Introductory and Background Material - The Earth's Ionosphere: Plasma Physics and Electrodynamics - page 17

where r is measured in units of earth radii is the magnetic

latitude, and L is the radius of the equatorial crossing point of the field line (also
measured in earth radii). A field line that crosses the equatorial plane at L

( R e = 6371 km ) , θ

= 4

at a magnetic latitude of 60 ◦ . Owing to the
dipole tilt, this field line is located at about 49 ◦ geographic latitude in the North
American sector and about 71 ◦ geographic latitude in the Euro-Asian region. As
indicated in Fig. 1.11, if the earth were surrounded by a vacuumwith no external
sources of electrical currents, the dipole field lines would extend in loops of ever
increasing dimension with the magnitude of B decreasing as 1

thus exits the earth's surface ( r = 1 )

r 3 .
The earth is, however, immersed in the atmosphere of the sun. Like the earth's
thermosphere, the upper atmosphere of the sun is very hot, so hot that the hydro-
gen and helium can escape gravitational attraction and form a steadily streaming
outflow of material called the solar wind. Because of its high temperature and
constant illumination by the sun, the solar wind is a fully ionized plasma (unlike
the ionosphere, which contains more neutral particles than plasma). One sur-
prising feature of the solar wind is that it is supersonic. Simply heating a gas
cannot create supersonic flow, but a combination of heating, compression, and
subsequent expansion can create this condition, as it does, for example, in a
rocket exhaust nozzle. In the solar wind case, the solar gravitational field acts
analogously to the rocket nozzle, and the solar wind becomes supersonic above a
few solar radii. The sun has a very complex surface magnetic field created by con-
vective flow of the electrically conducting solar material. Sunspots, in particular,
have associated high magnetic fields. The expanding wind drags the solar mag-
netic field outward, with the result that the earth's magnetic field is continually
bathed in a hot, magnetized, supersonic, collisionless plasma capable of conduct-
ing electrical current and carrying a large amount of kinetic and electrical energy.
The solar wind is a magnetohydrodynamic (MHD) generator, and some of
the solar wind energy flowing by the earth finds its way into the ionosphere and
the upper atmosphere. There it powers the aurora, creates magnetic storms and
substorms that affect power grids and communication systems, heats the polar
upper atmosphere, drives large neutral atmospheric winds, energizes much of the
plasma on the earth's magnetic field lines, and creates a vast circulating system
of hot plasma in and around the earth's nearby space environment. We cannot
come close to exploring these topics in detail, but we need a framework about
which to organize the ionospheric effects of these phenomena.
Suppose we first ignore the supersonic nature of the solar wind as well as the
interplanetary magnetic field (IMF) and surround the earth and its magnetic field
with a subsonic, streaming plasma. The magnetic force on a particle of charge q
moving at velocity V is

/

F = q V × B (1.1)

As illustrated in Fig. 1.12, and because of the polarity of the earth's field, this
force will deflect solar wind ions to the right and electrons to the left as they