, where a local magnetic well is formed. The equatorial plasma beta (β _eq ) can reach a local maximum with value larger than 50 and the cross-tail current density can be enhanced to over 10nA/m² as obtained from 3D quasi-static magnetospheric equilibrium solutions for the growth phase. The most unstable kinetic ballooning instabilities (KBI) are expected to be located in the tailward side of the strong cross-tail current sheet region. The field lines in the most unstable KBI region map to the transition region between the region-l and region-2 currents in the ionosphere, which is consistent with the observed initial brightening location of the breakup arc in the intense proton precipitation region. The KBI explains the AMPTE/CCE observations that a low frequency instability with a wave period of 50–75 seconds is excited about 2–3 min prior to substorm onset and grows exponentially to a large amplitude at the onset of current disruption (or current reduction). At the onset of current disruption higher frequency instabilities are excited so that the plasma and electromagnetic field fluctuations form a strong turbulent state. Plasma transport takes place due to the strong turbulence to relax the ambient plasma pressure profile so that the plasma pressure and current density are reduced and the ambient magnetic field intensity increases by more than a factor of 2–3 in the high-β _eq region and the field line geometry recovers from tail-like to dipole-like – dipolarization.     

Early results from ISEE-1 electric field measurements

The double probe, floating potential instrumentation on ISEE-1 is producing reliable direct measurements of the ambient DC electric field at the bow shock, at the magnetopause, and throughout the magnetosheath, tail plasma sheet and plasmasphere. In the solar wind and in middle latitude regions of the magnetosphere spacecraft sheath fields obscure the ambient field under low plasma flux conditions such that valid measurements are confined to periods of moderately intense flux. Initial results show: (a) that the DC electric field is enhanced by roughly a factor of two in a narrow region at the front, increasing B, edge of the bow shock, (b) that scale lengths for large changes in E at the sub-solar magnetopause are considerably shorter than scale lengths associated with the magnetic structure of the magnetopause, and (c) that the transverse distribution of B-aligned E-fields between the outer magnetosphere and ionospheric levels must be highly complex to account for the random turbulent appearance of the magnetospheric fields and the lack of corresponding time-space variations at ionospheric levels. Spike-like, non-oscillatory, fields lasting <0.2 s are occasionally seen at the bow shock and at the magnetopause and also intermittently appear in magnetosheath and plasma sheet regions under highly variable field conditions. These suggest the existence of field phenomena occurring over dimensions comparable to the probe separation and c/_pe (the characteristic electron cyclotron radius) where _pe is the electron plasma frequency.     

Fourier parameters of heliospheric current sheet and their significance

If the path of the neutral line on the coronal source surface is expressible as a singlevalued function (colatitude vs longitude ), then Fourier analysis of ctn with respect to leads to a simple algorithm for realistically mapping the neutral line outward to model the heliospheric current sheet (HCS) at distancesr1 AU. To be compatible with MHD, the source surface used for this mapping should be prolate (aligned with dipole axis) rather than spherical. Orientation of the Sun's magnetic-dipole moment is indicated by them=1 Fourier amplitude (a ₁ sin +b ₁ cos ) of ctn on the source surface. Physical features (including the neutral line) on a prolate source surface intrinsically map to lower dipole latitudes atr1 AU in the heliosphere, and Ulysses observations of a unipolar field at latitudes beyond 30°S (when the neutral line on the source surface still reached 39°S) confirm the expected geometry.     

Quantitative models of the magnetospheric magnetic field: Methods and results

The paper reviews various approaches to the problem of evaluation and numerical representation of the magnetic field distributions produced within the magnetosphere by the main electric current systems including internal Earth's sources, the magnetopause surface current, the tail plasma sheet, the large-scale systems of Birkeland current, the currents due to radiation belt particles, and the partial ring current circuit. Some basic physical principles as well as mathematical background for development of magnetospheric magnetic field models are discussed.A special emphasis is placed on empirical modeling based on datasets created from large bodies of spacecraft measurements. A review of model results on the average magnetospheric configurations and their dependence on the geomagnetic disturbance level and the state of interplanetary medium is given. Possibilities and perspectives for elaborating the instantaneous models capable of evaluating a current distribution of magnetic field and force line configuration based on a synoptic monitoring the intensity of the main magnetospheric electric current systems are also discussed. Some areas of practical use of magnetospheric models are reviewed in short. Magnetospheric plasma and energetic particle measurements are considered in the context of their use as an independent tool for testing and correcting the magnetic field models.     

The magnetotail and substorms

The tail plays a very active and important role in substorms. Magnetic flux eroded from the dayside magnetosphere is stored here. As more and more flux is transported to the magnetotail and stored, the boundary of the tail flares more, the field strength in the tail increases, and the currents strengthen and move closer to the Earth. Further, the plasma sheet thins and the magnetic flux crossing the neutral sheet lessens. At the onset of the expansion phase, the stored magnetic flux is returned from the tail and energy is deposited in the magnetosphere and ionosphere. During the expansion phase of isolated substorms, the flaring angle and the lobe field strength decrease, the plasma sheet thickens and more magnetic flux crosses the neutral sheet.In this review, we discuss the experimental evidence for these processes and present a phenomenological or qualitative model of the substorm sequence. In this model, the flux transport is driven by the merging of the magnetospheric and interplanetary magnetic fields. During the growth phase of substorms the merging rate on the dayside magnetosphere exceeds the reconnection rate in the neutral sheet. In order to remove the oversupply of magnetic flux in the tail, a neutral point forms in the near earth portion of the tail. If the new reconnection rate exceeds the dayside merging rate, then an isolated substorm results. However, a situation can occur in which dayside merging and tail reconnection are in equilibrium. The observed polar cap electric field and its correlation with the interplanetary magnetic field is found to be in accord with open magnetospheric models.     

High latitude electrodynamics: Observations from S3-2

The high spatial-temporal resolution of instrumentation on the polar-orbiting S3-2 satellite has allowed a wide variety of measurements of the electrodynamic characteristics of both large- and small-scale structures at high latitudes. Analyses of large scale features observed by S3-2 have shown that: (i) The IMF B _ydependence of polar cap convection, first observed in June 1969 by OGO-6 persists in other seasons. During periods of northward IMF B _zextensive regions of sunward convection may be found in the sunlit polar cap. (ii) In the dawn and dusk MLT sectors >90% of the region 1 currents lie equatorward of the convection reversal line. Potentials across the ionospheric projection of the low-latitude boundary layer are typically a few kV. (iii) The location of extra field-aligned currents, near the dayside cusp and poleward of the region 1 current sheet is dependent on the IMF B _ycomponent. (iv) Simultaneous observations by TRIAD and S3-2 show that sheets of field-aligned current extend uniformly for several hours in MLT, but may have an altitude dependence in the 1000–8000 km range. (v) During magnetic storms ionospheric irregularities occur in regions of poleward density gradients and downward field-aligned currents near the equatorward boundary of diffuse auroral precipitation. In the winter polar cap, density irregularities were also found in regions of highly structured electric fields and soft electron precipitation. (vi) During an intense magnetic storm the auroral zone height-integrated Pederson conductivity was calculated to be in the range 10–30 mho and downcoming energetic electron fluxes accounted for between 50% and 70% of the upward Birkeland currents.Analysis of small-scale structures (latitudinal width < 1°), observed by S3-2, have shown that: (i) Intense meridional electric fields (50–250 mV m^-1) generated by charge separation near the inner edge of the plasma sheet drive intense subauroral convection and are associated with field-aligned currents, on the order of 1–2 A m^-2. (ii) Case studies of discrete arcs in the auroral oval have shown that arcs are associated with pairs of small-scale, field-aligned currents embedded in the large-scale region 1/region 2 field-aligned current sheets. The maximum observed field-aligned current was an upward current of 135 A m^-2, confined to a latitudinal width of 2km and carried by field-aligned accelerated electrons. Return (downward) currents associated with arcs are limited to intensities of 10–15 A m^-2. At this limit the ionospheric plasma becomes marginally stable to the onset of ion-cyclotron turbulence. Two instances of plasma vortices, characteristic of auroral curls, have been observed in the region between the paired current sheets. (iii) Sun-aligned arcs in the polar cap are found in a region of negative electric field divergence, embedded in an irregular electric field pattern. The electrons producing the arcs have a temperature of 200 eV and have been accelerated through potential drops of 1 kV along the magnetic field. Return currents may appear on both sides of polar-cap arcs.     

Particle acceleration by magnetic reconnection and shocks during current loop coalescence in solar flares

This article reviews recent development of the theory of current loop coalescence and shock waves, giving particular attention to particle acceleration caused by these processes. First, explosive reconnection driven by the current loop coalescence and associated particle acceleration are studied by theoretical and magnetohydrodynamic simulation methods and the results are compared with observations of solar flares; this model gives a good explanation for the quasi-periodic structure of some solar flare bursts. Next follows a discussion of particle acceleration in association with fast magnetosonic shock waves. It is shown theoretically and by relativistic particle simulation that a quasi-perpendicular shock wave can accelerate trapped ions in the direction perpendicular to the ambient magnetic field up to speeds much greater than the Alfvén speed, . When the ambient magnetic field is rather strong ( _{ce pe} ), both ions and electrons can be accelerated to relativistic energies. For both the nonrelativistic and relativistic cases, the time needed for the acceleration is very short; it is for the ions. These results are compared with the rapid and simultaneous acceleration of ions and electrons in the impulsive phase of solar flares.     

Electromagnetic ion/ion instabilities and their consequences in space plasmas: A review

This paper reviews recent research on the theory and computer simulations of electromagnetic ion/ion instabilities and their consequences in space plasmas. Ion/ion instabilities are growing modes in a collisionless plasma driven unstable by the relative streaming velocity v ₀of two distinct ion components such that v ₀is parallel or antiparallel to the uniform background magnetic field B ₀0. The space physics regimes which display enhanced fluctuations due to these instabilities and which are reviewed in this paper include the solar wind, the terrestrial foreshock, the plasma sheet boundary layer, and distant cometary environments.     

Study of magnetospheric dynamics using energetic solar particles

Information can be obtained from energetic particle measurements through the chemical composition, energy spectrum, directional anisotropy, temporal and spatial intensity variations. This is equivalent to saying that there is a distribution functionf _k(p,r,t) wherek corresponds to thekth particle species of momentump at positionr and timet.Particle transport is described by the Boltzmann equation, and because the densities are generally low in the case of cosmic rays or energetic solar flare particles, collective transport effects can be neglected. In the absence of magnetospheric motion it is relatively easy to treat the problems of particle transport as simple propagation of charged particles in a stationary magnetic field configuration using, for instance, trajectory calculations in model fields. The method here is to use correlated measurements of the particle distribution at two points along a dynamic trajectory, and in this way to learn something about the geomagnetic field. This approach provides a good basis from which to study magnetospheric dynamics. If the magnetosphere moves, large scale electric fields, turbulent electromagnetic fields and sources and sinks affect the propagation of energetic particles considerably. These effects change the distribution functionf _k(p,r,t) and can thus be detected.In this paper, we shall show the importance of the single particle approximation (trajectories in a reference field) in forming the basis of our understanding of the quiet-time penetration of cosmic rays into the magnetosphere, we shall consider the steady dynamics such as wave-particle inter-action and field line reconnection, which is believed to exist nearly all the time, and finally we shall review the work which has been done in the much more complex and less well-understood field of impulsive dynamics such as geomagnetic storms and substorms. This last topic is only just beginning to be investigated in detail, and it is hoped that the study of impulsive dynamics, using energetic particles, may be as successful as the study of the quiet magnetosphere and the steady dynamics.     

Magnetic field reconnection theory and the solar wind — Magnetosphere interaction: A review

This review considers the theory of the magnetic field line reconnection and its application to the problem of the interaction between the solar wind and the Earth's magnetosphere. In particular, we discuss the reconnection models by Sonnerup and by Petschek (for both incompressible and compressible plasmas, for the asymmetric and nonsteady-state cases), the magnetic field annihilation model by Parker; Syrovatsky's model of the current sheet; and Birn's and Schindler's solution for the plasma sheet structure. A review of laboratory and numerical modelling experiments is given.Results concerning the field line reconnection, combined with the peculiarities of the MHD flow, were used in investigating the solar wind flow around the magnetosphere. We found that in the presence of a frozen-in magnetic field, the flow differs significantly from that in a pure gas dynamic case; in particular, at the subsolar. part of the magnetopause a stagnation line appears (i.e., a line along which the stream lines are branching) instead of a stagnation point. The length and location of the stagnation line determine the character of the interaction of the solar wind with the Earth's magnetosphere. We have developed the theory of that interaction for a steady-state case, and compare the results of the calculations with the experimental data.In the last section of the review, we propose a qualitative model of the solar wind — the Earth's magnetosphere interaction in the nonsteady-state case on the basis of the solution of the problem of the spontaneous magnetic field line reconnection.     

The Effects of Transverse Magnetic Field and Density Variations on the Particle Energy Spectra in a Reconnecting 3D Current Sheet

Electron and proton acceleration by a super-Dreicer electric field is further investigated in a non-neutral reconnecting current sheet (RCS) with a variable plasma density. The tangential B _z and transverse magnetic field components B _x are assumed to vary with the distances x and z from the X nullpoint linearly and exponentially, respectively; the longitudinal component (a ‘guiding field’) is accepted constant. Particles are found to gain a bulk of their energy in a thin region close to the X nullpoint where the RCS density increases with z exponentially with the index λ and the tangential magnetic field B _x also increases with z exponentially with the index α. For the RCS with a constant density (λ = 0), the variations of the tangential magnetic field lead to particle power-law energy spectra with the spectral indices γ₁ being dependent on the exponent α as: for protons and for electrons in a strong guiding field (β > 10⁻²) and for electrons in a moderate or weak guiding field (β > 10⁻⁴). For the RCS with an exponential density increase in the vicinity of the X nullpoint (λ≥ 0) there is a further increase of the resulting spectral indices γ that depends on the density exponent index λ as for protons and for electrons in weaker guiding fields and as for electrons in stronger guiding fields. These dependencies can explain a wide variety (1.5–10) of particle spectral indices observed in solar flares by the variations of a magnetic field topology and physical conditions in a reconnecting region. This can be used as a diagnostic tool for the investigation of the RCS dynamics from the accelerated particle spectra found from hard X-ray and microwave emission.