ELECTRICAL DISCHARGES AND THUNDERSTORMS

IN THE EARTH’S INTERIOR

A. A. VOROB'EV

In the Earth’s atmosphere, under certain conditions, the accumulation of electric charges in a thundercloud is possible. When the intensity of the electric field in the thundercloud reaches a value equal to the electric strength of the medium, a discharge occurs in the form of lightning. The charge accumulated in the cloud flows away along the lightning channel.

In the Earth’s interior, in the lithosphere, an analogous phenomenon is possible. The accumulation of a volume charge in dielectric rocks, whereby the magnitude of the field strength reaches the value of the electric strength of the dielectric. Breakdown will occur, and the accumulated volume charge will flow along the discharge channel [1].

Since the electric strength of solid dielectrics in the Earth’s interior may be three or four orders of magnitude higher than the electric strength of air, the electric charge accumulated in the Earth’s interior may correspondingly be several orders of magnitude higher than the charge in the atmosphere, while the length of the discharge may be several orders of magnitude smaller than the length of lightning. If charge accumulation occurs near the Earth’s surface, the discharge will occur into the atmosphere, whose electric strength is lower than that of rocks. The maximum charge recorded in a cloud reached values of up to 500 coulombs; the minimum value was 0.5 coulomb. The average amount of energy released in lightning was estimated at about 4 kWh, while the maximum was almost two orders of magnitude higher [2]. In the Earth’s interior these values will correspondingly be 3–4 orders of magnitude higher; in particular, one may expect the release of energy in a discharge up to \(1.44 \cdot 10^{16}\) ergs, which corresponds to the energy recorded in a weak earthquake. Since the discharge time may amount to only \(10^{17}\) sec and more, the instantaneous power that can be achieved in such a discharge will be \(10^{20}\) watts. This is a very high rate of energy release, which can be removed from the breakdown channel. The average power in earthquakes is \(10^{10}\) watts. Such power, recorded during earthquakes, is determined by the possibilities for the propagation of energy from the focus by means of seismic waves.

Some part of the energy from the discharge channel will be carried away by heat-radiation fluxes, seismic waves, and so forth. Under discharge conditions, inside dense opaque rock, most of the energy will be absorbed near the axis of the discharge channel and will go into heating the discharge plasma. Consequently, the physical processes in the region of the discharge channel will be adiabatic.

For the development of a hypothesis on the formation of thunderstorms in the Earth, it is of interest to investigate all stages of their preparation and course, namely: the determination of the sources of electric charges in the material of the Earth’s interior, the process of accumulation of a space charge, the conditions for the onset of discharge, the stages of discharge propagation in rocks and in the atmosphere, and the possible physical or geological processes under the action of electrical discharges in the Earth—for example, the occurrence of thermonuclear reactions in the plasma of the discharge channel.

The electrical conditions for the occurrence of an underground thunderstorm consist in the accumulation of a large electric charge in a dielectric rock. When the field strength reaches the value of the electric strength of the dielectric, an electrical discharge will occur. With increasing pressure, with improvement in the continuity of the body and an increase in the bonding forces in the dielectric, its mechanical strength grows rapidly. The mechanical strength of dielectrics under hydrostatic compression increases by several orders of magnitude and approaches the theoretical strength at normal pressure. Under one-sided pressure the electric strength of dielectrics, according to data of E. K. Zavodskaya, A. Gemogores and others, increases along a curve with a maximum. At high pressure cracking of the dielectric occurs and its strength decreases [3, 4]. Under hydrostatic pressure there is no cracking of the dielectric such as is observed under one-sided pressure. Thus, up to high pressures, at which the dielectric passes into a semiconductor and then into a metal, it should undergo strengthening. The dielectric acquires the properties of a metallic conductor at pressures corresponding to depths greater than one thousand kilometers. Let us note that the deepest earthquake foci have been recorded at a depth of about 700 km. With depth the temperature rises, and the ionic electrical conductivity of rocks should increase.

Taking into account the simultaneous action of pressure and temperature, it may be assumed that down to depths of several hundred kilometers the dielectric and semiconducting properties of the material of the Earth’s interior can be preserved. Down to a depth of 100 km the electric strength of the material of the interior will increase and may exceed by several orders of magnitude the maximum value of the electric strength of dielectrics under normal conditions, which in thin layers, under nanosecond pulses, reaches \(10^9\) V/cm [5], i.e., is of the order of the theoretical strength. In investigating thunderstorm phenomena in the depths of the Earth, it is essential to study integral processes and their regularities, which determine changes in electric fields and their intensities. It is also necessary to study the elementary processes of the appearance of electric charges, their distribution and migration under the physical conditions in which the material of the Earth’s interior occurs, which should exert a substantial influence on the development of electrical phenomena in rocks.

Free electric charges in minerals and rocks can arise under the influence of constantly acting factors, such as: petrostatic pressure, radioactive radiation, gradients of temperature, pressure, or concentration, changes in chemical composition, and so forth, as well as under temporary action. The latter include the passage of a shock-wave front, disturbance of the magnetic field, the passage of induction currents in the Earth caused by phenomena in the ionosphere, the appearance of electric charges during the splitting of minerals and during friction, since the displacement of rock masses is accompanied by friction and by the appearance of electric charges on surfaces. The occurrence of a potential difference of up to 335 kV [6] was observed during the filtration of insulating liquids or colloidal solutions. In a circuit, inclu—

of a body of varying conductivity \(\gamma\) and dielectric permittivity, voltage drops and field strengths are distributed nonuniformly. As a result, overvoltages are possible, the values of which are calculated theoretically [6].

An electric field can arise in the Earth’s interior from diffusion currents if the surfaces of equal planes and equal pressures do not coincide [7].

Changes in the microstructure of a solid dielectric and in its energy spectrum upon compression of a specimen lead to the appearance of an emf and currents in a short-circuited specimen.

The independent formation, in ionic crystals, of vacancies of positive and negative ions having different formation energies leads to the appearance of a volume charge. The appearance of an emf is observed under mechanical loading of crystals, under their irradiation, or under nonuniform heating to a high temperature [8, 9].

When the front of a shock wave passes, high electric fields are formed. Electric discharges have occurred, and the destruction of glass minerals has been observed as a result of internal discharges. The propagation velocity of shock waves increases with increasing strength of the body; therefore the steepness of the front, and consequently larger fields, will arise in mechanically stronger bodies at certain depths, where such strength is reached. A larger reserve of elastic energy will also accumulate in them, and therefore both the destruction of the body and the consequences of the discharge will be greater.

The passage of a seismic wave with a steep front during an earthquake of great power may be the cause of the formation of electric fields and discharges in the dielectrics of rocks. Various possible ways in which free charges appear and accumulate in solid dielectrics, some of them listed above, have been considered.

The spreading of charges from a charged volume in the interior proceeds according to the laws of discharge of a capacitance through a resistance. The higher the resistance of the dielectric in the breakdown channel, the less rapidly its discharge will occur. In a dielectric with higher resistance, a higher charge will accumulate and be preserved. If secondary phenomena are not taken into account, then the magnitude of the voltage \(U\) to which an isolated conductor can be charged by bombarding it with charged particles of mass \(m\), charge \(e\), and velocity \(v\), up to a voltage determined by the condition that the kinetic energy of the particle is equal to the work expended in overcoming the repulsive forces that arise as the particle approaches, i.e.,

\[ \frac{mv^2}{2}=eU. \tag{1} \]

An increase in the charge of a body can also be achieved when charged particles fly out from its surface. In this case condition (1) remains valid, but a very large charge can be accumulated even when particles of low energy leave the volume. If charges are supplied to the inner surface of a layer, then particles of arbitrarily small velocities may be used to charge it.

Hundreds of radioactive isotopes are known with half-lives varying over wide limits.

For the purposes under consideration, natural sources are of interest for charging substances in the Earth’s interior, although one may also imagine a charging scheme with an intermediate source that emits \(\alpha\)- and \(\beta\)-particles, positrons, and \(\gamma\)-rays. An intermediate radioactive source may be formed under irradiation. Most active

nuclei emit electrons with a continuous spectrum and positrons. The kinetic energy of α- and β-particles emitted in natural radioactive decay only slightly exceeds 10 MeV. For example, in the decay of ThC′, long-range α-particles have a maximum kinetic energy of 10.5 MeV. Among natural emitters, the greatest kinetic energy, 3.2 MeV, is possessed by electrons observed in the decay of RaC. The upper limit of the β spectrum in the radioactive decay of an artificial isotope reaches almost 12 MeV.

Electric volume charges can accumulate near the interface between radioactive and nonradioactive rocks with high resistivity. The resistivity of rocks in the Earth’s interior can reach \(10^{+18}\ \Omega\cdot\text{cm}\). Taking the radioactive rock as an emitter and the nonradioactive rock as a collector of charged particles (for example, β-particles), such a system may be regarded as a kind of nuclear generator, and its charge may be approximately calculated as the charge of a capacitor. The accumulation of charge \(q\) with time in such a system is determined by the equation:

\[ \frac{dq}{dt}=I_0-I_{\text{leak}}, \tag{2} \]

where \(q\) is the charge per unit surface area;

\[ I_0 \]

is the current density of charged particles;

\[ I_{\text{leak}} \]

is the leakage-current density. This current depends on the leakage resistivity \(R\) and the capacitance per unit area \(C\) of the interface:

\[ I_{\text{leak}}=q(RC)^{-1}. \]

From equation (2) it follows that:

\[ q=I_0RC\left(1-e^{-\frac{t}{RC}}\right). \tag{3} \]

The limiting charge is \(q_{\text{lim}}=I_0RC\), and the charging time is \(t_{\text{ch}}\approx 3RC\). If one takes the resistivity \(R=10^{20}\ \Omega\cdot\text{cm}\), and \(C=10^{-10}\ \text{F}\), then a charge close to the limiting value will accumulate in 1000 years. The maximum voltage that can be obtained with beta-active materials is probably 1–2 MeV. Assuming that the maximum voltage corresponds to the maximum charge, we obtain the activity of the material

\[ I_0=\frac{U}{R}\sim 10^{-20}\ \frac{\text{decays}}{\text{s}}. \]

The actual activity must be about two orders of magnitude greater, since some time after the beginning of charging the actual charging current will be less than \(I_0\), owing to the fact that low-energy particles of the beta spectrum will not reach the collector. The activity of the material, taking into account the spherical distribution of particles, must be of the order of \(10^{-18}\)–\(10^{-17}\) decays/s, i.e., \(10^{-8}\)–\(10^{-9}\) curie, which is a very small activity. Thus, a necessary condition for the prolonged accumulation of a large charge is low activity and a high resistivity of the rock, \(\sim 10^{20}\ \Omega/\text{mm}\). The time of charge accumulation is determined exclusively by the resistivity. The time at which accumulation ends is associated with the moment of discharge in the Earth; from it one can judge the resistivity of the rock and the depth at which it occurs.

Proceeding from the model under consideration, a large amount of energy will be released in the discharge if the latter occurs simultaneously over a larg—

large area. Per unit area, in \(1\ \mathrm{cm}^2\), the energy released will be

\[ W=\frac{CU^2}{2}\simeq 10^9\ \frac{\mathrm{erg}}{\mathrm{cm}^2}. \]

If the energy required for an earthquake is taken as \(10^{15}\) erg, then the area over which charges accumulate will be \(100\ \mathrm{m}^2\). For a more powerful discharge, a larger charged area is necessary. Charging of dielectrics is also possible when they are irradiated by gamma rays and radioelectrets are formed.

REFERENCES

1. A. A. Vorob'ev. On the question of the initiation of earthquakes by underground thunderstorm discharges.

2. A. A. Vorob'ev. High-Voltage Engineering. Moscow–Leningrad, GEI, 1945.

3. A. A. Vorob'ev, E. K. Zavadovskaya. Electrical Strength of Solid Dielectrics. GIZ, TTL, Moscow, 1956.

4. A. A. Vorob'ev. Violation of the Electrical Strength of Dielectrics and Their Breakdown. Tomsk, TSU Publishing House, 1962.

5. A. A. Vorob'ev. Physical conditions of occurrence of rocks in the Earth’s interior (in press).

6. A. A. Vorob'ev. Superhigh Electrical Voltages. Moscow–Leningrad, GEI, 1955.

7. Ya. I. Frenkel'. Kinetic Theory of Liquids. Moscow, Publishing House of the Academy of Sciences of the USSR, 1945.

8. L. V. Al'tshuler, S. B. Kormer, A. A. Bakanova, R. R. Trunin. ZhETF, 38, 790 (1960).

9. Yu. N. Tyunyaev, A. A. Urusovskaya, V. N. Mineev, A. G. Ivanov. FTT, 10, no. 11, 2399, 1968.

10. A. A. Vorob'ev. Electrical Superhigh Voltages. Moscow–Leningrad, GEI, 1955.