Space Physics and Aeronomy, Ionosphere Dynamics and Applications. Группа авторов

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СКАЧАТЬ in one location exerts a magnetic tension and pressure on adjacent elements, and stress is transmitted both along and across the field lines. In equilibrium, the three terms on the RHS of equation (2.9) balance each other. If the magnetosphere‐ionosphere system is disturbed, then flows are excited to return the system to equilibrium. As discussed in the following sections, these forces are responsible for magnetospheric convection and its manifestation in the ionosphere.

2.3 STEADY‐STATE MAGNETOSPHERIC/IONOSPHERIC CONVECTION

      Maxwell stress together with pressure variations associated with plasma density and temperature are responsible for maintaining the magnetospheric shape presented in Figure 2.2a, in equilibrium with the solar wind flow and its associated ram pressure. If this equilibrium is disturbed, for instance dayside and nightside reconnection cause erosion of the magnetopause and inward collapse of the magnetotail, respectively, then large‐scale magnetospheric flows are excited to rebalance the system. As described in section 2.2.1, in a steady state this causes a continuous circulation of the magnetospheric flux and plasma, and this magnetospheric convection is coupled to the ionosphere by tension forces and gives rise to ionospheric convection. Antisunward motions of open field lines and sunward motions of closed field lines give rise to the general twin‐cell convection pattern shown in Figure 2.1. The nature of this steady‐state flow and the associated electrodynamics are discussed in the following sections.

      2.3.1 Electrostatic Potential and Magnetic Flux Transport

Magnetospheric convection coupled to the ionosphere results in a twin‐cell convection pattern, sketched schematically in Figure 2.3a. In the nonrotating rest‐frame of the Earth, these plasma motions are equivalent to an electric field given by equation (2.5). At polar latitudes, the magnetic field is roughly vertical, with a magnitude B ≈ 50,000 nT, so the electric field is roughly horizontal. The pattern of electric fields associated with the flow is shown in Figure 2.3a as blue arrows. A typical ionospheric drift speed of 500 m s⁻¹ equates to an electric field strength of 25 mV m⁻¹.

In the dipolar inner magnetosphere and the ionosphere, where the magnetic field strength is high, the magnetic pressure is such that, on timescales longer than a few seconds, the field lines cannot be compressed (magnetic pressure waves can propagate, but are of little importance for convection) and only interchange motions are possible (∇ ∙ V = 0, or the flow is incompressible). A consequence of the rigidity of the field is that , which requires from Faraday's law, equation (2.7), that the electric field distribution associated with convective motions must have the property that ∇ × E = 0. As presented schematically in Figure 2.3a, it becomes convenient to express E as the gradient of an electrostatic potential, Φ,

(2.10)

      as the curl of the gradient of a scalar field has the useful mathematical property that ∇ × ∇ Φ ≡ 0 for any Φ, satisfying ∇ × E = 0. The “zero” of Φ is chosen to be equatorward of the low latitude boundary of the convection, and Φ(A) at a position A is the integral of the electric field from the zero boundary to A:

      (2.11)

      where the value of the integral is independent of the path taken (a requirement for a conservative force that can be represented by a potential). The convection electric field is usually presented as a contour plot of the equipotentials of Φ, as for instance in Figure 2.1. The expression for E × B drift can be written

      (2.12)

      which indicates that the ionospheric flow is perpendicular to B (i.e., roughly horizontal) and perpendicular to the gradient in Φ, or in other words that equipotentials of Φ are equivalent to streamlines of the flow.

      From equation (2.5), it is apparent that E is perpendicular to B, which can be written as B ∙ E = 0 or B ∙ ∇ Φ = 0. This indicates that there is no gradient of Φ along the magnetic field direction, that is, field lines are also equipotentials of Φ. This is the same as saying that the component of the electric field parallel to the magnetic field is zero, E_‖ ≈ 0, which occurs because electrons are highly mobile along the magnetic field and can arrange themselves to nullify any field line voltage. If changes in the magnetospheric B field are assumed to be slow, the electric field distribution represented by Φ can be “mapped” upward along magnetic field lines to infer the electric field throughout the magnetosphere. In early models of convection, it was assumed that this electric field originated in the solar wind flow and mapped down along open magnetic field lines to drive E × B drift in the ionosphere (e.g., Stern, 1973; Lyons, 1985; Toffoletto & Hill, 1989). However, when temporal changes in magnetosphere/ionosphere convection are considered, and induced electric fields become important, it is clear that this view is too simplistic. Instead, the physics of stress balance, outlined above, comes to the fore (e.g., Parker, 1996; Vasyliunas, 2005).

      The potential difference (or voltage) between two positions A and B in the convection pattern (in the ionosphere or anywhere in the magnetosphere) is

      (2.13)

      This is a measure of the amount of magnetic flux frozen into the flowing plasma that is carried across any path between A and B in unit time, that is ∆Φ represents the rate of transport of magnetic flux in the convection. The “cross‐polar cap potential” (CPCP) or “transpolar voltage,” usually written Φ_PC, is defined as the voltage between the dawn and dusk sides of the polar cap, a measure of the antisunward magnetic flux transport in the Dungey cycle. If the polar cap is 2,000 km across and the antisunward flow speed is 500 km s⁻¹ (an electric field of 25 mV m⁻¹), then Φ_PC is 50 kV.

      2.3.2 Convection, Corotation, and Dawn‐Dusk Asymmetries

The twin‐cell convection pattern does not extend to the equator but is confined to high latitudes, which can be understood by considering the competition between the reconnection‐driven Dungey cycle and “corotation” (that is, rotation with the planet), as described by Wolf (1970) and Volland (1973). The magnetospheric ends of the field lines move under the influence of the Dungey cycle flow discussed СКАЧАТЬ