The existence of the Earth's magnetospheric cusp was discussed originally by Chapman and Ferraro (1930). Although their work pre-dates the concept of a magnetosphere confined by the solar wind, they argued that there would be a singular magnetic field line extending from the Earth's surface to a boundary, now known as the magnetopause. Considering for example the noon-midnight plane, field lines slightly displaced from this line separate at the magnetopause, and close either on the dayside or nightside. In this picture, the cusp can be defined as the singular field line, a separatrix, which spreads over the whole magnetopause. This definition carries over to a modern magnetosphere where the magnetopause connects to the cusp, and can be seen in models of a closed magnetosphere (Tsyganenko, 1989).

Of course the real cusp is much more complex, and its properties are determined by the nature of the interaction of the solar wind, and especially the interplanetary

1 Space and Atmospheric Physics, The Blackett Laboratory, Imperial College London, London, UK

2Los Alamos National Laboratory, Los Alamos, NM, USA

3Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, Surrey, UK

4CETP/IPSL, Velizy, France

5Space Science Division, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, UK

6ESTEC, Noordwijk, The Netherlands

7International Space Science Institute, Bern, Switzerland

8Space Sciences Laboratory, University of California, Berkeley, CA, USA

Space Science Reviews 118: 321-366, 2005.

DOI: 10.1007/s11214-005-3835-0 © Springer 2005

magnetic field (IMF), with the magnetosphere. An all-inclusive definition of the cusp is difficult, and indeed may not be entirely desirable, but a working definition is that it is (a) part of the magnetosphere in the vicinity of the polar region at high magnetic latitudes, where a significant quantity of magnetosheath plasma is detected inside the nominal magnetopause position and (b) a region that encompasses the demarcation between dayside and nightside field lines. It should be noted that when examining in-situ particle and field measurements, the cusp tends to identify itself readily by its location and by the presence of magnetosheath plasma, and electromagnetic turbulence.

At low altitudes, where it was first discovered (Heikkila and Winningham, 1971; Frank, 1971), the cusp is located near magnetic noon and extends 1-2° in latitude and 1-2 hours in magnetic local time, MLT (Newell and Meng, 1988). Its position responds to both external changes like the solar wind ram pressure and IMF direction, and to internal changes like the dipole tilt angle and the geomagnetic activity, and can be found between 73° and 80° magnetic latitude and between 10:30 and 13:30 MLT (Newell and Meng, 1994; Yamauchi et al., 1996; Newell et al., 1989, and references therein). Since Cluster does not sample the low-altitude cusp, it is not discussed further in this chapter. At mid-altitudes, Cluster samples a very complex region of precipitating, mirrored and upwelling ions and electrons, with associated magnetic and electric field perturbations and turbulence. This is a reflection of the key role that the cusp plays in the transport of energy from the magnetopause to the ionosphere, as well as reflecting the ionospheric response to this energy input.

However, understanding what is seen in the cusp at low and middle altitudes requires knowledge of what is happening at the high-altitude cusp and associated magnetopause. This is a complex region of the magnetosphere, with the complexity arising from both the global interaction of the IMF with the magnetosphere, and the special local nature of the terrestrial magnetic field at the high-altitude cusp. It is now accepted that magnetic reconnection has a major influence on magneto-spheric dynamics. In simple terms, for southward IMF, reconnection may occur in the vicinity of the sub-solar region, and for northward IMF, it can occur at the lobes. The cusp plays a special role since it is the reversal of the terrestrial magnetic field with respect to the IMF around the cusp that permits both southward and northward IMFs to reconnect.

For southward IMF, the high-altitude cusp will be influenced by the reconnection process as field lines reconnected at low latitudes are swept tailwards with the magnetosheath flow (Shelley et al., 1976; Reiff et al., 1977, 1980). How reconnected pulses and field lines evolve as they move along the magnetopause is unknown (see Smith and Lockwood, 1990, for suggestions). However, major effects in the cusp should be the presence of tailward convection and associated plasma mantle (Rosenbauer et al., 1975) and the necessity that the magnetic boundary with the magnetosheath be a rotational discontinuity (RD) (e.g., Vasyliunas, 1995). For a northward IMF, lobe reconnection will influence the cusp from the tailward side (Gosling et al., 1991; Kessel et al., 1996). The effect here is less clear, since for large enough magnetosheath plasma flows (i.e., super-Alfvenic), reconnected field lines should be swept tailward.

In the above scenarios, the cusp simply is a region that responds to what is happening elsewhere on the magnetopause: in other words a transit point in the flow of magnetic flux and particles in the magnetosphere. However, the cusp may also have its own intrinsic properties. For example, at the cusp, the Earth's magnetic field will have a region of relative weakness, leading to the suggestion that the magnetopause can sag inwards there, and that the magnetosheath flow needs to be deflected accordingly (Haerendel et al., 1978; Haerendel, 1978). A complex system of shock and rarefaction waves would be needed to accomplish this, as has been discussed by, for example, Walters (1966); Yamauchi and Lundin (2001); Taylor and Cargill (2002), and could lead to the injection of solar wind plasma independent of reconnection elsewhere on the magnetopause.

A related issue is that if one considers the cusp to be a funnel, with magnetic field lines converging from 360°, then local magnetic reconnection of anti-parallel fields would appear to be inevitable in the cusp vicinity for any IMF orientation, not just at the low-latitude magnetopause or at the lobes (see also Chapter 8). Also, a number of studies have shown the probable occurrence of multiple reconnections in the cusp region, eventually leading to turbulent mixing and entry penetration (e.g., Savin et al., 2004).

9.1.1 Previous work Mid-altitude

The mid-altitude cusp region has been the subject of previous studies based on missions such as ISEE, Dynamics Explorer, Viking and Polar. This region is located near 12 MLT, and is characterised by direct penetration of magnetosheath plasma into the Earth's magnetosphere/ionosphere. Under southward IMF conditions, energy-latitude dispersions in ion data are the most pronounced cusp signature, and are usually interpreted as evidence of magnetosheath plasma entry following reconnection. The anti-sunward convection of open field lines through the polar ionosphere, and finite and different velocities of the magnetosheath ions entering from a sub-solar reconnection site give rise to the velocity filter effect.

Under steady northward IMF it seems likely that reconnection can occur at the high-latitude magnetopause and the observed 'reversed' ion dispersion signatures (Woch and Lundin, 1992b,a) have been interpreted as a consequence of this 'lobe reconnection' (Bosqued et al., 1985; Fuselier et al., 2000a). There is also evidence that component merging at the low-latitude magnetopause leads to cusp injections (Chandler et al., 1999). Finally, the IMF By component influences plasma convection in the polar region (e.g., Gosling et al., 1990; Cowley et al., 1991). For ex ample, for IMF By > (<)0, flows in the cusp show a strong dawnward (duskward) bias.

More complex ion behaviour is often seen, such as steps in the cusp ion dispersion signatures (e.g., Escoubet et al., 1992; Lockwood and Smith, 1992). Models in which particle motions are traced from a magnetopause reconnection site down cusp field lines and into the ionosphere have been developed (e.g., Onsager et al., 1993; Smith and Lockwood, 1996) and such models reproduce the observed ion signatures including the cusp ion energy steps (e.g., Lockwood et al., 1995). This was interpreted as a signature of variations in the reconnection rate. However, Trattner et al. (1999, 2002) have suggested that some of these features can also be explained by sampling of spatially separated structures in some cases.

Another interesting phenomenon is the possibility of 'double reconnection', which is believed to produce two auroral forms that can be observed simultaneously on the equatorward and poleward side of the cusp (0ieroset et al., 1997; Sandholt et al., 1998, 2001) as well as the so-called 'double cusp' (Wing et al., 2001; Pitout et al., 2002). In support of this conjecture, modelling carried out by Wing et al. (2001) showed that when there was a strong IMF By with either a small negative or positive Bz, reconnection can take place both on the dayside and near the lobes, and so produce simultaneously two cusp injections at different locations. Although quite rare, such observations do exist in the DMSP database.

Lockwood et al. (1985) noted persistent outflows of low-energy O+ ions at altitudes of 2000 - 5000 km. It was suggested that they had their origin in the dayside cleft/cusp region and manifested themselves as spatially-dispersed field-aligned flows at higher altitude (e.g., Moore et al., 1986). Such outflows have been suggested as a major source of magnetospheric heavy ion populations (Andre and Yau, 1997). Observations have shown strong localised perpendicular energisation of these ions (Moore et al., 1999), which can be attributed to wave-particle interactions. For example, the energisation has been associated with enhanced broad band extra low frequency (BBELF) wave power in the frequency range between 1 Hz and 1 kHz (Andre et al., 1990, 1998; Norqvist et al., 1998), as well as with electromagnetic ion cyclotron (EMIC) waves and/or lower hybrid waves (Moore et al., 1999). However, the free energy source for the wave growth and the identification of the wave modes responsible for ion heating are still open issues. High-altitude

There have been five previous major missions that have led to progress in understanding the high-altitude cusp: HEOS-1 and -2 (1969 - 1974), Hawkeye (1973 -1975), Polar (1996 - present) and Interball (1997 - 2000). All had different orbits from Cluster, and the precise orbit plays a critical role in determining which parts of the high-altitude cusp and its surroundings are sampled. The HEOS and Hawkeye spacecraft had apogees many RE outside the bow shock near to the positive GSE-Z axis, and so cut through the high-altitude cusp. Polar has an apogee of 8.9 RE , and so skims through the lower part of this region. Interball had a highly eccentric orbit with a 63° inclination, leading to the crossing of the cusp and plasma mantle regions mostly at very high magnetic latitudes.

There was recognition from the time of the HEOS mission that the cusp represented a region where magnetosheath plasma was located inside a 'nominal' magnetopause, and that the plasma flow in this region was weaker and more disordered than in the neighbouring magnetosheath (Rosenbauer et al., 1975; Paschmann et al., 1976; Haerendel, 1978; Haerendel et al., 1978). However, the lack of a solar wind monitor upstream of the Earth at these times rendered the identification of the regions and boundaries complicated. Further evidence of extensive solar wind plasma penetration through the magnetopause and into the cusp came from analysis of data from the Hawkeye (Eastman et al., 2000) and Polar (Zhou et al., 1999) missions.

The location of the magnetopause was defined by Haerendel et al. (1978) as the innermost sharp change in the magnetic field vector. Despite extensive analysis of data from the HEOS and Hawkeye spacecraft (e.g., Dunlop et al., 2000; Zhou and Russell, 1997; Eastman et al., 2000), the question of whether such a magnetopause was 'indented' has been of enduring interest. Moreover the definition of the magnetopause at the cusp is ambiguous because the region is likely to have boundaries with both the magnetosheath and magnetosphere. In this chapter a working definition of the magnetopause is the outermost magnetic boundary, usually identified as an abrupt deviation of the field direction from a magnetospheric orientation. An additional complication is that the cusp boundaries and properties are likely to be influenced by the occurrence of magnetic reconnection at the magnetopause either on the dayside or at the lobes (e.g., Lockwood and Smith, 1992; Gosling et al., 1991; Vasyliunas, 1995). In particular, the nature of the boundaries and associated plasma flows play a key role in establishing the penetration mechanisms of solar wind plasma into the cusp.

9.1.2 How Cluster investigates the cusp

Cluster is very well suited to investigate the cusp because of its comprehensive suite of instruments, and the ability of multiple spacecraft to obtain accurate measurements of the motion and structure of boundaries and waves, as well as of small-scale plasma micro-processes. The orbit is such that Cluster encounters the high-altitude cusp in the late winter and spring, and the mid-altitude cusp in the late summer and fall. Not only does Cluster sample the cusp over a large range of latitudes within a single orbit, but the inertial orbit implies that the cusp is also sampled widely in local time, hence building up a very extensive data base of cusp measurements.

The high-altitude cusp was defined as a major target of the Cluster mission. With solar wind monitors being continually available, the orbit of the spacecraft allows an investigation of the detailed structure and dynamics of this region as a function of the solar wind conditions, whose exact role is still to be established, in particular for northward IMF.

When analysing data in the different cusp regions, an important parameter is the speed of the spacecraft with respect to the speed of the cusp boundaries (Lockwood and Smith, 1994). In the high-altitude cusp the spacecraft speed is roughly 2-3 kms-1, while the speed of the boundaries can be more than 10 times larger. The spacecraft can then be considered as almost stationary with respect to motion of the cusp. At very low altitude (< 1RE ), the opposite situation arises since the spacecraft speed (a few kms-1) is much larger than the convection speed. Here the spacecraft give a snapshot of the cusp.

At mid-altitude, the spacecraft have a speed comparable to the convection and boundary speeds and therefore the observations are a mixture of spatial and temporal effects. These can be disentangled since, when the four Cluster spacecraft cross the mid-altitude cusp in their 'string-of-pearls' configuration, three spacecraft follow each other within a few minutes while the fourth arrives later (depending on the spacecraft separation). This configuration permits the investigation of spatial and temporal variations there.

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