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

Figure 2.3 (a) The relationship between ionospheric flow, electric field, and electrostatic potential. The magnetic field points everywhere into the page. The green circle represents the low‐latitude boundary of the ionospheric convection, also the zero potential contour. Red arrows indicate directions of ionospheric flow, with the associated electric field distribution shown in blue. The potential Φ at a point A or B is determined by integrating −E ∙ dl from a point of zero potential along any path (e.g., purple line) to that location. Contours of potential (or equipotentials) are shown by the black curves, at potential steps of 10 kV. The voltage between two points A and B is the integral of −E ∙ dl between them, also given by Φ_B − Φ_A. The red dashed line shows the polar cap boundary. (b) The association of ionospheric current systems and FACs with the convection pattern

      (from Milan et al., 2017; Reproduced with permission of Springer Nature).

The ionosphere is a magnetized plasma, comprising free charge carriers suffused by the Earth's dipolar magnetic field. Hence, electric and magnetic forces play an important role in determining the dynamics and structure of the ionosphere and its interaction with the magnetosphere and solar wind. The next section introduces the basic plasma physics necessary to understand the magnetosphere‐ionosphere coupled system.

      2.2.2 Plasma Physics in the Magnetosphere‐Ionosphere System

      A charged particle of mass m and charge q moving with velocity v in the presence of an electric field E and magnetic field B, experiences the Lorentz force

      (2.1)

      such that the momentum equation for individual ions and electrons is

(2.2)

      where we consider singly charged positive ions for simplicity (mainly protons in the magnetosphere and heavier ions such as O⁺ and O₂ ⁺ in the ionosphere), we have used q = e and q = − e for ions and electrons, and the last terms on the RHS represent momentum loss due to collisions with a background of uncharged particles, such as the atmosphere, with collision rates (frequencies) ν_i and ν_e. We assume initially that ν_i = ν_e = 0.

In a situation with no electric field, E = 0, and uniform magnetic field B, the momentum equations can be solved to show that the magnetic force causes particles to move in a circle in a plane perpendicular to B (Fig. 2.4a), of radius r_g with angular frequency Ω, where

      (2.3)

the gyration being in a right‐handed sense about the field direction if q < 0 and left‐handed if q > 0. In a given field strength B, the gyroradius depends on the speed of the particle perpendicular to the magnetic field, v_⊥, such that the gyrofrequency is the same for all particles of a particular species (that is, with a given charge to mass ratio ). Hotter plasma (a larger range of v_⊥) will tend to have larger gyroradii. In a uniform magnetic field, the particles experience no force along the magnetic field direction, their initial parallel speed v_‖ is unchanged, and, in general, they are highly mobile along magnetic field lines. Each particle forms a current loop, but in a uniform plasma, the currents of adjacent particles cancel out. However, where there are gradients in plasma density or temperature (and hence pressure), a net magnetization current can flow. If the magnetic field has a gradient along its length, as shown in Figure 2.4d, then qv × B has a component that modifies v_‖ and expels particles from high‐field regions. In this way, particles are kept away from the Earth by this “mirror force” (see converging B regions near the Earth in Fig. 2.2) and tend to be trapped within the magnetosphere. Gradients in field strength perpendicular to B, such as in the Earth's inner dipole, lead to variations in gyroradius that cause charge‐dependent “gradient drift” and hence an electric current to flow (Fig. 2.4e). Gradient drift is enhanced by the curvature of the dipole field. This combined “gradient‐curvature drift” is significant for hot plasma with large gyroradii and rapid field‐parallel motions.

Figure 2.4 Schematic of (a) gyrating particles, (b) E × B drifting particles, (c) E × B drifting particles in the presence of neutrals, (d) particles mirroring in a high field region, and (e) a gradient in B producing charge‐dependent drift.

      If the magnetic field is uniform, and an electric field is introduced (Fig. 2.4b), charged particles initially at rest are accelerated by the electric force, caused to deviate by the magnetic force, and then are decelerated by the electric force, performing a half gyration before coming to a rest again. The cycle repeats, and the particles follow cycloid trajectories with an average bulk drift in the E × B direction with a speed E/B E/B, that is a velocity

      (2.4) (2.4)

      An observer moving with the plasma would just see circular gyrations (as in Fig. 2.4a), the trajectories that are expected in the presence of a magnetic field but no electric field. This demonstrates that the electric field is dependent on one's frame of reference, a consequence of the theory of special relativity, and in a frame in which a magnetized plasma is drifting with velocity V, a motional electric field E exists, where

(2.5)

The above discussion is appropriate for the magnetosphere and F region ionosphere, where collisions can be discounted. Figure 2.4c shows how Figure 2.4b must be modified in the E and D region ionosphere where a dense background of neutrals exists, such that the collisional terms of equation (2.2) become significant. As the particles E × B drift, they are occasionally brought to a rest by collisions, before being re‐accelerated by the electric field. The particles' drift motion in the E × B direction is slowed by the collisions, and ions and electrons acquire an additional drift parallel and antiparallel to E, respectively,