Dayside Merging Research Articles

Finite Element Numerical Modeling of Stationary Two-Dimensional Magnetosphere with Defined Boundary

A finite element numorical procedure is developed for two-dimensional modeling of stationary magnetosphere. The whole magnetic field is supposed to be a sum of given internal fields and a searched divergent-free and curl-free field of the magnetopause shielding current system. The boundary condition on the given boundary is the Neumann one on the magnetopause part of the computational region boundary and the Dirichlet condition on the segment part, closing this region at the tail. The algorithms used for automatic grid generation and grid transformation allow wide flexibility in determining the region shape and the assigned internal fields. Some numerical implementations not only demonstrate the method capabilities, In the frame of the two-dimensional approach these implementations could be considered as a tentative simulation of some typical features of magnetosphere magnetic field topology, which is intrinsically three-dimensional. The magnetopause geometry influence on the cusp inclination is shown. The impact of the northward and the flow-aligned field on dayside merging and tail asymmetry is aluminized. A two-dimensional approach to modelling the crosstail currents is proposed for the Earth type and Uranus type magnetospheres.

Modeling ionospheric convection during a major geomagnetic storm on October 22‐23, 1981

Following the passage of an interplanetary shock at ∼0500 UT, a major geomagnetic storm developed on October 22‐23, 1981. Numerous auroral substorms occurred during this storm leading to an AE index greater than 1000 nT. We have used the expanding/contracting polar cap (ECPC) model (Moses et al., 1989) and data from the Dynamics Explorer 2 spacecraft to study the ionospheric electric fields for 12 consecutive traversals of the polar regions. The ECPC model can determine the voltage drops across the dayside merging and nightside reconnection gaps. We determined the relationship of the AL index (i.e., the intensity of the westward electrojet) to the nightside reconnection potential drop. An excellent linear correlation was found between the nightside reconnection gap voltage drop and the AL index. These results show that the solar wind strongly drives the magnetosphere‐ionosphere system throughout the geomagnetic storm. A substantial level of dayside merging seems to occur throughout the event. Nightside reconnection varies from satellite pass to satellite pass and within the substorm recovery phase. We find that tail reconnection is an important feature of the recovery phase of substorms.

Convection as a free boundary problem: The substorm cycle

Magnetohydrodynamic solutions are presented for the problem of time‐dependent magnetospheric convection. They include regions of both taillike and dipolelike flux tubes and the interaction and flux transfer between them. The only external input is the rate of dayside merging. The problem is solved as a free boundary problem for both the high‐latitude boundary between taillike and dipolelike tubes and the low‐latitude boundary defined by plasma penetration. A constraint of no equatorward component to the convection is used to resolve the β problem in the region where the plasma sheet is on dipolar field lines. This constraint imposes a three‐dimensional nightside topology and determines the boundaries and the flux transfer rate into the nightside dipolar region. It also leads to a major asymmetry in the rate at which the amount of taillike flux can increase or decrease and hence accounts for the existence of the substorm phases. The narrow‐channel approximation, developed a number of years ago by the author, is used to obtain analytic solutions. Extensive comparison of the results of the theory with the observed aspects of convection and substorms is carried out. Values predicted by the model are in agreement with observations, and most major properties of the substorm are explained, including the existence of activity at two separated latitudes in the recovery phase.

How does magnetospheric convection relate to the expansion onset of substorms?

The suddenness of substorm expansions suggests that they are instabilities in the magnetosphere. The convection during the growth phase of isolated substorms is examined with the intent of determining conditions leading to the instability. Properties of the large-scale two-celled convection considered are the intensity of the convection, the size of the convection cells and the time rate of change of both of these. There is considerable variation in values of the intensity, its rate of change, and the size of the convection cells just before expansion onset. On the other hand, onsets frequently occur when the rate of increase of the size of the convection cell is slowing down or has reached zero. Since the time-scale of this ‘slowing down’ is an order of magnitude greater than the time-scale of expansion, the slowing down is not a result of the instability, but is one of the conditions leading up to the onset of instability. A number of examples of this behaviour of the growth of the size of the convection cells are discussed. The following interpretation is proposed. The slowing down indicates that the magnetospheric convection cells are approaching a steady-state size which corresponds to the enhanced dayside merging rate that exists in growth phases. However, the steady-state is unstable against contractions in size and this is the cause of expansions. Triggered substorms and substorms without growth phases occur when a decrease in the dayside merging rate requires a contraction of the cell size. Theories of substorms compatible with this behaviour include the ballooning instability theory and a model in which magnetospheric dipolar convection controls merging in the tail.

The quiet time polar cap: DE 1 observations and conceptual model

Auroral activity increases over the polar caps during quiet times, which are associated with northward interplanetary magnetic field (IMF) components. Polar cap auroras (Sun‐aligned arcs, theta auroras, and horse collar auroras) occur under these conditions. DE 1 data show that the theta and horse collar auroras are generally characterized by sunward convection, closed field lines, auroral hiss, and inverted‐V events. These phenomena are similar to those observed along the auroral oval but have somewhat lower electron energies. Adjacent dark regions of the polar caps appear to contain open field lines and antisunward convection. A conceptual northward IMF merging model containing lobe cells, merging cells, and viscous cells is shown to be consistent with the observations. As the IMF becomes more northward, the polar arc configuration changes from the “horse collar” pattern to the theta aurora pattern in the model, and this is shown to be generally true for the set of published data on these phenomena. The model involves dayside merging both at high latitudes on open field lines and at lower latitudes on closed field lines. The ratio between the merged flux produced by the high‐latitude merging to that produced by the lower‐latitude merging increases as the IMF becomes more northward. Two types of open field lines, equator‐crossing and non‐equator‐crossing, are produced by the higher‐ and lower‐latitude merging, respectively. The equator‐crossing field lines have a strong azimuthal component of convection as they flow around the magnetopause, while the non‐equator‐crossing field lines can convect more or less directly across the polar cap, leading to an antisunward flow channel across the central polar cap. This antisunward flow region grows as the IMF becomes less northward, causing dual polar cap arcs to spread out into the horse collar configuration. The sunward flow segments of the lobe cells are associated with induced electric fields, thus accounting for the particle energization leading to auroral forms.

Response of the ionospheric convection pattern to a rotation of the interplanetary magnetic field on January 14, 1988

Ionospheric convection signatures observed over the polar regions are provided by the DMSP F8 satellite. We consider five passes over the southern summer hemisphere during a time when the z component of the interplanetary magnetic field was stable and positive and the y component changed slowly from positive to negative. Large‐scale regions of sunward flow are observed at very high latitudes consistent with a strong z component. When By and Bz are positive, but By is greater than Bz, strong evidence exists for dayside merging in a manner similar to that expected when Bz is negative. This signature is diminished as By decreases and becomes smaller than Bz resulting in a four‐cell convection pattern displaced toward the sunward side of the dawn‐dusk meridian. In this case the sign of By affects the relative sizes of the two highest‐latitude cells. In the southern hemisphere the duskside high‐latitude cell is dominant for By positive and the dawnside high‐latitude cell is dominant for By negative. The relative importance of possible electric field sources in the low‐latitude boundary layer, the dayside cusp, and the lobe all need to be considered to adequately explain the observed evolution of the convection pattern.

IMF draping around the Geotail: IMP 8 observations

This paper gives maps of magnetosheath magnetic field lines in a roughly 12RE thick annulus circling the tail approximately 30RE downwind from Earth. There are maps for northward and southward IMF and for quasi‐equatorial IMF (the usual case). The maps are based on IMP 8 data taken during the 127 orbits (four years) when ISEE 3 measured the upstream IMF. In these four years, IMP 8's orbit swept the mapped annulus eight times. The maps project the field onto a plane perpendicular to the sun‐earth line, after correcting for solar wind aberration and tail flaring. Each shows draping around the tail: The field enters from one side, bifurcates at the tail boundary, “flows” around in both directions, rejoins at the opposite side, and exits. A new finding is that, contrary to expectations, the draping pattern is rotated relative to the plane formed by the IMF and the aberrated x‐axis. For example, it is rotated relative to the equatorial plane when the IMF lies in the equatorial plane. The degree of rotation varies from essentially zero for strongly northward and southward IMF to a peak ∼17° for moderately southward IMF. The sense of rotation is clockwise for toward IMF sectors and counterclockwise for away IMF sectors—the same as the dayside merging line. We also find that the tail is fatter and the magnetosheath field less ordered for strongly southward IMF than for strongly northward IMF. The new findings are understandable in terms of dayside magnetic merging.

Magnetic field configuration of the Theta aurora

The theta aurora is an approximately Sun-aligned transpolar arc that often extends the entire length of the polar cap, linking the dayside and nightside auroral zones. It is a remarkable manifestation of polar cap auroral activity that appears during periods of northward interplanetary magnetic field (IMF). In this paper we describe a magnetic configuration of the open magnetosphere that is conducive to the formation of the theta aurora when the IMF has a significant northward component. We present a magnetic field topology and polar cap configuration that is derived from a quantitative model of the open magnetosphere that incorporates Crooker's antiparallel merging hypothesis. Under this hypothesis, when the IMF has a northward component, the dayside merging line bifurcates, leaving a large fraction of the subsolar magnetopause untouched by the merging process. The polar cap, defined by tracing magnetic field lines that connect from the solar wind to the Earth, is similarly bifurcated, leaving a sun-aligned stagnation region that is not magnetically connected to the solar wind and may plausibly be associated with the sun-aligned “bar” of the theta aurora. The model provides testable predictions with regard to the position of this “convection gap” in both northern and southern hemispheres as functions of IMF direction.

The influence of IMF-Bz and/or AE on the polar cusp: An overview of observations from the AUREOL-3 satellite

Experimental evidence for direct or indirect effects of the polarity and amplitude of the IMF- Bz component and the activity index AE on particle precipitation in the low-altitude cusp have been searched for, using the particle data from the AUREOL-3 satellite. The observations show that the precipitation of H + and He ++ ions often display energy-latitude dispersions over 1 to 2° in latitude which reflect the signature of the direct injection of plasma from the magnetosheath and the subsequent effect of the velocity filter. The ion dispersions explained by sunward convection over the polar cap are preferentially observed when Bz>0, and over the summer hemisphere. In this case their localization implies that the poleward boundary of the cusp is directly connected to a region of dayside merging between the IMF and the tail lobe field lines. We also present a statistical study of the position of the cusp boundaries and their relation to Bz and AE. Cross-correlation analysis shows that the best correlation with both AE and Bz is obtained when the ion precipitation in the cusp is organized with ion dispersions. The boundary directly linked to the plasma entry/reconnection region, equatorial for Bz < 0, polar for Bz > 0, is most strongly correlated with Bz shifted 30–40 minutes in time. Under the same conditions, the correlation with the instantaneous AE index is also very strong. Finally we suggest that the cusp position is only indirectly controlled by Bz, with a delay of about 40 minutes necessary for establishing a new convection system and stable ionospheric currents inside the magnetosphere.

Mapping of the solar wind electric field to the Earth's polar caps

In this paper we describe a quantitative model of a magnetically interconnected (open) magnetosphere, developed as a perturbation to Voigt's closed magnetosphere model with a given magnetopause shape. The “interconnection” (perturbation) field is obtained as a solution to a Neumann boundary value problem, with the magnetopause normal component distribution as a boundary condition. The normal component at the magnetopause is required to be time independent, and is specified in accordance with one of two hypotheses: the subsolar point merging hypothesis and Crooker's antiparallel merging hypothesis. The resulting open magnetospheric configuration is used to map the magnetopause electric field down to the polar cap ionosphere. We present ionospheric convection patterns derived from three representative interplanetary magnetic field (IMF) orientations for each of the two dayside merging geometries. Both merging geometries reproduce the observed convergence of convection streamlines near noon in a convection “throat,” and the east‐west deflection of these streamlines in response to the east‐west IMF component. The major difference between the two dayside merging geometries occurs for nonsouthward IMF, and consists of a Sun‐aligned convection gap that bifurcates the polar cap in the case of the antiparallel merging geometry but not in the subsolar point merging geometry. This convection gap may plausibly be associated with the “theta aurora” structure observed when the IMF has a northward component.

Ionospheric convection signatures and magnetic field topology

We present here a statistical study of signatures of the high‐latitude ionospheric convection pattern and the simultaneously observed energetic electron precipitation. We most often find convection cells in which the sunward flowing region contains auroral particle precipitation but the antisunward flowing region does not. However, our observations also show the frequent occurrence of convection cells in which neither the antisunward nor the sunward flowing plasma region contains auroral particle precipitation. These findings may appear within the dawnside or duskside convection pattern and strongly suggest that such convection cells may be associated with open magnetic field lines that thread the magnetotail lobes. Examination of the interplanetary magnetic field (IMF) data shows that this “lobe cell” convection signature is most likely to be accompanied by the signature of dayside merging when the IMF has a significant y component but is directed southward. A lobe convection cell has a location and sense of circulation that are dependent on the sign of By. For the northern hemisphere, clockwise circulation displaced to the duskside appears roughly 35% of the time when By is positive, and anticlockwise circulation displaced to the dawnside appears when By is negative. The same circulation sense and location exist in the southern hemisphere for the opposite polarity of By. At times of northward IMF, the circulation within the polar cap can be at least partially on closed field lines and cannot be easily reconciled with merely a distortion of the standard “two‐cell” convection pattern. The significance of these results to several models of the solar wind/magnetosphere interaction is discussed.

IMF By and day‐night conductivity effects in the expanding polar cap convection model

During southward Bz periods the open field line region in the ionosphere (polar cap) expands due to increased dayside merging. Ionospheric plasma flow patterns result which can be classified by the sign of the interplanetary magnetic field (IMF) By component. In this paper we construct a time‐dependent ionospheric convection model to simulate these flows. The model consists of a spiral boundary with a gap in it. The sign of the IMF By component determines the geometry of the gap. A potential is applied across the gap and distributed around the boundary. A flow results which enters the polar cap through the gap and uniformly pushes the boundary outward. Results of the model show that By effects are greatest near the gap and virtually unnoticeable on the nightside of the polar cap. Adding a day‐night ionospheric conductivity gradient concentrates the polar cap electric field toward dawn. The resulting flow curvature gives a sunward component that is independent of By. These patterns are shown to be consistent with published observations.

On the limits of energy transfer through dayside merging

Empirical studies indicate that the rate of energy transfer to the magnetosphere increases as solar wind coupling parameters increase, up to a certain limit, and then the rate remains constant. The split separator line merging model undergoes the same behavior. When the model interplanetary magnetic field (IMF) magnitude exceeds a critical value, the field configuration in the Chapman‐Ferraro current plane ceases to expose closed field lines to the solar wind. The critical value depends upon IMF orientation, stagnation pressure, and earth's dipole tilt angle. The absence of exposed closed field lines prevents closed‐to‐open flux transfer and, consequently, energy transfer. Further, the limit on energy transfer governed by the model dipole tilt angle affords the first explanation of both the semiannual and UT variations of geomagnetic activity completely in terms of merging.

Magnetospheric convection observed between 0600 and 2100 LT: Solar wind and IMF dependence

Using data from the GEOS 2 electron gun experiment, we have analyzed the dependence of the dayside convection electric field at L = 6.6 (averaged into 3‐hour LT bins) on solar wind and interplanetary magnetic field conditions. The convection electric field does not correlate at all with the solar wind momentum flux density (correlation coefficients of &lt;0.25). Hence viscous interaction plays only a minor role for equatorial magnetospheric convection at L = 6.6. The correlation coefficients for convection electric field versus merging electric field are of the order of 0.5–0.6, thus indicating that dayside convection is predominantly driven by dayside merging. The regression coefficients, describing the (LT‐dependent) transfer of the merging electric field to synchronous orbit, are of the order of 0.1–0.2. Their LT dependence follows approximately that described by a Volland‐Stern model with γ = 2, except that the regression analysis yields a dawn‐dusk asymmetry with the dusk sector electric fields being about twice as strong as those in the dawn sector. For the above shielding factor (γ = 2) the regression coefficients are consistent with a merging efficiency of about 20%. The regression constants (of the order of 0.05 mV/m) apparently describe an electric field stemming from the ionospheric wind dynamo. A comparison of the electric field described by the regression constants and two empirical models of quiet day electric fields implies that these models still include a substantial dawn‐to‐dusk electric field, thus indicating the presence of solar wind dynamo action even during quiet intervals.

Polar cap inflation and deflation

Dayside and nightside merging rates usually differ; first one dominates and then the other to maintain long‐term flux balance. The polar cap, defined as the area in the ionosphere penetrated by open field lines, expands when closed field lines open during dayside merging and contracts when open field lines close during tail merging. The patterns of convection, electric field and current for polar cap inflation and deflation differ from those of steady state convection. This report models the flow and electrical parameters of polar cap inflation and deflation. We treat the idealized case of uniform conductivity, a planar ionosphere, and “pure Bz” merging (i.e., no By effect, although we note how the approach used here is readily modified to account for the By effect). For this idealized case, the potential associated with polar cap inflation and deflation is seen to be described by the same equations that govern the two‐dimensional hydrodynamic flow into and out of an expanding and contracting cylinder with a gap in its side. The gap corresponds to the breach in the polar cap boundary through which magnetic flux passes as a result of merging. The calculated potential pattern displays the usual two cell convection configuration, but the foci of the two cells are the edges of the flux gaps. Thus the cells are displaced sunward during dayside merging and tailward during tail merging.

Downstream properties of magnetic flux transfer events

We consider the downstream evolution of the tubes of field lines known as flux transfer events (FTE's) formed by the localized, dayside, sporadic merging of magnetosheath and magnetosphere magnetic field lines. FTE's have magnetic field and plasma properties distinct from those of the nearby unmerged magnetosheath and magnetosphere field lines. Tailward advection stretches these earth‐rooted flux tubes and orients them parallel to the field in the magnetotail lobes. Following dayside merging, magnetosheath plasma flows into the magnetosphere part of the FTE. This flow is modeled by a self‐similar expansion of a plasma into a vacuum. The magnetosheath part of the FTE empties, and the magnetosphere part fills with time. After the FTE has moved 200 RE down the tail, the drained portion of the FTE reaches about 25 RE radially outward from the tail boundary. We suggest that most multiple crossings of the tail boundary observed by spacecraft are encounters with tailward moving FTE's. This interpretation explains fully the way boundary normals behave during multiple crossings. The previously favored interpretation, tailward moving boundary waves, only partly explains the known behavior. The model explains how the sign of the interplanetary magnetic field (IMF) causes the observed dawn‐dusk asymmetries in the thickness of the magnetotail boundary layer and in the pattern of “lobe filling.” It also predicts that multiple boundary crossings should be correlated with negative IMF Bz.

Duality of the magnetic flux tube and electric current descriptions of magnetospheric plasma and energy flow

The duality between electric current and magnetic flux tubes is outlined for the magnetosphere. Magnetic flux tubes are regarded as fluid elements subject to various stresses. Current closure then becomes the dual of stress balance, and Poynting vector energy flow a dual of J · E dissipation. The stresses acting on a flux tube are magnetic stresses, which correspond to currents at a distance, and plasma stresses, which correspond to local currents. The duality between current and stress is traced for ionospheric ion drag forces, solar wind stresses at the magnetopause, inertial effects, and the effects of energetic plasma on flux tubes. The stress balance and dual current systems are outlined for idealized magnetospheres of increasing complexity. For a simple magnetosphere with no convective flow, the balanced stresses are solar wind pressure and neutral sheet plasma pressure. The corresponding current systems are the Chapman‐Ferraro magnetopause currents and the magnetotail current system. The introduction of convective flow introduces further stresses: ionospheric ion drag, Alfvén layer shielding, and an imbalance in day‐night magnetic stresses due to transport of flux tubes to the nightside by the solar wind. These stresses balance, and hence the corresponding additional currents (the ionospheric Pedersen current and the electrojets, the partial ring current, and two other current systems from the magnetopause and tail) must form a closed current system and do so by the region I and II field‐aligned currents of Iijima and Potemra. The energy flow in the above models is described in terms of both Poynting vectors and the above current systems. Temporal variations examined are (1) an increase in dayside merging and/or nightside reconnection, (2) an increase in the energy density of plasma in the plasma sheet, (3) an increase in ionospheric conductivity, and (4) an increase in solar wind pressure. Each of the first three requires an increase in all the currents and stresses associated with convective flow. The symptoms of variation 3 are very similar to many of those observed during magnetospheric substorms, and it is concluded that ionospheric conductivity enhancement is important in substorms, since it represents a major change in the forces affecting the flow and, in the dual picture, of the currents associated with the flow. Finally, the effect of aurora‐associated magnetic‐field‐aligned electric fields are considered, and the variation in the flows when the east‐west component of electric field parallel to the arc is included. Quite different plasma transport may result even though the north‐south meridian cross sections are the same.

Comment on ‘Dayside aurora and relevance to substorm current systems and dayside merging’ by R.H. Eather, S.B. Mende, and E.J. Weber

Comment on ‘Dayside aurora and relevance to substorm current systems and dayside merging’ by R.H. Eather, S.B. Mende, and E.J. Weber

Reply [to “Comment on ‘Dayside aurora and relevance to substorm current systems and dayside merging’ by R. H. Eather, S. B. Mende, and E. J. Weber”

Reply [to “Comment on ‘Dayside aurora and relevance to substorm current systems and dayside merging’ by R. H. Eather, S. B. Mende, and E. J. Weber”

Dayside aurora and relevance to substorm current systems and dayside merging

Photometric keograms from South Pole Station are used to investigate dayside auroral precipitation. Identification of cusp auroral signatures allows cusp movements to be monitored and correlated with substorm activity and interplanetary magnetic field direction. We conclude that any erosion of dayside field is not a direct result of southward turning Bz. On the other hand, cusp position is intimately related to substorm timing and intensity. We suggest the associated dayside field reconfiguration results from diversion of near‐tail magnetopause currents through the nightside electrojet because of enhanced auroral ionosphere conductivity. This interpretation implies that substorms result from increased efficiency of the extraction of energy from the solar wind rather than from a release of internally stored magnetic energy in the tail.