Atmospheric electricity

The Earth is surrounded by a magnetic field, and from a height of about 80 km a substantial fraction of atmospheric gases is in an ionised state (cf. section 2.3.1). It is thus clear that electromagnetic forces play an important role in the upper atmosphere. Manifestations of electromagnetic energy in the lower parts of the atmosphere are well known in the form of lightning. Speculations on the possibility of extracting some of the electrical energy contained in a thunderstorm have appeared. An estimation of the amounts of energy involved requires knowledge of the electrical properties of the atmosphere.

In Fig. 3.80, calculated values of the electrical conductivity of the atmosphere are shown as a function of height for the lowest 200 km (Webb, 1976). It is shown that the conductivity is low in the troposphere, increases through the stratosphere and increases very sharply upon entering the ionosphere. Strong horizontal current systems are found in the region of high conductivity at a height of around 100 km (the "dynamo currents"). Vertical currents directed towards the ground are 6-7 orders of magnitude smaller for situations of fair weather, averaging about 10-12 A m-2 in the troposphere. Winds may play a role in generating the horizontal currents, but the energy input for the strong dynamo currents observed at mid-latitudes is believed to derive mainly from absorption of ultraviolet solar radiation by ozone (Webb, 1976; see also Fig. 2.16).

Figure 3.80. Electric conductivity of the atmosphere at noon on a clear day as a function of height (at about 105 m height, a substantial night-time reduction in X takes place) (based on Webb, 1976).

The fair weather downward current of 10-12 A m-2 builds up a negative charge on the surface of the Earth, the total value of which on average is around 105 C. Locally, in the thunderstorm regions, the current is reversed and much more intense. Together these currents constitute a closed circuit, the flow through which is 500-1000 A, but in such a way that the downward path is dispersed over most of the atmosphere, while the return current in the form of lightning is concentrated in a few regions (apart from being intermittent, causing time variations in the charge at the Earth's surface). The power P associated with the downward current may be found from

P = J I2 X"1 dz, where I (~ 10-12 A m-2) is the average current and X(z) is the conductivity function (e.g. Fig. 3.80 at noon), or more simply from

P = IV = I Q/C, where C is the capacitance of the Earth relative to infinity (V the corresponding potential difference) and Q (~ 105 C) is its charge. The capacitance of a sphere with the Earth's radius rs (6.4 x 106 m) is C = 4ne0 rs = 7 x 10-4 F (e0 being the dielectric constant for vacuum), and thus the average power becomes P ~ 6 x 10-5 W m-2.

The energy stored in the charge Q of the Earth's surface, relative to a situation in which the charges were all moved to infinity, is

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