Abstract: The Earth's plasmasphere is dynamical influenced by magnetospheric and ionospheric electric fields. To first order, it comprises the region where closed corotating field lines contain trapped plasma. Studies have shown that plasmasphere is highly variable both spatially and temporally, responding to changes in geomagnetic indices, ring current, penetration and shielding electric fields, and subauroral electric fields. Consequently the plasmasphere exhibits erosion, emptying, and refilling during active times, along with a high level of structure. Plasmasphere modeling has improved with better understanding of these electric fields, but more work remains, notably with regard to subauroral electric fields. The plasmasphere has important influences on space weather, as illustrated by interactions with the radiation belts and ionosphere.

Introduction

The plasmasphere demonstrates influences of both the magnetosphere and ionosphere, making it an interesting topic in this system. This review of the plasmasphere will begin by defining it and giving a brief historical comment. A summary of relevant aspects of the magnetosphere and ionosphere follows. This provides context first for a description of the steady state plasmasphere, as influenced by magnetospheric electrodynamics, followed by discussion of how variations in such electrodynamics give rise to broad variations in the plasmasphere. Some findings regarding smaller-scale plasmasphere structure as influenced by electric fields are summarized, then mention of signatures of the plasmasphere in the radiation belts and the ionosphere. Finally, some pending questions are identified.

The plasmasphere is a torus of plasma in the innermost region of the magnetosphere, comprising the corotating region of the magnetosphere. Magnetic field lines there are closed and approximately dipolar, permitting filling of the plasmasphere by plasma escaping from the Earth's ionosphere. Plasmasphere plasma is mostly H⁺ at high densities (10 to 10³ cm^-3) and low temperatures (1 eV) relative to the rest of the magnetosphere. The outer limit of the plasmasphere is the plasmapause, the outer boundary of the region of cold dense plasma. During quiet steady state conditions, this tends to correspond to the corotation region. During active times, however, this boundary is dynamic and highly structured.

The plasmasphere was independently identified by in situ plasma measurements and ground-based whistler observations in the early 1960s. Gringauz (1963) used plasma observations from the Lunik Moon probes to identify a steep density gradient corresponding to the outer edge of the plasmasphere. Carpenter (1963) used observations of whistlers, radio waves propagating along geomagnetic field lines, to identify this same density gradient (figure 1a). Later in the 1960s the basic theoretical picture emerged with the plasmasphere as the magnetosphere region where corotation dominates over the cross-tail electric field. Observations from a variety of satellites have since helped identify it as quite dynamic, with the plasmapause contracting Earthward during geomagnetic storms. In 2000 the IMAGE satellite began providing direct imagery of the plasmasphere from outside. An illustrative observation is shown in figure 1b, which shows a variety of plasmaspheric structures.

Fig. 1. Illustrative plasmasphere observations. a) Early plasmasphere density observations by Carpenter and Gringauz. Solid line shows density vs. location as derived from whistler observations, as opposed to the expected gradient (dashed line). Points indicate Lunik density measurements. (from Lemaire and Gringauz, 1998). b) Illustrative IMAGE EUV (30.4 nm) observation of plasmasphere, taken 24 May 2000 from 6.0 R_E and MLAT=73°. (from Sandel et al., 2003).

Overview of magnetosphere and ionosphere

Magnetosphere. The magnetosphere (figure 2) results from the interaction of the Earth's magnetic field and plasma environment with the solar wind and interplanetary magnetic field (IMF). The terrestrial magnetic field is approximately a dipolar field with its axis inclined 10° to the Earth's rotation axis. Interaction with the solar wind and IMF compresses the geomagnetic field on the sunward side and produces an extended antisunward magnetotail; the magnetopause separates the enclosed geomagnetic cavity from the IMF. Solar wind plasma encounters the magnetopause, with differing gyromotions depending on particle charge, resulting in the magnetopause current around the sides of the magnetosphere. This magnetopause boundary region is also called the magnetosheath.

Fig. 2. Magnetosphere structure and current systems; see text for discussion (from Hargreaves, 1992).

The motion of the solar wind past the geomagnetic cavity produces a cross tail electric field and a sunward convection of plasma up the tail. The cross tail electric field is essentially an E=vxB field, with solar wind velocity v past the magnetic field B at the magnetopause. Sunward convection is understood to result both from viscous interaction between magnetosphere plasma and the solar wind at the magnetopause and from the effects of linkage between the IMF and geomagnetic fields. The resulting sunward moving plasmasheet is thin in the vertical direction, corresponding to the sharp gradient between sunward and antisunward magnetic field lines dragged from the geomagnetic field. Plasma particles undergo both gradient drift and curvature as they approach the Earth, causing drift of ions westward and electrons eastward around the Earth. The result is the ring current, directed westward around the Earth. Ring current intensity is highly dependent on geomagnetic activity and is indirectly measurable by ground-based magnetometers, contributing to the Dst index. Another phenomena where the plasmasheet approaches the Earth is formation of polarization electric fields which tend to "shield" the inner magnetosphere from the external electric fields. These shielding electric fields respond to changing solar wind/IMF conditions on a timescale of minutes. Because of this delay, overshielding or undershielding can result during active periods; such imbalances are called penetration electric fields.

Near the geomagnetic poles, magnetic field lines connect to the magnetopause and thence to the IMF. At the Earth this region of open field lines is called the polar cap; it is surrounded by the auroral oval, where field lines are stretched through the tail plasmasheet or through the magnetosheath. Energetic particles from these sources are guided along magnetic field lines until they collide with particles in the Earth's atmosphere, resulting in the aurorae themselves.

The radiation belts are located near the Earth where the geomagnetic field is approximately dipolar. These belts comprise charged particles trapped in the field, with gyro motion around the field lines and mirroring between points at lower altitudes. Such particles are lost when scattered such that their mirror point is low enough for collisions within the atmosphere.

Ionosphere. The ionosphere is the region of the Earth's atmosphere partially ionized by solar radiation. This plasma density as a function of altitude tends to peak as described by the Chapman function, with density limited at higher altitudes by fewer neutrals available for photoionization and at lower altitudes by reduced penetration of ionizing photons. The actual structure includes the F-region (peak about 300 km) and E-region (lesser peak about 100 km) and varies with available solar radiation, latitude, and photochemistry. Dominant ion species range from O⁺ and molecular ions at lower altitudes to He⁺ and H⁺ at higher altitudes (of order 800 km to 1500 km). The ionosphere is a conductive medium linked to the magnetosphere, with consequent interaction. Region 2 field aligned currents (FAC), closed through the auroral zone, and region 1 FAC, closed through the polar cap boundary, link to magnetosphere currents including the ring current and magnetosheath current.

Steady state models of plasmasphere

Convection-corotation model. To first order, the plasmasphere is the region in the inner magnetosphere where the corotation electric field dominates over the cross tail electric field. The cross tail electric field, directed from dawn to dusk, tends to produce equipotentials parallel to the Sun-Earth axis. The geomagnetic field, rotating with the Earth, produces a vxB electric field about the Earth. The outer boundary of the plasmasphere, the plasmapause, is approximately where these two fields are equal, i.e. near an L value such that

E_T = (B₀/L³) L R_E ω

Fig. 3. Magnetospheric plasma convection in the tail and plasmasphere (from Hargreaves, 1992).

Magnetic field lines in the plasmasphere are closed and nearly dipolar. The toroidal surface of the plasmasphere intersects the Earth's surface at high latitudes (for L=4, MLAT=60°), roughly corresponding to the equatorward boundary of the auroral zone. Beyond the plasmasphere, magnetic field lines are drawn westward and stretched down the magnetotail on the nightside. The closed magnetic flux tubes within the plasmasphere fill with escaping ionospheric plasma on a timescale of days. This is mostly H⁺ and understood to be of ionospheric origin. Typical densities are of order 10-10³ cm^-3 and energies ~1 eV. In contrast, outside the plasmasphere densities are in the range 0.1-10 cm^-3 and temperatures greater; this plasma is believed to be solar wind material that crossed the magnetopause and was convected toward the Earth. Sample observations of plasmasphere density versus geocentric distance, based on whistler observations, are shown in figure 4 (whistlers are briefly explained in the appendix).

Fig. 4. Electron density in the equatorial plane based on whistler observations, showing the plasmapause location near 4 R_E (from Lemaire and Gringauz, 1998).

Stern-Volland model. An early modification to the simple convection-corotation is the Stern-Volland model (Volland, 1973; Stern, 1975), which includes a semi-empirical shielding effect. Previously mentioning shielding electric fields result from polarization in the plasmasheet as it approaches the Earth, tending to shield the inner magnetosphere from the convection electric field. The previously discussed convection-corotation model gives a potential

Φ = -E_T y - B₀ ω R_E³/r,

Φ = -A₀ y r - B₀ ω R_E³/r = -A₀ r^γ sin Θ - B₀ ω R_E³/r

Plasmasphere dynamics associated with convection

Stormtime changes. Even in the 1960s, study of the plasmasphere showed dynamic behavior in response to solar activity and geomagnetic conditions. The basic convection-corotation model suggests a teardrop shape that will change in size with changes solar/geomagnetic activity. These changes are observed along with additional storm-related dynamics and structure.

During periods of high solar/geomagnetic activity, the region of closed field lines is compressed closer to the Earth. At such times the plasmapause may be at L=2, compared to L=4-6 in typical conditions. When considered relative to K_p index, the response in plasmapause location is delayed on the order of hours. Carpenter and Park (1973) found an empirical relation for the plasmapause location

L_pp = 5.7 - 0.47 K_p,

L_pp = 5.9 - 0.43 K_p,

The delayed response of plasmapause location to these indices is partly explainable in terms of erosion and refilling processes. Consider the quiet time plasmasphere, filled with plasma out to the last closed flux tubes. With the onset of a geomagnetic storm, the convection electric field strengthens and the formerly closed field lines in the outer plasmasphere become open, connected to the magnetopause. This permits depletion of plasma from these flux tubes, to be lost through the magnetopause, (although Carpenter and Lemaire (1997) note that a significant fraction of eroded plasma may remain within the outer magnetosphere for some time). Until this erosion is complete, the plasmapause (in terms of density gradient) is outside the corotation limit. When activity drops and the field lines return to the previous state, these closed flux tubes refill with plasma only after a time delay of order hours to days. During refilling, the plasmapause (in terms of density gradient) is inward of the corotation limit. Horwitz et al. (1986) report observations of two density knees during refilling, with a second plasmapause inward of the main (outer) plasmapause. Thus, description of the plasmasphere must consider the recent history of the magnetosphere as well as structure in the magnetosphere.

Dent et al. (2006) studied plasmasphere depletion and refilling using data from both IMAGE and from ground-based magnetometers. (The IMAGE satellite is described in the next section.) They found the history of local conditions to be important. Depletion took 1-2 days and 3-4 days for two observed depletion episodes, and there were suggestions that refilling took place in two stages, with the rate of refilling increasing significantly on the third day. They also observed limited emptying effects from short intervals of enhanced convection.

Dayside bulge. The simple model of plasmapause shape driven by combined corotation and convection electric fields suggests a teardrop shape with a duskside bulge. The duskside bulge is indeed observed, but the bulge exhibits more dynamical behavior than this model would imply and is understood as related to additional phenomena. Chappell et al. (1971a) found structure including regions of dense plasma on the dayside apparently detached from the main plasmasphere (these may relate to drainage plumes since identified by IMAGE observations). Similarly, the bulge was also found to be disconnected. Moldwin et al. (1994) characterized bulge dynamics using observations from several geosynchronous satellites. With circular equatorial orbits at 6.62 R_E, such satellites often encounter the plasmapause duskside bulge. As shown in figure 5, while the bulge was usually centered in the duskside, the location varied significantly, and varied most significantly for quiet time conditions.

Fig. 5. Location of center of plasmasphere bulge vs. K_p index, based on crossing observations by geosynchronous satellites. From Moldwin et al. (1994).

Plasmasphere dynamics at smaller scales

IMAGE. Launch of IMAGE considerably advanced observations of plasmasphere dynamics and revealed new degrees of structure. The IMAGE satellite was launched in March 2000 into a polar orbit ranging (currently) from 1400 km altitude to 45400 km, or 8 R_E. Of its instruments, the EUV imagers have been of particular interest. The three EUV imagers, with overlapping fields of view, are sensitive to the 30.4 nm line scattered by He⁺ (Sandel et al., 2000). Since the plasmasphere is about 5-10% He⁺, this permits direct imaging of the plasmasphere when IMAGE is near apogee. Using such images when apogee occurs well above/below the equatorial plane, the images may be reprojected into the plane of the magnetic equator and the plasmapause extracted. These observations revealed previously unknown levels of structure in the plasmasphere, including shoulders, notches, plumes, and crenulations (figure 6).

Fig. 6. Sequence of IMAGE EUV images from 9-11 April 2001 showing plasmasphere structure. Sunward is towards the bottom. The brightest feature is atmospheric airglow. The plasmasphere is visible by light scattered from He⁺, with the Earth's shadow in the plasmasphere apparent. An auroral oval is clear in the last image. From Sandel et al., IMAGE EUV web site (2006).

Notches. Notches are deep radial evacuated features in the outer plasmasphere boundary. These features may extend over 2 R_E in radial distance and 3 hours in MLT in the magnetic equatorial plane. Some notches develop a dense inner plasma plume, producing a W- or M-shaped feature (Gallagher et al., 2005); this is common for larger notches (Sandel et al., 2003). While irregularities in the plasmasphere radius of order 1 R_E were known by the early 1970s (Carpenter and Park, 1973), only with IMAGE could they be properly characterized.

The long lifetime of some notches (up to 60 hours) observed by IMAGE revealed sub-corotation of these features: Sandel et al. (2003) report that notches were observed to rotate at an average rate of 88% of corotation; Gallagher et al. (2005) found an average of 90% of corotation with a range from 44% to near 100% of corotation. The rotation rate of individual notches may vary during their lifetimes. This sub-corotation has been explained by Burch et al. (2004) as a result of corotation lag in the upper ionosphere. They correlated IMAGE observations of notches to DMSP observations of ionospheric drifts, i.e. to sub-corotation in the ionosphere. The lag in the upper ionosphere is, they conclude, a result of the disturbance dynamo. During storm times, the auroral ionosphere is heated by particle precipitation and joule heating. The heating produces equatorward winds which are deflected westward by the Coriolis force, producing a lag behind the Earth's rotation in these regions.

Shoulders. Plasmaspheric shoulders are abrupt changes in the radial location of the plasmapause with respect to MLT; an example is shown in figure 1b. Pierrard and Lemaire (2004) modeled shoulder formation based on temporal changes in the convection electric field, specifically, with a decrease in K_p leading to outward expansion of the plasmapause in the post-midnight sector. Pierrard and Cabrera (2005), comparing simulations to IMAGE observations, find that shoulder formation precedes a sharp decrease in K_p by one or two hours. Goldstein et al. (2002) examined one observed feature and suggested that it resulted from northward turning of the IMF. Two observed sudden northward turnings would result in an overshielding electric field, where shielding of the inner magnetosphere suffers delayed response to the change in the convective field. This overshielding electric field would oppose the cross tail field and produce antisunward convection; their simulations indicated a resulting plasma eddy contributing to formation of a bulge where the shoulder was observed.

Plumes. Plasmasphere erosion and refilling during episodes of changing convection were described in the previous section. IMAGE has permitted observation of details of this process, including the evolution of drainage plumes. These tend to be observed in the noon-to-dusk sector during periods of erosion. Figure 7 shows a sequence of observations showing the pre-erosion plasmasphere, a sunward convection surge of plasma following contraction of the corotation region, and the evolution of a sunward plasma plume. The process, to first order, is consistent with the picture of plasmasphere response to changing convection electric field (Li and Xu, 2005). Goldstein and Sandel (2005) interpreted the large-scale behavior in the event shown in figure 7 as the result of dayside magnetopause reconnection (DMR) during southward IMF; this reconnection drives magnetospheric convection changes with results for the plasmasphere. However, they note some differences between their model and observations, probably associated with subauroral and penetration electric fields. Plumes such as these have been observed to wrap around the plasmasphere, as the plume base rotates with the plasmasphere, resulting in channels (Sandel et al., 2003). This may partly explain older observations of "detached" plasmas on the dayside Chappell et al. (1971a).

Fig. 7. Sequence of IMAGE observations on 18 June 2001 showing plasmasphere erosion and plume formation. From Goldstein (2004).

Electric fields. Several studies have shown that subauroral electric fields must be considered in accounting for plasmasphere dynamics. Subauroral polarization streams (SAPS) refer to zones of westward ion flows equatorward of the auroral boundary in the nightside. SAPS result from differences in the electron and ion precipitation from the plasmasheet, mapped to the ionosphere along field lines; due to the low conductivity equatorward of the auroral region this results in polarization electric fields, driving eastward ion flows. Less frequent are latitudinally narrow (1-3°) regions of fast ion drift (over 1000 m/s) in the pre-midnight region; these are called subauroral ion drifts (SAID) (or polarization jets). These particular enhancements result from recombination chemical reactions which locally deplete ion density, leading to larger polarization electric fields and larger ion drifts (Anderson et al., 1993). Both phenomena are associated with substorms. SAPS and SAID sufficiently influence plasmasphere structure that they must be taken into account. Carpenter and Lemaire (1997) note that plasma regions poleward of SAID channels could become effectively detached from the plasmasphere. Anderson (2004) used DMSP observations to determine cross-polar-cap and subauroral potential drops, finding subauroral potential drops exceeding 60 kV at times during the observed April 2002 storms. Since more quantitative descriptions of subauroral electric fields are needed to improve plasmasphere modeling, such DMSP-based analyses are a useful tool.

Goldstein et al. (2003) modeled the plasmapause location accounting for inner magnetosphere electric fields with and without an empirical SAPS model, simulating a substorm event on 2 June 2001. Model results were compared to the observed plasmapause location, derived from IMAGE EUV observations. The inclusion of the simple SAPS model significantly improved matching between model and observations. Specifically, this fixed discrepancy on the duskside, where plume formation was poorly simulated without the SAPS model. This empirical approach was subsequently generalized by Goldstein et al. (2005a) and Goldstein et al. (2005c), the former considering 13 events and the latter concentrating on 22-23 April 2001, shown in figure 8. The effect of SAPS on the plasmapause is to move it inward, cause smoothing across MLT, and sometimes to produce narrow duskside plumes. The indentation in figure 8b is the result of overshielding and consequent sunward flow in the postmidnight sector. The shoulder formation in figure 8j is also a result of overshielding; the model failed to reproduce this, corresponding to the incorrect temporal behavior of the empirical model. The authors note that improved modeling of SAPS is needed to better reproduce plasmasphere dynamics.

Fig. 8. Observed plasmapause location from IMAGE (black dots) and modeled location by Goldstein et al. (2005c) (colored curves), including effects of DMR and SAPS. Grey curves indicate regions of ion density exceeding 10 cm^-3 at geosynchronous orbit. Right is sunward.

Other structure. Other expressions of structure in the outer plasmasphere also relate to electric fields. Moldwin et al. (1995) describe, at geosynchronous orbit (L~6.62) interspersed regions of cold dense plasma characteristic of the plasmasphere with plasma at lower densities and warmer temperatures (2-10 eV), with scale sizes of order 1000 km or less. They associate these structures with penetrating substorm electric fields. Complexities in density and temperatures near the plasmapause are well known. Instead of the typical steep gradient at the plasmapause, a gradual density decrease or more complex behavior may occur (Horwitz et al., 1990). Composition and temperature variations have been observed for the plasmasphere. Unusual enhancements in heavy ion densities near L=3-4 were observed by DE-2 (Chappell, 1982). Other observations indicate a warm ion component near the plasmapause (Lemaire and Gringauz, 1998). Heating in part results from overlap of the ring current and the outer plasmasphere (Gurgiolo et al., 2005). Carpenter and Lemaire (2004) propose the term plasmasphere boundary layer (PBL) to describe the plasmapause region, given that there is a transition between the plasmasphere and the magnetosphere beyond.

Plasmasphere signatures in radiation belts and ionosphere

Radiation belts. The plasmasphere extent bears some relation to the radiation belts. The energetic electron belts include an inner belt near L=1.5-2 and an outer belt around L=3-8. The low radiation "slot" region in between exists in part because whistler-mode waves act to scatter trapped particles into the loss cone, allowing collisional loss in the Earth's atmosphere. Goldstein et al. (2005b) used IMAGE EUV data during early 2001 along with SAMPEX energetic particle observations and found that the inner edge of the radiation belt corresponded well with a 3.5-day running average of the plasmapause location. Baker et al. (2004) examined the late October 2003 geomagnetic storm, during which the plasmapause contracted to L=1.5. Correspondingly, the outer radiation belt was also displaced inward into the slot region. Summers et al. (1998) found that enhanced electromagnetic ion cyclotron (EMIC) waves within the plasmasphere tend to scatter trapped electrons into the loss cone, depleting radiation belt particles inside the plasmapause. In contrast, outside the plasmapause whistler-mode waves tend to energize trapped electrons. Regions associated with these waves are shown in figure 9. Consequently, the evolution of the plasmasphere during active times can significantly affect the outer radiation belt.

Fig. 9. Relationship of plasmasphere to relativistic electron drifts. See text for explanation. From Summers et al. (1998).

Ionospheric signatures. Many ionospheric signatures of the plasmapause have been proposed. In general, these links are not one-to-one correspondences and suffer from limitations in simultaneous measurements in the ionosphere and plasmasphere. Rycroft and Burnell (1970) used Alouette satellite observations to link the midlatitude electron density trough with the plasmapause. The correspondence has also been observed with whistler data (Foster et al., 1978). However, with higher K_p index this trough occurs at lower latitudes than the plasmapause (Kohnlein and Raitt, 1977). Yizengaw et al. (2005) found a good correlation with TEC using GPS data. The subauroral electron temperature enhancement (SETE), which is a latitudinally narrow peak in ionospheric topside electron temperature, was found to coincide with the plasmapause by Brace and Theis (1974) in ISIS-1 data and by Horwitz et al. (1986) in DE-1/DE-2 data. The precipitating electron boundary is also a suggested signature (Foster et al., 1978). Stable auroral red arcs, auroral arcs near 400 km altitude with 630 nm oxygen line emissions, have been found to correspond with the plasmapause (e.g. Chappell et al., 1971b). A good correspondence (although still not one-to-one) is suggested for the light ion trough, or the steep latitudinal gradient in H⁺/He⁺ density observed near the equatorial edge of the auroral zone (Taylor and Walsh, 1972). Limitations in this correspondence include variations of the thermal plasma density gradient invariant latitude with altitude, possibly resulting from coupling dynamics (Foster et al., 1978).

These plasmapause ionospheric signatures are expressions of magnetosphere-ionosphere interactions. Understanding of these signatures and their limitations has a practical application in permitting the use of data obtained by ionospheric satellites, which offers greater coverage than satellites in the plasmasphere alone. As an example, figure 10 shows initial efforts to map the ionospheric light ion trough observed by DMSP satellites to a corresponding equatorial plasmapause location. Here, the light ion trough is mapped along magnetic field lines as modeled by the Tsyganenko magnetosphere field model (Tsyganenko and Sitnov, 2005) to where those field lines cross the equatorial plane, corresponding to mapping of the IMAGE data.

Fig. 10. Mapping of DMSP-observed ionospheric signatures to equatorial plasmapause. Reprojected IMAGE observations from 18 June 2001 are shown, with red traces showing DMSP F13 and F15 orbit tracks mapped to the equatorial plane. Red crosses show the DMSP-observed light ion trough (from Anderson et al., 2005).

Conclusion

Plasmasphere studies have advanced notably in the last decade, with reasons for this including the wealth of information made available by IMAGE observations and the improved capabilities of numerical models. Three pending topics in plasmaspheric studies are identified by Ganguli et al. (2000): dynamics during geomagnetic storms, refilling following storms, and plasmasphere-ionosphere coupling. Coupling to the ionosphere is emerging as a limiting issue in modeling; better understanding of this coupling will benefit modeling as well as improve understanding of storm dynamics. Subauroral electric fields in particular need to be better described and modeled. Understanding of the plasmasphere is important from a space weather standpoint.

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Appendix. Whistlers

VLF signals from sources such as lightning tend to propagate in the direction of the geomagnetic field and can thus travel from one hemisphere to the other and possibly return after reflection. The resultant signals display a travel time-frequency relation and are called whistlers. The travel time t is a function of electron density and signal frequency f along the propagation path:

Figure A1 below illustrates interpretation of whistler data. The top graph shows time-frequency curves for individual whistlers. The minimum in time from each curve is plotted in the middle graph, showing a discontinuity corresponding to a sharp density gradient. Resulting calculations of density versus geocentric distance are shown in the last graph, indicating plasmapause location near 3.3 R_E in this case.

Fig. A1. Schematic of whistler observations and derived density results. See text for explanation. From Lemaire and Gringauz (1998).

© 2006 by Wm. Robert Johnston.
Last modified 17 September 2006.
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