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UPPER-ATMOSPHERE ELECTRIC-FIELD SOURCES 197 fields tend to be imposed on the plasma as a result of the dynamo processes to be discussed, the plasma quickly is set into motion at the velocity given by Eq. (14.4). A further important consequence of the MHD approximation, when combined with the Faraday law of magnetic induction, is the following: all plasma particles lying along a common magnetic-field line at one instant of time will forever remain on a common field line. The magnetic field may vary both temporally and spatially, and the plasma may move from one region of space to another, but plasma ions and electrons will continue to share a field line with the same partners. This result affects both the magnetic-field configuration and the plasma velocity. In the solar wind, the magnetic field is distorted to follow the motions of the plasma. Nearer the Earth, where the magnetic field is so strong that it is not easily distorted, the constraint means that all particles on a dipolar field line must move simultaneously together to another field line. convection of plasma thus can be mapped between the outer magnetosphere and the ionosphere along magnetic-field lines. The electric field similarly maps along the magnetic field. The MHD approximation is useful in interrelating plasma motions with electric and magnetic fields, but it breaks down under a number of important circumstances, especially where electric current densities are large. Furthermore, the approximation does not explain the distribution of currents, which are a central element in the processes giving rise to upper-atmospheric electric fields. Current flow across magnetic-field lines exerts a force on the medium, a force that must either be balanced by other forces, like pressure gradients, or else result in acceleration of the medium. Consideration of force and momentum balance thus is an important part of understanding currents in plasmas. One place where the MHD approximation breaks down is in the lower ionosphere, below 150 km, where collisions between ions and the much more numerous air molecules are sufficiently frequent to prevent the ions from maintaining the velocity given by Eq. (14.4). In this region electric current readily flows across magnetic-field lines. As we shall see, neutral-air winds in the lower ionosphere lead to generation of electric currents and fields, and for this reason the height range of roughly 90-150 km is called the "dynamo region" of the ionosphere. Unlike the outer magnetosphere, the ionosphere behaves as an Ohmic medium, with the current density linearly related to the electric field under most circumstances. The conductivity, however, is highly anisotropic owing to the presence of the geomagnetic field. The conductivity in the direction of the magnetic field is very large, so that the electric-field component in this direction is almost entirely shorted out, and magneticfield lines are nearly electric equipotential lines at all altitudes above 90 km. The conductivity characteristics perpendicular to the magnetic field depend on the rate of ion-neutral collisions, and they change with altitude as the neutral density varies. Figure 14.2 shows typical mid-latitude conductivity profiles for day and night conditions. In the nighttime auroral oval the conductivity is more akin to the "Day" profile in Figure 14.2 than to the "Night" profile because of ionization production associated with the aurora. Although the ionospheric plasma density typically maximizes at around 300 km altitude, the conductivity perpendicular to the magnetic field maximizes at around 110 km, with a large day-night difference owing to the day-night difference in ionospheric density. The current component perpendicular to the magnetic field flows in a direction as much as 88Â° different from the electric-field direction, as also shown in Figure 14.2. This effect results from the fact that electrons are relatively little influenced by collisions above 80 km and move perpendicular to the electric field as given by Eq. (14.4), while positive ions are strongly affected by collisions below 130 km and are unable to cancel current carried by the drifting electrons. SOLAR WIND/MAGNETOSPHERE DYNAMO In an analogy with a dynamo-electric machine that generates electricity by rotating a conducting armature through a magnetic field, the motion of a plasma through a magnetic field produces an electromotive Figure 14.2 Typical profiles of the ionospheric conductivity component perpendicular to the geomagnetic field for day and night conditions (left) and angle between the current and electric-field components perpendicular to the geomagnetic field (right).
UPPER-ATMOSPHERE ELECTRIC-FIELD SOURCES 198 force and current flow and can also be considered a dynamo. The solar wind/magnetosphere dynamo results from the flow of the solar wind around and partly into the magnetosphere, setting up plasma motion in the magnetosphere as well an electric field and currents (e.g., Stern, 1977; Hill, 1979; Roederer, 1979; Cowley, 1982). All details of this process are not yet understood, but a number of features have become clear. Strong evidence exists that the magnetosphere is partly open, that is, that some magnetic-field lines traced from the Earth extend indefinitely into interplanetary space (Hill and Wolf, 1977; Stern, 1977; Lyons and Williams, 1984). The amount of magnetic flux that connects to the interplanetary magnetic field may be as great as the entire flux passing through the polar caps. Figure 14.3 shows a schematic figure of the magnetic-field configuration for the simple case where the IMF is directed southward. If the IMF had an east-west component, as it usually does, we would require a three-dimensional representation of the magnetic-field interconnection. Details of the magnetic-field configuration are not yet resolved, so Figure 14.3 should be treated more as a conceptual tool than as a true representation of the magnetosphere. The essential features are the four classes of magnetic-field lines denoted in Figure 14.3: (1) closed field lines connected to the Earth in both northern and southern hemispheres; (2) interplanetary field lines unconnected to the Earth; (3) open field lines connecting the northern polar cap to interplanetary space; and (4) open field lines connecting the southern polar cap to interplanetary space. The interplanetary electric field, obtained from Eq. (14.3), is directed out of the page in Figure 14.3. To the extent that the MHD approximation is valid and electric fields map along the magnetic field, the polar ionosphere is also subject to an electric field out of the page, Figure 14.3 Schematic diagram of magnetic field and plasma flow in the solar wind/magnetosphere environment (from Lyons and Williams, 1984). Continuous lines show the magnetic field for the case where the IMF is purely southward. Open arrows show the plasma velocity direction. Numbers 1-4 denote magnetic regions of different topology, as discussed in the text. causing ionospheric plasma to convect antisunward. The magnitude of the ionospheric electric field is greater than that of the interplanetary electric field because the bundling of magnetic-field lines at the ionosphere causes electric potential gradients to intensify. On the other hand, the plasma drift velocity in the upper ionosphere, given by Eq. (14.4), is much less than the solarwind velocity because of the inverse dependence on magnetic-field strength. the polar-cap electric field is typically 20 mV/m, giving an ionospheric convection velocity of roughly 300 m/sec. Other directions of the IMF than shown in Figure 14.3 result in a somewhat altered pattern of polar-cap ionospheric convection, but a usual feature is the general antisunward flow. More about IMF influence on the high-latitude electric field is discussed in a later section. The physical processes that determine the amount of magnetic flux that interconnects the geomagnetic field and the IMF are not well understood and are the subject of much study (e.g., Cowley, 1982). They clearly involve a violation of the MHD approximation since the ionospheric and solar-wind plasmas coexisting on an open magnetic- field line at one instant of time could not have lain on a common magnetic-field line throughout their entire histories. The violations of this approximation occur to some extent throughout the magnetosphere but are particularly important in at least two regions: at the sunward magnetopause and somewhere in the magnetospheric tail. At the sunward magnetopause plasma flows together through unconnected interplanetary and magnetospheric magnetic fields and flows out northward and southward on interconnected magnetic-fields lines (Figure 14.3). In the tail plasma flows together on interconnected field lines and flows out through unconnected magnetospheric and interplanetary magnetic fields. In the closed portion of the magnetosphere plasma flows generally toward the Sun, passing around the Earth on the morning and evening sides (out of the plane of Figure 14.3). However, some of the outermost portions of the closed-field region convect away from the Sun because of momentum transfer from the nearby solar wind (e.g., Hones, 1983). Magnetospheric plasma convection has a number of important consequences, one of which is the energization of plasma and particle precipitation into the ionosphere. As plasma flows from the tail toward the Earth it is compressionally heated because the volume occupied by plasma on neighboring magnetic-field lines is reduced as the magnetic-field strength increases and as the length of field lines decreases. Other particle acceleration processes also help to energize the plasma. Some of the energized particles precipitate into the ionosphere and create ionization enhancements, especially in the auroral oval. The energized plasma also has an impor