Possible relations between the rotational axis of the Earth's inner core and the magnetic dipole axis

The geomagnetic field is maintained by amagnetohydrodynamic dynamo process within the liquid outer core. The distribution of the associated electric currents is modified if the outer core is bounded by electrically conducting material. Then, eddy currents and the related magnetic fields are generated within these regions. In particular, the relative rigid rotation of the inner core produces a secondary magnetic field, which is superimposed on the dynamo field. The angle between the dipole axis of the total field and the rotational axis of the inner core is an important quantity needed for the theory of polar motion of the Earth. This angle is investigated for a broad spectrum of angular velocities of the inner core. To simplify the mathematical procedure, we model the dynamo field using an axisymmetric field generated by a system of electric currents within the outer core. The conductivity of the mantle is neglected. We find that the position of the dipole axis depends on the angular velocity of the inner core as well as on the distribution of the current system within the outer core. Coincidence of both axes can be reached if the angular velocity is high enough and if the current system is concentrated within a thin sheet near the outer core-inner core boundary.     

Polar magnetic substorms

From the world distribution of geomagnetic disturbance, the connection between the electric current in the ionosphere, the field-aligned current and asymmetric equatorial ringcurrent in the magnetosphere is discussed. The partial ring-current in the afternoon-evening region, whose intensity is closely correlated with the AE-index, usually develops and decays earlier than the symmetric ring-current in the course of magnetic storms. The partial ringcurrent seems to have a direct connection with the positive geomagnetic bay in high latitudes in the evening hours through the ionizing effect of the particles leaking from the partial ringcurrent. The dawn-to-dusk electric field in the magnetospheric tail is transferred to the polar ionosphere, producing there the twin vortex Hall current responsible for polar cap geomagnetic variation. The magnetic effect of the associated Pedersen current in the ionosphere is shown to be small but still worth considering. The electrojet near midnight along the auroral oval is thought to appear when the electric conductivity of the ionosphere is locally increased under the presence of large scale dawn-to-dusk electric field. The occasional appearance of a localized abnormal geomagnetic disturbance with reversed direction near the geomagnetic pole seems to suggest the occasional reversal of electric field near the outer surface of the magnetospheric tail, especially when the interplanetary magnetic field is northward.     

Outline of a theory of solar wind interaction with the magnetosphere

Some new ideas on the interaction of the solar wind with the magnetosphere are brought forward. The mechanism of reflection of charged particles at the magnetopause is examined. It is shown that in general the reflection is not specular but that a component of momentum of the particle parallel to the magnetopause changes. A critical angle is derived such that particles whose trajectories make an angle less than it with the magnetopause enter the magnetosphere freely, so transferring their forward momentum to it. Spatially or temporally non-uniform entry of charged particles into the magnetosphere causes electric fields parallel to the magnetopause which either allow the free passage of solar wind across it or vacuum reconnection to the interplanetary magnetic field depending on the direction of the latter. These electric fields can be discharged in the ionosphere and so account qualitatively for the dayside agitation of the geomagnetic field observed on the polar caps. The solar wind wind plasma which enters the magnetosphere creates (1) a dawn-dusk electric field across the tail (2) enough force to account for the geomagnetic tail and (3) enough current during disturbed times to account for the auroral electrojets. The entry of solar wind plasma across the magnetosphere and connection of the geomagnetic to interplanetary field can be assisted by wind generated electric field in the ionosphere transferred by the good conductivity along the geomagnetic field to the magnetopause. This may account for some of the observed correlations between phenomena in the lower atmosphere and a component of magnetic disturbance.     

Criticism of reconnection models of the magnetosphere

Reconnection involves singular lines called X-lines on the day and night sides of the magnetosphere, and the reconnection rate is proportional to the component of the electric field along the X-line. Although there is some indirect support for this model, nevertheless direct support is totally lacking. However, there are two distinct pieces of clearly contradictory observational evidence on the dayside. First is the failure to account for the implied energy dissipation by the magnetopause current, over 10¹¹ W, which should be easily observable as heating or enhanced flow of the plasma near the magnetopause. In marked contrast to this prediction, HEOS-2 satellite data reveal a plasma with decreased energy density and reduced flow. Second, the boundary of closed magnetic field lines is in the wrong location. In the reconnection process the plasma outflow would cut across open field lines toward higher latitudes; there should be a band of open field lines equatorward of the cleft. Observations of trapped energetic particles indicate closed field lines within the entry layer and cleft. Either one of these pieces of evidence is sufficient by itself to require drastic revision, even rejection, of the reconnection model. There is also contradictory evidence on the night side. The last closed field line capable of trapping energetic particles is poleward of auroral arcs. The implication is that the X-line is at the distant magnetopause, and not in the plasma sheet. Consequently, even if the reconnection process were operative at the nightside X-line, it would be isolated from steady state plasma sheet and auroral processes. On the other hand, substorm phenomena, in which stored magnetic energy is converted into particle kinetic energy, necessarily involve an induced electric field; that is excluded in theories of the reconnection process in which it is assumed that curl E = 0. Nevertheless, the observed easy access of energetic solar flare particles to the polar caps, and especially the preservation of interplanetary anisotropies as differences between the two polar caps, argues strongly for an open magnetosphere, with interconnection between geomagnetic and inter-planetary magnetic field lines. It is suggested that the resolution of this apparent paradox involves electric fields parallel to the magnetic field lines somewhere on the dawn and dusk sides of the magnetosphere, with an equipotential dayside magnetopause.     

Geomagnetic storm fields near a synchronous satellite

An apparent early recovery of the main phase of geomagnetic storms at the distance of the synchronous satellite is examined in terms of changing electric current distributions in the magnetosphere during magnetic storms. It is suggested that a rapid recession of the edge of the plasma sheet (after the advance toward the Earth during an early epoch of the main phase) is partly responsible for the early recovery. Relevant plasma sheet variations during geomagnetic storms are found to be in agreement with the inferred variations.     

Energy and pitch angle distributions for auroral ions using the current sheet acceleration model

Using a dipole plus tail magnetic field model, H⁺, He⁺⁺ and O ₁₆ ⁺⁶ ions are followed numerically, backward in time, from an output plane perpendicular to the axis of the geomagnetic tail, to their point of entrace to the magnetosphere as solar wind particles in the magnetosheath. An adiabatic or guiding center approximation is used in regions where the particles do not interact directly with the current sheet. A Maxwellian distribution with bulk flow is assumed for solar wind particles in the magnetosheath. Bulk velocity, density, and temperature along the magnetopause are taken from the fluid calculations of Spreiter. Using Liouville's theorem, and varying initial conditions at the output plane, the distribution function is found as a function of energy and pitch angle at the output plane. These results are then mapped to the auroral ionosphere using guiding center theory. Results show that the total precipitation rate is sufficient only for particles which enter the magnetosphere near the edges of the current sheet. Small pitch angles are favored at the output plane, but mappings to the auroral ionosphere indicate isotropic pitch angle distributions are favored with some peaking of the fluxes parallel or at other angles to the field lines. Perpendicular auroral pitch angle anisotropies are at times produced by the current sheet acceleration mechanism. Therefore, caution must be used in interpreting all such observations as ‘loss cone-trapping’ distributions. Energy spectra appear to be quite narrow for small cross-tail electric fields, and a little broader as the electric field increases. Comparisons of these results with experimental observations are presented.     

Large-scale transport of plasma in the Earth's plasma sheet: comparative analysis for adiabatic and non-adiabatic cases

A system of multi-fluid MHD-equations is used to compare adiabatic and non-adiabatic transport of the energetic particles in the magnetospheric plasma sheet. A “slow-flow” approximation is considered to study large-scale transport of the anisotropic plasma consisting of energetic electrons and protons. Non-adiabatic transport of the energetic plasma is caused by scattering of the particles in the presence of both wave turbulence and arbitrary time-varying electric fields penetrating from the solar wind into the magnetosphere. The plasma components are devided into particle populations defined by their given initial effective values of the magnetic moment per particle. The spatial scales are also given to estimate the non-uniformity of the geomagnetic field along the chosen mean path of a particle. The latters are used to integrate approximately the system of MHD-equations along each of these paths. The behaviour of the magnetic moment mentioned above and of the parameter which characterizes the pitch-angle distribution of the particles are studied self-consistently in dependence on the intensity of non-adiabatic scattering of the particles. It is shown that, in the inner magnetosphere, this scattering influences the particles in the same manner as pitch-angle diffusion does. It reduces the pitch-angle anisotropy in the plasa. The state of the plasma may be unstable in the current sheet of the magnetotail. If the initial state of the plasma does not correspond to the equilibrium one, then, in this case, scattering influences the particles so as to remove the plasma further from the equilibrium state. The coefficient of the particle diffusion across the geomagnetic field lines is evaluated. This is done by employing the Langevin approach to take the stochastic electric forces acting on the energetic particles in the turbulent plasma into account. The behaviour of the energy density of electrostatic fluctuations in the magnetosphere is estimated.     

Adiabatic plasma convection in a dipole field: Variation of plasma bulk parameters with L

We here investigate the motion of particles in a dipole magnetic field under the assumption of conservation of the first two adiabatic invariants. The results are then combined with Liouville's theorem to obtain the variation of the distribution function, and hence the plasma bulk parameters with L-shell. A comparison of the numerical results with recently published analytical approximations is made. Finally, the results are used to describe the structure of the ring current plasma in the outer radiatoin zone, the effects of the Alfvén layers being quantitatively evaluated for a simple electric field model.     

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.     

Meridional ionospheric electric field caused by curvature current in the magnetosphere

The bending of geomagnetic field lines towards the geotail produces a curvature drift of charged particles parallel to the geomagnetic axis. The divergence of the current so produced forms Birkeland current to the ionosphere where a meridional electric field is created. This field would drive ionospheric currents to form a negative magnetic bay in the dawn sector of the auroral zone and a positive one in the dusk sector. Also it would cause a dawn-dusk field across the polar cap.     

The reason for magnetospheric substorms and solar flares

It has been proposed that magnetospheric substorms and solar flares are a result of the same mechanism. In our view this mechanism is connected with the escape, or attempted escape, of energized plasma from a region of closed magnetic field lines bounded by a magnetic bottle. In the case of the Earth, it must be plasma that is able to maintain a discrete auroral arc, and we propose that the cross-tail current connected to the arc is filamentary in nature to provide the field-aligned current sheet above the arc. A localized meander of such an intense current filament could be caused by a tearing instability in the neutral sheet. Such a meander will cause an inductive electric field opposing the current change everywhere. In trying to reduce the component of the induction electric field parallel to the magnetic field lines, the plasma must enhance the transverse or cross-tail component; this action leads to eruptive behavior, in agreement with tearing theories. This enhanced induction electric field will cause a discharge along the magnetic neutral line at the apex of the magnetic arches, constituting an impulsive acceleration of all charged particles originally near the neutral line. The products of this phase then undergo betatron acceleration for a second phase. This discharge eventually reduces the electric field along the neutral line, and thereafter the enclosed magnetic flux through the neutral line remains nearly constant. The result is a plasmoid that has definite identity; its buoyancy leads to its escape. The auroral breakup (and solar flare) is the complex plasma response to the changing electromagnetic field.     

Substorm related changes in the geomagnetic tail: the growth phase

Changes in the configuration of the geomagnetic tail are known to play a fundamental role in magnetospheric substorms. Observations with the UCLA magnetometer on the eccentric orbiter OGO-5 indicate that the most pronounced changes in the midnight meridian occur in the cusp between 8 and 11 R_e. In order to organize the observations it is necessary to separate effects on the tail due to the solar wind magnetic field and effects due to substorms. Provided there are no changes in the solar wind there are two distinct phases of a substorm in the near tail: a growth phase and an expansion phase. During each phase the observations depend on the location of the satellite relative to the plasma sheet boundaries. Far behind the Earth is the pure tail region which consists of the lobe and the plasma sheet. In the lobe the field magnitude is characteristically enhanced relative to the dipole. Closer to the Earth is a region of transition. The field magnitude is close to that of the dipole but its orientation is distorted forming a cusp-like field line. Near the Earth is a region of depressed field. Here the field magnitude is much less than that of the dipole, but its orientation is similar. The growth phase of a substorm appears to be the direct consequence of the onset of a southward solar wind magnetic field. In the pure tail region the lobe field begins to increase in magnitude and the plasma sheet thins. The transition region moves earthward and the field lines become more tail-like as the field magnitude increases. In the inner region of depressed field, the field magnitude decreases rapidly. The onset of the expansion phase appears to be a process internal to the magnetosphere and independent of the solar wind. In the depressed field region there is a rapid, turbulent increase in field magnitude. In the transition region there is a sudden decrease in the field magnitude and a return to dipolar orientation. In the tail region the plasma sheet expands rapidly with the field becoming quite dipolar, decreasing slowly in the lobe of the tail.     

Fluid description of a collisionless plasma and electric current systems in cosmic plasmas

The large-scale structure of a collisonless, two-component plasma with a typical Larmor radius of ions ? and scale-lengthL is discussed using Maxwell transport equations. Special attention is paid to the situations in which the usual one-fluid model of plasma based on the expansion of the transport equations in the powers of the ratio ?/L is not a satisfactory approximation. The one-fluid model fails if the magnetic-field-aligned component of the mass velocity or the magnetic-field-aligned component of the typical random velocity of particles is much larger than the other components of the mass and random velocities. The model also fails if the component of the typical random velocity of particles, which is perpendicular to the field lines, substantially exceeds the mass velocity of particles across the field lines. A quasi-static plasma is discussed as an example of plasmas on which the expansion in the powers of ?/L is not applicable. The relation between the electric current flowing in a quasi-static plasma (or in a hot plasma streaming along the field lines) and the topology of the magnetic lines of force is analysed. There are two distinguishable currents of different origin in such a plasma. Magnetic field generated by the currents acquires a geometry in which one current flows in the surfaces perpendicular to the binormals to the field lines while the other current flows along the binormals.     

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.     

Some properties of the current sheet in the geomagnetic tail

The topic of this report is that of the influence of noise, and of the finite length and width of the tail on the behaviour of the current sheet.The presence of a weak magnetic field linking through the current sheet leads to plasma containment and counterstreaming, with the consequence that both the plasma temperature and density are increased in the vicinity of the current sheet. The effect of these changes on the relationship between steady bulk parameters is discussed.The finite length of the tail significantly modifies the equilibrium situation in the near Earth tail, for streams mirroring at the Earthwards end of field lines lead to a reduction of merging. The finite width of the tail restricts the region of reduced merging rate to a triangular shaped area extending from the dusk magnetopause into the tail. The finite tail width is also important in the more distant tail, where magnetosheath particles which penetrate the magnetopause ends of the current sheet may become major current carriers, especially if B_z, is small and northwards.Finally, it is shown that the above factors, together with a non-adiabatic current sheet, are important to our understanding of the temporal behaviour of the tail.     

Acceleration of energetic particles of the outer regions of planetary magnetospheres: Inferences from laboratory and space experiments

High energy particles, with energies above those attainable by adiabatic or steady-state electric field acceleration, have been observed in and around the outer regions of planetary magnetospheres. Acceleration by large amplitude sporadic cross-tail electric fields over an order of magnitude greater than steady-state convection fields is proposed as a source of these particles. It is suggested that such explosive electric fields will occur intermittently in the vicinity of the tail neutral line in the expansive phases of substorms. We use laboratory Double Inverse Pinch Device (DIPD) and satellite evidence to estimate this electric potential for substorms at Earth; values of 500 kV to 2 MV are calculated, in agreement with particle observations. It is further suggested that these particles, which have been accelerated in the night side magnetosphere, drift to the dayside on closed field lines, and under certain interplanetary conditions can escape to regions upstream of the bow shock.     

On the existence of a long range correlation in the Geomagnetic Disturbance storm time (Dst) index

The Dst (Disturbance storm time) index is a measurement of earth geomagnetic activity and is widely used to characterize the geomagnetic storm. It is calculated on the basis of the average value of the horizontal component of the earth’s magnetic field at four observatories, namely, Hermanus (33.3° south, 80.3° in magnetic dipole latitude and longitude), Kakioka (26.0° north, 206.0°), Honolulu (21.0° north, 266.4°), and San Juan (29.9° north, 3.2°) and is expressed in nano-Teslas. The strength of the low-latitude surface magnetic field is inversely proportional to the energy content of the ring current around earth caused by solar protons and electrons, which increases during geomagnetic storms. Thus a negative Dst index value indicates that the earth’s magnetic field is weakened which is specifically the case during solar storms. Predicting Dst index is a difficult task due to its structural complexity involving a variety of underlying plasma mechanism. For characterizing and forecasting this complex time series, a formal model must be established to identify the specific pattern of the series. Persistent demand for a fool proof model of Geomagnetic Dst index prompted us to investigate the Dst Time Series mechanism with a very recent technique called Visibility Algorithm and it is observed that the Dst time series follows the same model that of a Stochastic Fractional Brownian motion having long range correlation.     

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.     

Geoeffective Analysis of CMEs Under Current Sheet Magnetic Coordinates

Using 100 CME–ICME events during 1997.01–2002.11, based on the eruptive source locations of CMEs and solar magnetic field observations at the photosphere, a current sheet magnetic coordinate (CMC) system is established in order to statistically study the characteristics of the CME–ICME events and the corresponding geomagnetic storm intensity. The transit times of CMEs from the Sun to the Earth are also investigated, by taking into account of the angle between the CME eruption normal (defined as the vector from the Sun center to the CME eruption source) and the Sun-Earth line. Our preliminary conclusions are: 1. The distribution of the CME sources in our CMC system is obviously different from that in the ordinary heliographic coordinate system. The sources of CMEs are mainly centralized near the heliospheric current sheet (HCS), and the number of events decreases with the increment of the angular distance from the CME source to the HCS on the solar surface; 2. A large portion of the total events belong to the same–side events (referring to the CME source located on the same side of the HCS as the Earth), while only a small portion belong to the opposite–side events (the CME source located on the opposite side of the HCS as the Earth). 3. The intense geomagnetic storms are usually induced by the same–side events, while the opposite side events are commonly associated with relatively weak geomagnetic storms; 4. The angle between the CME normal and the Sun–Earth line is used to estimate the transit time of the CME in order to reflect the influence of propagation characteristic of the CME along the Sun–Earth direction. With our new prediction method in context of the CMC coordinate, the averaged absolute error for these 100 events is 10.33 hours and the resulting relative error is not larger than 30% for 91% of all the events.     

Quasi-Alfvén oscillations of magnetic surfaces

A system of equations has been derived for the modes of free oscillation of the magnetosphere when it is regarded as an adiabatic magnetic dipole trap filled with cold inhomogeneous plasma. The limiting case of infinite longitudinal conductivity corresponding to the assumption that the electric field is orthogonal to the geomagnetic field has been studied. The boundary at the ionosphere is supposed to be perfectly conducting.The eigenmode spectrum has been found to have discrete and continuous components. The eigenmodes of the discrete component correspond to quasi-magnetosonic modes and the eigenmodes of the continuous component to quasi-Alfvén modes.Assuming the magnetosphere to be axisymmetric, a general expression in the form of a Frobenius series has been derived for quasi-Alfvén oscillations of magnetic shells near resonant magnetic surfaces.