A Summary of the NATO ASI on Polar Cap Boundary Phenomena

The polar cap boundary is a subject of central importance to current magnetosphere-ionosphere research and its applications in “space weather” activities. The problems are that it has a number of definitions, and that the most physically meaningful definition (namely the open-closed field line boundary) is very difficult to identify in observations. New understanding of the importance of the structure and dynamics of the boundary region made the time right for a meeting reviewing our knowledge in this area. The Advanced Study Institute (ASI) on Svalbard in June 1997 discussed the boundary on both the dayside and the nightside, mapping magnetically to the dayside magnetopause and to tail plasma sheet/lobe interface, respectively. We held a “brainstorming” session, in which different ideas which arose from the presented papers were discussed and developed, and a summary session, in which session convenors gave a personal view of progress that has been made and problems which still need solving. Both were designed as ways of promoting further discussion. This paper attempts to distil some of the themes that emerged from these discussions.

Ion populations on open field lines within the dayside low-latitude boundary layer: theory and observations during a transient event

We analyze of ion populations observed by the NOAA-12 satellite within dayside auroral transients. The data are matched with an open magnetopause model which allows for the transmission of magnetosheath ions across one or both of the two Alfvén waves which emanate from the magnetopause reconnection site. It also allows for reflection and acceleration of ions of magnetospheric origin by these waves. From the good agreement found between the model and the observations, we propose that the events and the low-latitude boundary precipitation are both on open field lines.

On the longitudinal extent of magnetopause reconnection pulses

The open magnetosphere model of cusp ion injection, acceleration and precipitation is used to predict the dispersion characteristics for fully pulsed magnetic reconnection at a low-latitude magnetopause X-line. The resulting steps, as would be seen by a satellite moving meridionally and normal to the ionospheric projection of the X-line, are compared with those seen by satellites moving longitudinally, along the open/closed boundary. It is shown that two observed cases can be explained by similar magnetosheath and reconnection characteristics, and that the major differences between them are well explained by the different satellite paths through the events. Both cases were observed in association with poleward-moving transient events seen by ground-based radar, as also predicted by the theory. The results show that the reconnection is pulsed but strongly imply it cannot also be spatially patchy, in the sense of isolated X-lines which independently are intermittently active. Furthermore they show that the reconnection pulses responsible for the poleward-moving events and the cusp ion steps, must cover at least 3 h of magnetic local time, although propagation of the active reconnection region may mean that it does not extend this far at any one instant of time.

Variability of dayside high latitude convection associated with a sequence of auroral transients

10 second resolution ionospheric convection data covering the invariant latitude range from 71° to 76°, obtained by using the EISCAT UHF and VHF radars, are combined with optical data from Ny Ålesund during a sequence of auroral transients in the post-noon sector (∼ 15 MLT). Satellite observations of polar cap convection patterns suggest negative BZ and BY components of the interplanetary magnetic field. Burst-like enhancements of westward (sunward) post-noon convection were accompanied by eastward moving auroral forms at higher latitudes, above the convection reversal boundary. In this case the background convection was weak, whereas the integrated potential drop across the radar field-of-view associated with the westward flow bursts was typically ∼ 20-35 kV. The auroral phenomenon consists of a series of similar events with a mean repetition period of 8 min. A close correlation between the auroral activity and convection enhancements in the cleft ionosphere is demonstrated.

Events of enhanced convection and related dayside auroral activity

In this paper we study the high-latitude plasma flow variations associated with a periodic (∼8 min) sequence of auroral forms moving along the polar cap boundary, which appear to be the most regularly occuring dayside auroral phenomenon under conditions of southward directed interplanetary magnetic field. Satellite data on auroral particle precipitation and ionospheric plasma drifts from DMSP F10 and F11 are combined with ground-based optical and ion flow measurements for January 7, 1992. Ionospheric flow measurements of 10-s resolution over the range of invariant latitudes from 71° to 76° were obtained by operating both the European incoherent scatter (EISCAT) UHF and VHF radars simultaneously. The optical site (Ny Ålesund, Svalbard) and the EISCAT radar field of view were located in the postnoon sector during the actual observations. The West Greenland magnetometers provided information about temporal variations of high-latitude convection in the prenoon sector. Satellite observations of polar cap convection in the northern and southern hemispheres show a standard two-cell pattern consistent with a prevailing negative By component of the interplanetary magnetic field. The 630.0 nm auroral forms located poleward of the persistent cleft aurora and the flow reversal boundary in the ∼1440–1540 MLT sector were observed to coincide with magnetosheath-like particle precipitation and a secondary population of higher energy ions, and they propagated eastward/tailward at speeds comparable with the convection velocity. It is shown that these optical events were accompanied by bursts of sunward (return) flow at lower latitudes in both the morning and the afternoon sectors, consistent with a modulation of Dungey cell convection. The background level of convection was low in this case (Kp =2+). The variability of the high-latitude convection may be explained as resulting from time-varying reconnection at the magnetopause. In that case this study indicates that time variations of the reconnection rate effectively modulates ionospheric convection.

Location and characteristics of the reconnection X line deduced from low-altitude satellite and ground-based observations: 2. Defense Meteorological Satellite Program and European Incoherent Scatter data

We present an analysis of a cusp ion step, observed by the Defense Meteorological Satellite Program (DMSP) F10 spacecraft, between two poleward moving events of enhanced ionospheric electron temperature, observed by the European Incoherent Scatter (EISCAT) radar. From the ions detected by the satellite, the variation of the reconnection rate is computed for assumed distances along the open-closed field line separatrix from the satellite to the X line, do. Comparison with the onset times of the associated ionospheric events allows this distance to be estimated, but with an uncertainty due to the determination of the low-energy cutoff of the ion velocity distribution function, ƒ(ν). Nevertheless, the reconnection site is shown to be on the dayside magnetopause, consistent with the reconnection model of the cusp during southward interplanetary magnetic field (IMF). Analysis of the time series of distribution function at constant energies, ƒ(ts), shows that the best estimate of the distance do is 14.5±2 RE. This is consistent with various magnetopause observations of the signatures of reconnection for southward IMF. The ion precipitation is used to reconstruct the field-parallel part of the Cowley D ion distribution function injected into the open low-latitude boundary layer in the vicinity of the X line. From this reconstruction, the field-aligned component of the magnetosheath flow is found to be only −55±65 km s−1 near the X line, which means either that the reconnection X line is near the stagnation region at the nose of the magnetosphere, or that it is closely aligned with the magnetosheath flow streamline which is orthogonal to the magnetosheath field, or both. In addition, the sheath Alfvén speed at the X line is found to be 220±45 km s−1, and the speed with which newly opened field lines are ejected from the X line is 165±30 km s−1. We show that the inferred magnetic field, plasma density, and temperature of the sheath near the X line are consistent with a near-subsolar reconnection site and confirm that the magnetosheath field makes a large angle (>58°) with the X line.

Ionospheric Signatures of Pulsed Magnetopause Reconnection

The concept of zero-flow equilibria of the magnetosphere-ionosphere system leads to a large number of predictions concerning the ionospheric signatures of pulsed magnetopause reconnection. These include: poleward-moving F-region electron temperature enhancements and associated transient 630nm emission; associated poleward plasma flow which, compared to the pulsed variation of the reconnection rate, is highly smoothed by induction effects; oscillatory latitudinal motion of the open/closed field line boundary; phase lag of plasma flow enhancements after equatorward motions of the boundary; azimuthal plasma flow bursts, coincident in time and space with the 630nm-dominant auroral transients, only when the magnitude of the By component of the interplanetary magnetic field (IMF) is large; azimuthal-then-poleward motion of 630nm-dominant transients at a velocity which at all times equals the internal plasma flow velocity; 557.7nm-dominant transients on one edge of the 630nm-dominant transient (initially, and for large |By|, on the poleward or equatorward edge depending on the polarity of IMF By); tailward expansion of the flow response at several km s-1; and discrete steps in the cusp ion dispersion signature between the polewardmoving structures. This paper discusses these predictions and how all have recently been confirmed by combinations of observations by optical instruments on the Svalbard Islands, the EISCAT radars and the DMSP and DE satellites.

On the voltage and distance across the low latitude boundary layer

A pass of the AMPTE-UKS satellite through the low-latitude boundary layer (LLBL) at 8:30 MLT is studied in detail. The magnetosheath field is predominantly northward. It is shown that multiple transitions through part or all of the layer of antisunward flow lead to overestimation of both the voltage across this layer and its width. The voltage is estimated to be only about 3 kV and this implies that the full LLBL is about 1200 km thick, consistent with previous studies.

Dynamic auroral structure in the vicinity of the polar cusp - multipoint observations during southward and northward IMF

The low- and high-latitude boundary layers of the earth's magnetosphere [low-latitude boundary layer (LLBL) and mantle] play important roles in transferring momentum and energy from the solar wind to the magnetosphere-ionosphere system. Particle precipitation, field-aligned current, auroral emission, ionospheric ion drift and ground magnetic perturbations are among the low-altitude parameters that show signatures of various plasma processes in the LLBL and the magnetopause current layer. Magnetic merging events, Kelvin-Helmholtz waves, and pressure pulses excited by the variable solar wind/magnetosheath plasma are examples of boundary phenomena that may be coupled to the ionosphere via field-aligned currents. Optical auroral observation, by photometry and all-sky TV cameras, is a unique technique for investigating the spatial and temporal structure of the electron precipitation associated with such phenomena. However, the distinction between the different boundary layer plasma populations cannot in general be unambiguously determined by optics alone. Additional information, such as satellite observations of particle boundaries and field-aligned currents, is needed in order to identify the plasma source(s) and the magnetosphere-ionosphere coupling mode(s). Two categories of auroral activity/structure in the vicinity of the polar cusp are discussed in this paper, based on combined ground and satellite data. In one case, the quasi-periodic sequence of auroral events at the polar cap boundary involves accelerated electrons (< 1 keV) moving poleward (< 1 km s-1) and azimuthally along the persistent cusp/cleft arc poleward boundary with velocities (< 4 km s-1), comparable to the local ionospheric ion drift during periods of southward IMF. A critical question is whether or not the optical events signify a corresponding plasma flow across the open/closed field line boundary in such cases. Near-simultaneous observations of magnetopause flux transfer events (FTEs) and such optical/ion drift events are reported. The reverse pattern of motion of discrete auroral forms is observed during positive interplanetary magnetic field (IMF) B(Z), i.e. equatorward motion into the cusp/cleft background arc from the poleward edge. Combined satellite and ground-based information for the latter cases indicate a source mechanism, poleward of the cusp at the high-latitude magnetopause or plasma mantle, giving rise to strong momentum transfer and electron precipitation structures within a approximately 200 km-wide latitudinal zone at the cusp/cleft poleward boundary. The striking similarities of auroral electrodynamics in the cleft/mantle region during northward and southward IMF indicate that a qualitatively similar solar wind-magnetosphere coupling mode is operating. It is suggested that, in both cases, the discrete auroral forms represent temporal/spatial structure of larger-scale convection over the polar magnetosphere.

Periodic auroral events at the high-latitude convection reversal in the 16 MLT region

Combined optical and radar observations of two breakup-like auroral events near the polar cap boundary, within 74–76° MLAT and 1210 – 1240 UT (roughly 1540 – 1610 MLT) on 9 Jan. 1989 are reported. A two-component structure of the auroral phenomenon is indicated, with a local intensification of the pre-existing arc as well as a separate, tailward moving discrete auroral event on the poleward side of the background aurora, close to the reversal between well-defined zones of sunward and tailward ion flows. The all-sky TV observations do not indicate a connection between the two components, which also show different optical spectral composition. The 16 MLT background arc is located on sunward convecting field lines, as opposed to the 12–14 MLT auroral emission observed on this day. Although the magnetospheric plasma source (s) of the 16 MLT events are not easily identified from these ground-based data alone, it is suggested that the lower and higher latitude components, may map to the plasma sheet boundary layer and along open field lines to the magnetopause boundary, respectively. The events occur at the time of enhancements of westward ionospheric ion flow and corresponding eastward electrojet current south of 74° MLAT. Thus, they seem to be very significant events, involving periodic (10 min period), tailward moving filaments of field-aligned current/discrete auroral emission at the 16 MLT polar cap boundary.

Low-altitude signatures of the cusp and flux transfer events

The usual interpretation of a flux transfer event (FTE) at the magnetopause, in terms of time-dependent and possibly patchy reconnection, demands that it generate an ionospheric signature. Recent ground-based observations have revealed that auroral transients in the cusp/cleft region have all the characteristics required of FTE effects. However, signatures in the major available dataset, namely that from low-altitude polar-orbiting satellites, have not yet been identified. In this paper, we consider a cusp pass of the DE-2 spacecraft during strongly southward IMF. The particle detectors show magnetosheath ion injection signatures. However, the satellite motion and convection are opposed, and we discuss how the observed falling energy dispersion of the precipitating ions can have arisen from a static, moving or growing source. The spatial scale of the source is typical of an FTE. A simple model of the ionospheric signature of an FTE reproduces the observed electric and magnetic field perturbations. Precipitating electrons of peak energy ∼100eV are found to lie on the predicted boundary of the newly-opened tube, very similar to those found on the edges of FTEs at the magnetopause. The injected ions are within this boundary and their dispersion is consistent with its growth as reconnection proceeds. The reconnection potential and the potential of the induced ionospheric motion are found to be the same (≃25kV). The scanning imager on DE-1 shows a localised transient auroral feature around DE-2 at this time, similar to the recent optical/radar observations of FTEs.

Ion flows and heating at a contracting polar-cap boundary

Data recorded by the POLAR experiment run on the EISCAT radar during the international GISMOS campaign of 3–5 June 1987 are studied in detail. The polar-cap boundary, as denned by an almost shear East-West convection reversal, was observed to jump southward across the EISCAT field of view in two steps at 02:00 and 03:00 Magnetic Local Time and subsequently to contract back between 04:00 and 07:00 M.L.T. An annulus of enhanced ion temperature and non-thermal plasma was observed immediately equatorward of the contracting boundary due to the lag in the response of the neutral-wind pattern to the change in ion flows. The ion flow at the boundary is shown to be relatively smooth at 15 s resolution and directed northward, with velocities which exceed that of the boundary itself. The effect of velocity shears on the beamswinging technique used to derive the ion flows is analyzed in detail and it is shown that, for certain orientations of the cap boundary, spurious flows into the cap can be generated. However, these are much smaller than the observed flows into the polar cap and cannot explain the potential difference across the observed segment of the cap boundary (extending over 2 h of M.L.T.) which is roughly 7 kV. Similarly, an observed slowing of the zonal flow near the boundary cannot be explained as an error introduced by the use of the beamswinging technique. The results could be interpreted as being due to reconnection occurring on the dawn flank of the magnetopause (mapping to the polar cap at 04:30 06:30 M.L.T.). However, they are more consistent with recent observations of slow anti-sunward flow of closed field lines on the flanks of the geomagnetic tail, which appears to be generated by some form of “viscous” coupling to the magnetosheath plasma.

A new source of suprathermal O+ions near the dayside polar cap boundary

A new dayside source of O+ ions for the polar magnetosphere is described, and a statistical survey presented of upward flows of O+ ions using 2 years of data from the retarding ion mass spectrometer (RIMS) experiment on board DE 1, at geocentric distances below 3 RE and invariant latitudes above 40°. The flows are classified according to their spin angle distributions. It is believed that the spacecraft potential near perigee is generally less than +2 V, in which case the entire O+ population at energies below about 60 eV is sampled. Examples are given of field-aligned flow and of transversely accelerated “core” O+ ions; in the latter events a large fraction of the total O+ ion population has been transversely accelerated, and in some extreme cases all the observed ions (of all ion species) have been accelerated, and no residual cold population is observed (“toroidal” distributions). However, by far the most common type of O+ upflow seen by DE RIMS lies near the dayside polar cap boundary (particularly in the prenoon sector) and displays an asymmetric spin angle distribution. In such events the ions carry an upward heat flux, and strong upflow of all species is present (H+, He+, O+, O++, and N+ have all been observed with energies up to about 30 eV, but with the majority of ions below about 2 eV); hence, these have been termed upwelling ion events. The upwelling ions are embedded in larger regions of classical light ion polar wind and are persistently found under the following conditions: at geocentric distances greater than 1.4 RE; at all Kp in summer, but only at high Kp in winter. Low-energy conical ions (<30 eV) are only found near the equatorial edge of the events, the latitude of which moves equatorward with increasing Kp and is highly correlated with the location of field-aligned currents. The RIMS data are fully consistent with a “mass spectrometer effect,” whereby light ions and the more energetic O+ ions flow into the lobes and mantle and hence the far-tail plasma sheet, but lower-energy O+ is swept across the polar cap by the convection electric field, potentially acting as a source for the nightside auroral acceleration regions. The occurrence probability of upwelling ion events, as compared to those of low-altitude transversely accelerated core ions and of field-aligned flow, suggests this could be the dominant mechanism for supplying the nightside auroral acceleration region, and subsequently the ring current and near-earth plasma sheet, with ionospheric O+ ions. It is shown that the total rate of O+ outflow in upwelling ion events (greater than 10^25 s^{−1}) is sufficient for the region near the dayside polar cap boundary to be an important ionospheric heavy ion source.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.