The pulsating cusp

Recent observations at the magnetopause and of the high-latitude ionosphere, suggest that the cusp may be pulsed in nature. Specifically ground-based observations in the dayside auroral oval reveal transient optical features accompanied by bursts of enhanced plasma flow. Also, recent interpretation has shown cusp satellite data to be consistent with a burst of enhanced reconnection. In this paper we use these observations to produce a scenario in which both the satellite and ground-based observations can be fitted. The scenario we develop is based on the flux transfer event (FTE) models of Southwood et al. and Scholer and shows that the signatures, at both low and high altitudes, can be interpreted in terms of FTEs.

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.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

An optical study of multiple NEIAL events driven by low energy electron precipitation

Optical data are compared with EISCAT radar observations of multiple Naturally Enhanced Ion-Acoustic Line (NEIAL) events in the dayside cusp. This study uses narrow field of view cameras to observe small-scale, short-lived auroral features. Using multiple-wavelength optical observations, a direct link between NEIAL occurrences and low energy (about 100 eV) optical emissions is shown. This is consistent with the Langmuir wave decay interpretation of NEIALs being driven by streams of low-energy electrons. Modelling work connected with this study shows that, for the measured ionospheric conditions and precipitation characteristics, growth of unstable Langmuir (electron plasma) waves can occur, which decay into ion-acoustic wave modes. The link with low energy optical emissions shown here, will enable future studies of the shape, extent, lifetime, grouping and motions of NEIALs.

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.

Polar cap patch segmentation of the tongue of ionization in the morning convection cell

Two types of poleward moving plasma concentration enhancements (PMPCEs) were observed during a sequence of pulsed reconnection events, both in the morning convection cell: Type L (low density) was associated with a cusp flow channel and seems likely to have been produced by ionization associated with particle precipitation, while Type H (high density) appeared to originate from the segmentation of the tongue of ionization by the processes which produced the Type L events. As a result, the Type L and Type H PMPCEs were interspersed, producing a complex density structure which underlines the importance of cusp flow channels as a mechanism for segmenting and structuring electron density in the cusp and shows the necessity of differentiating between at least two classes of electron density patches.

Information and efficiency: goal arrival in soccer betting

An efficient market incorporates news into prices immediately and fully. Tests for efficiency in financial markets have been undermined by information leakage. We test for efficiency in sports betting markets – real-world markets where news breaks remarkably cleanly. Applying a novel identification to high-frequency data, we investigate the reaction of prices to goals scored on the ‘cusp’ of half-time. This strategy allows us to separate the market's response to major news (a goal), from its reaction to the continual flow of minor game-time news. On our evidence, prices update swiftly and fully.

The importance of moisture distribution for the growth and energetics of mid-latitude systems

A primitive equation model is used to study the sensitivity of baroclinic wave life cycles to the initial latitude-height distribution of humidity. Diabatic heating is parametrized only as a consequence of condensation in regions of large-scale ascent. Experiments are performed in which the initial relative humidity is a simple function of model level, and in some cases latitude bands are specified which are initially relatively dry. It is found that the presence of moisture can either increase or decrease the peak eddy kinetic energy of the developing wave, depending on the initial moisture distribution. A relative abundance of moisture at mid-latitudes tends to weaken the wave, while a relative abundance at low latitudes tends to strengthen it. This sensitivity exists because competing processes are at work. These processes are described in terms of energy box diagnostics. The most realistic case lies on the cusp of this sensitivity. Further physical parametrizations are then added, including surface fluxes and upright moist convection. These have the effect of increasing wave amplitude, but the sensitivity to initial conditions of relative humidity remains. Finally, 'control' and 'doubled CO2' life cycles are performed, with initial conditions taken from the time-mean zonal-mean output of equilibrium GCM experiments. The attenuation of the wave resulting from reduced baroclinicity is more pronounced than any effect due to changes in initial moisture.

Modeling the observed proton aurora and ionospheric convection responses to changes in the IMF clock angle: 2. Persistence of ionospheric convection

We apply a numerical model of time-dependent ionospheric convection to two directly driven reconnection pulses during a 15-min interval of southward IMF on 26 November 2000. The model requires an input magnetopause reconnection rate variation, which is here derived from the observed variation in the upstream IMF clock angle, q. The reconnection rate is mapped to an ionospheric merging gap, the MLT extent of which is inferred from the Doppler-shifted Lyman-a emission on newly opened field lines, as observed by the FUV instrument on the IMAGE spacecraft. The model is used to reproduce a variety of features observed during this event: SuperDARN observations of the ionospheric convection pattern and transpolar voltage; FUV observations of the growth of patches of newly opened flux; FUVand in situ observations of the location of the Open-Closed field line Boundary (OCB) and a cusp ion step. We adopt a clock angle dependence of the magnetopause reconnection electric field, mapped to the ionosphere, of the form Enosin4(q/2) and estimate the peak value, Eno, by matching observed and modeled variations of both the latitude, LOCB, of the dayside OCB (as inferred from the equatorward edge of cusp proton emissions seen by FUV) and the transpolar voltage FPC (as derived using the mapped potential technique from SuperDARN HF radar data). This analysis also yields the time constant tOCB with which the open-closed boundary relaxes back toward its equilibrium configuration. For the case studied here, we find tOCB = 9.7 ± 1.3 min, consistent with previous inferences from the observed response of ionospheric flow to southward turnings of the IMF. The analysis confirms quantitatively the concepts of ionospheric flow excitation on which the model is based and explains some otherwise anomalous features of the cusp precipitation morphology.

Motion of the dayside polar cap boundary during substorm cycles: II. Generation of poleward-moving events and polar cap patches by pulses in the magnetopause reconnection rate

Using data from the EISCAT (European Incoherent Scatter) VHF and CUTLASS (Co-operative UK Twin- Located Auroral Sounding System) HF radars, we study the formation of ionospheric polar cap patches and their relationship to the magnetopause reconnection pulses identified in the companion paper by Lockwood et al. (2005). It is shown that the poleward-moving, high-concentration plasma patches observed in the ionosphere by EISCAT on 23 November 1999, as reported by Davies et al. (2002), were often associated with corresponding reconnection rate pulses. However, not all such pulses generated a patch and only within a limited MLT range (11:00–12:00 MLT) did a patch result from a reconnection pulse. Three proposed mechanisms for the production of patches, and of the concentration minima that separate them, are analysed and evaluated: (1) concentration enhancement within the patches by cusp/cleft precipitation; (2) plasma depletion in the minima between the patches by fast plasma flows; and (3) intermittent injection of photoionisation-enhanced plasma into the polar cap. We devise a test to distinguish between the effects of these mechanisms. Some of the events repeat too frequently to apply the test. Others have sufficiently long repeat periods and mechanism (3) is shown to be the only explanation of three of the longer-lived patches seen on this day. However, effect (2) also appears to contribute to some events. We conclude that plasma concentration gradients on the edges of the larger patches arise mainly from local time variations in the subauroral plasma, via the mechanism proposed by Lockwood et al. (2000).

Motion of the dayside polar cap boundary during substorm cycles: I. Observations of pulses in the magnetopause reconnection rate

Using data from the EISCAT (European Incoherent Scatter) VHF radar and DMSP (Defense Meteorological Satellite Program) spacecraft passes, we study the motion of the dayside open-closed field line boundary during two substorm cycles. The satellite data show that the motions of ion and electron temperature boundaries in EISCAT data, as reported by Moen et al. (2004), are not localised around the radar; rather, they reflect motions of the open-closed field line boundary at all MLT throughout the dayside auroral ionosphere. The boundary is shown to erode equatorward when the IMF points southward, consistent with the effect of magnetopause reconnection. During the substorm expansion and recovery phases, the dayside boundary returns poleward, whether the IMF points northward or southward. However, the poleward retreat was much faster during the substorm for which the IMF had returned to northward than for the substorm for which the IMF remained southward – even though the former substorm is much the weaker of the two. These poleward retreats are consistent with the destruction of open flux at the tail current sheet. Application of a new analysis of the peak ion energies at the equatorward edge of the cleft/cusp/mantle dispersion seen by the DMSP satellites identifies the dayside reconnection merging gap to extend in MLT from about 9.5 to 15.5 h for most of the interval. Analysis of the boundary motion, and of the convection velocities seen near the boundary by EISCAT, allows calculation of the reconnection rate (mapped down to the ionosphere) from the flow component normal to the boundary in its own rest frame. This reconnection rate is not, in general, significantly different from zero before 06:45 UT (MLT<9.5 h) – indicating that the X line footprint expands over the EISCAT field-of-view to earlier MLT only occasionally and briefly. Between 06:45 UT and 12:45UT (9.5

A comparison between ion characteristics observed by the POLAR and DMSP spacecraft in the high-latitude magnetosphere

We study here the injection and transport of ions in the convection-dominated region of the Earth’s magnetosphere. The total ion counts from the CAMMICE MICS instrument aboard the POLAR spacecraft are used to generate occurrence probability distributions of magnetospheric ion populations. MICS ion spectra are characterised by both the peak in the differential energy flux, and the average energy of ions striking the detector. The former permits a comparison with the Stubbs et al. (2001) survey of He2+ ions of solar wind origin within the magnetosphere. The latter can address the occurrences of various classifications of precipitating particle fluxes observed in the topside ionosphere by DMSP satellites (Newell and Meng, 1992). The peak energy occurrences are consistent with our earlier work, including the dawn-dusk asymmetry with enhanced occurrences on the dawn flank at low energies, switching to the dusk flank at higher energies. The differences in the ion energies observed in these two studies can be explained by drift orbit effects and acceleration processes at the magnetopause, and in the tail current sheet. Near noon at average ion energies of _1 keV, the cusp and open LLBL occur further poleward here than in the Newell and Meng survey, probably due to convectionrelated time-of-flight effects. An important new result is that the pre-noon bias previously observed in the LLBL is most likely due to the component of this population on closed field lines, formed largely by low energy ions drifting earthward from the tail. There is no evidence here of mass and momentum transfer from the solar wind to the LLBL by nonreconnection coupling. At higher energies (_2–20 keV), we observe ions mapping to the auroral oval and can distinguish between the boundary and central plasma sheets. We show that ions at these energies relate to a transition from dawnward to duskward dominated flow, this is evidence of how ion drift orbits in the tail influence the location and behaviour of the plasma populations in the magnetosphere.