Proceedings of the Tomsk Polytechnic Institute
named after S. M. Kirov

Volume 264　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1976

INERTIAL-PLASMA HYPOTHESIS OF THE EARTH’S INTRINSIC MAGNETIC AND ELECTRIC FIELDS

L. A. VOROB'EV

§ 1. Introduction

It is generally accepted that the general magnetic field of our planet is created as a result of electromagnetic processes occurring in the Earth’s interior [1]. To a first approximation, the geomagnetic field is the field of a dipole located at the center of the Earth. Its dipole moment is
$P = 8.1 \cdot 10^{25}\ \text{gs}\cdot\text{cm}^3$. The field intensity at the pole is $0.62\ \text{gs}$. The dipole axis intersects the Earth’s surface at the points $78.3^\circ$ N, $69.0^\circ$ W and $78.3^\circ$ S, $111.0^\circ$ E. Other approximations are also known (Fig. 1).

The general field of the Sun until 1958 was antiparallel to the geomagnetic field. It changed its polarity in such a way that since 1958 the two fields have become parallel. For the time being, measurements of the Sun’s general magnetic field are unreliable, which makes it difficult to construct a theoretical scheme for describing the formation of the Sun’s magnetic field. Observations of the displacements of the sunspot zone indicate the existence, in the region between the photosphere and the center, of a general magnetic field with a source magnetic moment:

$$ P = 2.1 \cdot 10^{33}\ \text{gs}\cdot\text{cm}^3 \quad [2]. $$

Magnetic fields are a common property of rapidly rotating class-A stars with a convective core. Stars with variable magnetic fields are known. There is a magnetic field in the plane of the Galaxy and at large distances from it. A possible value of the intensity of the galactic magnetic field, $10^{-6}$—$10^{-5}\ \text{gs}$, is given in [2]. The magnetic fields of celestial bodies are widespread properties of theirs. An attempt has been made to explain magnetism as a property of rotating masses. However, not every rotating mass has a magnetic field. For example, the Moon and, probably, Mercury do not have magnetic fields. Jupiter, however, possessing a greater mass, has its own magnetic field [2].

We have made the supposition that the emergence of the magnetic properties of celestial bodies is connected with such fundamental properties of theirs as rotation and the presence of plasma in the composition of the core of the celestial body. To substantiate this hypothesis, regularities from magnetohydrodynamics and seismology [4] have been used. When considering seismic phenomena, in a first approximation the planet is usually regarded as an elastic medium. In a materially ideally elastic medium two types of elastic waves propagate: longitudinal waves of the $P$ type with velocity

$$ \alpha = \sqrt{\frac{\lambda + 2\mu}{\rho}} = \sqrt{\frac{K + \frac{4}{3}\mu}{\rho}} \tag{1} $$

Fig. 1. Main layers of the Earth and near-Earth space

Labels in the figure:

• Ionosphere
• Crust
• Mantle
• Outer core
• Inner core
• Dipole magnetic field
• Electric field lines
• Inferred winds of electrons and protons
• Boundary of the magnetosphere
• Higher electrons in the radiation zones
• Low protons of charge \(1/4\) mass
• Protons of low energy \((1/4\ \text{MeV})\)
• Plasma regions with charges of different sign
• Plasma streams, turbulent region
• Plasma layer \(\approx 6370\ \text{km}\)
• Earth radius \(= 6370\ \text{km}\)
• Distance from the Earth’s surface, km
• \(U\)—electron charge
• \(U\)—proton charge
• Boundary of the geomagnetic field (magnetosphere, up to \(75000\ \text{km}\))
• Poynting vector
• Belts of charged particles in the radiation zones according to Van Allen, 1962.

and transverse waves of the \(S\)-type with velocity

\[ \beta=\sqrt{\frac{\mu}{\rho}},\quad \beta<\alpha, \]

where \(\rho\) is the density of the medium, and \(\lambda=K-\frac{2}{3}\mu\),

\(\lambda\) and \(\mu\) are Lamé constants, \(K\) is a parameter of an elastic isotropic medium, and \(\mu\) is the rigidity or shear modulus.

If \(\mu\ne 0\), then the medium is ideally rigid; at \(\mu=0\) the medium is ideally fluid, for which \(\beta=0\) and transverse waves of the \(S\)-type do not pass through. If \(\frac{k}{\rho}\to\infty\), while \(\frac{\mu}{\rho}\) is a finite quantity, then only transverse waves pass through such a medium, having a finite velocity in an incompressible solid body. The ratio of pressure to the compression produced by it measures the compressibility, or bulk modulus of compression \(K\), at the point \(P_1\). The compression modulus \(K\), density \(\rho\), and shear modulus \(\mu\) are the three parameters whose values determine the physicomechanical properties of deep material as a continuous medium.

Both types of waves, \(P\) and \(S\), can be plane-polarized. In seismology the following designations are adopted: an \(S\)-wave in which all particles move in the horizontal plane is denoted \(SH\); an \(S\)-wave in which all particles oscillate in the vertical plane containing the direction of wave propagation is denoted \(SV\) [1] (in the case of incidence on a horizontal boundary). The physicomechanical state of the Earth’s shell permits waves of the \(P\)- and \(S\)-type to pass through it. This proves that it is in a solid state down to the boundary of the outer core at a depth of 2900 km.

From data obtained in the study of seismograms it follows that only waves of the \(P\)-type can pass through the outer core \(E\), while waves of the \(S\)-type (transverse oscillations) do not pass through. From these data it was concluded that the outer core is in a liquid state. Conclusions about the low rigidity of the greater part of the Earth’s core are also in agreement with astronomical measurements. Data on the motion of the Earth’s poles and observations of tides in the body of the Earth provide information about the rigidity of the Earth as a whole.

Theoretical calculations show that the rigidity of the outer core constitutes a small fraction of its compression modulus, or is close to zero [1]. From observations of the passage of \(P\)-waves in 1936, Lehmann concluded that an inner core exists in which the velocity of \(P\)-waves is considerably higher than in the surrounding region of the outer core [1]. From the expression for the magnitude \(\alpha\) it follows that its increase may occur either with a decrease in the density of the substance \(\rho_1\), but such an assumption must be excluded, or as a consequence of an increase in the parameters \(K\) and \(\mu\)—the rigidity of the system.

If it is assumed that the core is liquid, then the shear modulus \(\mu\) will not increase with increasing pressure; consequently, the increase of \(\alpha\) must be determined by a very large increase of \(K\). Therefore K. E. Bullen in 1946 came to the conclusion that the core should be regarded as being in a solid state. \(S\)-waves can pass through a solid core, but they will not pass into it or emerge from it through the liquid outer core \(E\). Thus, there are no data on the passage of \(P\)- and \(S\)-waves through the inner core, and none can be obtained. Bullen cast doubt on Caloi’s data, according to which he had supposedly observed on seismograms a phase characteristic of \(P\)- and \(S\)-waves [1].

Figure 2 presents the variation in the velocities of \(P\)- and \(S\)-waves as a function of radius. As can be seen, at the boundary of the outer core no propagation of \(S\)-waves is observed. It is interesting to note that, as ...

Fig. 2. Distribution of the velocities of \(P\)- and \(S\)-waves in the Earth’s interior

approach to the core, the velocity of \(P\)-type waves increases. According to Jeffreys, between the inner and outer cores there exists a transition region \(F\), about 150 km thick, which is characterized by a negative value of the velocity gradient. From the condition that transverse \(S\)-waves do not penetrate deeper than 2900 km, it has been concluded that this depth is the lower boundary of the substance of the Earth’s interior in the solid state (the mantle) and the upper boundary of the substance in the liquid state that forms the Earth’s outer core. It is sometimes assumed that at this boundary, within a certain region about 150 km wide, the velocity of \(P\)-waves decreases, then increases somewhat and remains constant.

The plasma hypothesis set forth below explains the observed course of the change in the velocity of seismic waves in the Earth’s core without the assumptions cited above.

§ 2. Hypothesis of the Plasma State of the Planet’s Core

According to A. F. Kapustinskii [4], in the outer core, at a temperature of \(2000^\circ\)C and a pressure of about \(1.4 \cdot 10^6\) atm, no chemical transformations of atoms, manifestations of differences in the chemical properties of atoms, or formation of chemical compounds are possible. Under these conditions, according to A. F. Kapustinskii, matter is practically identical to a pure crystal at \(0^\circ\)K.

In our opinion, in the region of the core, under high pressure, atoms are ionized; their electron shells are rearranged in such a way that the atoms lose their chemical properties. As a result, chemical bonds are disrupted. A plasma is formed with a particle concentration of \(10^{23}\)—\(10^{25}\ \text{cm}^{-3}\).

Usually plasma is a gas of charged particles. In the present case, a high particle concentration is obtained, exceeding by one or two orders of magnitude the particle concentration in a solid. The plasma filling the Earth’s interior will be described by the equations of magnetohydrodynamics and will have the properties of a conducting liquid; it may therefore be called a plasma liquid, which is consistent with the macroscopic regularities established by Roberts [5]. The viscosity of the substance of the Earth’s core is small. This circumstance made it possible to regard it as liquid, metallic. The same circumstance makes it possible to assume a plasma state of the substance filling the Earth’s core. Such a liquid, consisting of charged particles, must possess high electrical conductivity. Being a quantum system, the plasma liquid will have low viscosity, as has been established for liquid helium at temperatures near absolute zero. Owing to the low viscosity of the plasma filling the core, it is possible to assume that the angular velocity of its rotation will differ from the rotation velocity of the planet. A plasma liquid consisting of ionized particles and electrons will be

have the temperature characteristic of the Earth’s core. In the Earth’s core the plasma is under the action of the possible electric field of the Earth, about which nothing is known, and of the magnetic field. Therefore the plasma parameters must be considered with allowance for these fields. In a plasma liquid there is a high concentration of free electrons and positively charged remnants of atoms. Even in a metal the equilibrium between positive and negative charges is disturbed because of the action of the gravitational field, which displaces the electrons downward. In a piece of metal the concentration of free electrons at the bottom will be greater than in the upper part [6].

According to [6], the gravitational change in the mass of an electron is no more than 9%. The measured force of attraction of an electron to the Earth is approximately equal to the force of electrostatic attraction of an electron to a proton separated from it by a distance of 5 m. By the principle of relativity, the magnetic field of charges located in the core cannot be detected on the Earth’s surface if all geospheres rotate with the same angular velocity. According to Bullard’s hypothesis [1], the rotational velocities of the planet’s geospheres may be different. Owing to the low viscosity of the plasma, the core will rotate with an angular velocity different from the rotational velocity of the planet. Therefore particles located in different geospheres will be displaced relative to one another. The magnetic field created by circular currents of charged particles rotating together with the core will be felt in other geospheres.

Having considered the behavior of a compressible electrically conducting medium placed in a homogeneous magnetic field and compressed in a direction perpendicular to the magnetic flux, we arrive at the following conclusion.

In transverse compression of the medium, the magnetic field $H$ creates a restoring force, the so-called magnetic pressure, equal to $H^2/8\pi$. For this reason compression waves, or magnetosonic waves, arise in the plasma. They propagate perpendicular to the magnetic field as a result of the simultaneous action of hydrostatic and magnetic pressure [2, 7, 8, 9].

The motion of plasma in a magnetic field, which will be forced, for example, by an incident seismic wave, leads to charge separation in the plasma and to the appearance of an electric field and electrostatic oscillations. In the case of the motion of different regions of the plasma with different velocities, the electric fields that arise create currents. The interaction of the magnetic fields and of these currents with the Earth’s magnetic field leads to the appearance of forces which, under certain conditions, change the character of the motion of the medium itself. Thus, the hydrodynamic motion and the electromagnetic phenomena (in the plasma of the core) will be coupled. To describe the processes when seismic waves pass through a core filled with plasma located in a magnetic field, one should use the equations of magnetic hydrodynamics. In an ordinary gas or liquid, small oscillations propagate in the form of longitudinal waves of compression and rarefaction $P$ (pressure waves). In a conducting plasma or plasma liquid in a magnetic field, transverse magnetohydrodynamic waves (MHD), discovered by H. Alfvén [2], may also propagate.

Rikitake [11, 10], in 1952, while studying seismic waves reflected from the surface of the core, tried to detect the occurrence of MHD waves in it, but was unsuccessful. However, his use of rays with small angles of incidence and of dynamic amplitude ratios raises objections. Rikitake’s result contradicts the data of Roberts [5], who showed that, at least for waves of the seismic-frequency range, the core may be regarded as an ideal conductor.

Probably, to detect MHD waves and magnetosonic waves one should

one should use not amplitude ratios of the reflected waves, but a statistical analysis of the kinematic features (apparent velocities) of waves that have passed through the core. Waves whose electric vector is parallel or perpendicular to the external magnetic field may be considered independently of one another. A wave whose electric vector is directed along the external magnetic field is a plasma wave when it propagates along the field, and an electromagnetic wave when it propagates across the field. For waves propagating along the external magnetic field, the intrinsic magnetic field will be parallel to the external, applied one [8]. In the general case of wave propagation in a plasma, the electric and magnetic vectors will be oriented at an arbitrary angle with respect to the external magnetic field. Such waves are called oblique. The electric vector of an oblique wave will necessarily have a component along and across the external magnetic field. It is known that in such cases elliptical polarization arises.

When waves propagate in a plasma in which the gas pressure is considerably smaller than the magnetic pressure, the ordinary and extraordinary waves that arise may be low-frequency magnetohydrodynamic waves with different directions of circular polarization, or high-frequency electromagnetic waves [7, 8]. When a wave propagates across the field, the extraordinary wave is a magnetosonic wave, and the ordinary wave is an electromagnetic wave whose electric vector is directed parallel to the external magnetic field. Oscillations in a plasma of low concentration located in a magnetic field have been well studied. Some general regularities can be transferred to processes that may occur in a plasma of high concentration. Plasma waves propagate in the direction of the acting electric field. In the same direction the oscillation of particles also occurs. As the plasma density increases, the damping of plasma oscillations grows. The mechanism of oscillations in a plasma propagating along the magnetic field consists in the bending of magnetic lines of force together with the plasma “frozen” to them. The velocity of motion of matter in this case proves to be perpendicular to the direction of propagation, and magnetohydrodynamic, or Alfvén, transverse waves are formed. H. Alfvén proposed that magnetohydrodynamic waves in a conducting liquid plasma be regarded as oscillations of magnetic lines of force by analogy with transverse oscillations of a string [9]. In the mechanism of an ordinary liquid or gas, such transverse oscillations have no analogue. In general, transverse oscillations are characteristic only of an elastic solid body and of the surface of a liquid. Thus, the magnetic field imparts elasticity of form to the plasma, making it to some extent similar to a solid body [7, 8].

At low frequencies the propagation velocity of magnetohydrodynamic transverse oscillations along the field is equal to the velocity of magnetic sound in a cold plasma, which is called the Alfvén velocity. If a wave propagates in a plasma along the magnetic field, while the oscillations occur in an arbitrary plane, then such a wave may conveniently be resolved into two independent ones. The electric vector of one wave is directed parallel to the magnetic field, and that of the other perpendicular to it. For such waves a separate method of consideration may be applied. At small oscillation frequencies the plasma in a magnetic field behaves like a conducting liquid, and its properties are described by the equations of magnetic hydrodynamics.

In the region of low frequencies (below the frequency of ion oscillations without a magnetic field), magnetohydrodynamic waves propagate parallel to the magnetic field, and perpendicular to it—magneto-

sound waves. Magnetosonic waves are longitudinal in the hydrodynamic sense. In plasma, waves of expansion and compression propagate. The “frozen-in” lines of force of the magnetic field are associated with the plasma. The current and the electric field of the wave are directed perpendicular to the magnetic field and to the hydrodynamic velocity of motion of the matter, which coincides in direction with the direction of propagation. Consequently, magnetosonic MHD waves, in the hydrodynamic sense, are longitudinal waves, while in the electrodynamic sense they are transverse. The propagation velocity of longitudinal magnetosonic waves is determined in the same way as the propagation velocity of sound, but in addition to the pressure value \(P\) one must add the magnetic pressure \(H^2/8\pi\) and write the equation in the form

\[ U_{\text{sv}}^{2}=\gamma \frac{P}{\rho}+\gamma_M \frac{H^2}{8\pi\rho}, \tag{1} \]

where \(\rho=n\cdot m\) is the plasma density,
\(n\) is the ion concentration,
\(m\) is the ion mass,
\(\gamma\) and \(\gamma_M\) are the adiabatic exponents for the pressure in expression (1).

For a “frozen-in” magnetic field, the density \(\rho\) is proportional to \(H\), and the magnetic pressure \(P_M\sim H^2\sim \rho^2\), whence \(\gamma=2\). Therefore the velocity of longitudinal sound waves in plasma across the magnetic field is determined by

\[ U_{\text{sv}}^{2}=C^2+\frac{H^2}{4\pi n m}, \tag{2} \]

where \(C\) is the speed of sound without a magnetic field.

\[ C=\gamma \frac{P}{\rho}=\gamma \frac{T}{m}, \tag{3} \]

where \(T\) is the temperature.

It follows from [1] that the velocity of longitudinal waves in a plasma located in a magnetic field increases in proportion to its intensity. Such a regularity is observed in the region of the outer core. The velocity decreases with increasing plasma density. The propagation velocity of magnetohydrodynamic waves along the magnetic field will be determined by the same formula (1). In magnetohydrodynamic waves the hydrodynamic velocity of matter and the vector of the electric field are directed across the magnetic field; therefore these waves are transverse in the hydrodynamic and electrodynamic sense. At low frequencies in the magnetoacoustic region, the propagation velocities of both magnetohydrodynamic waves and magnetosonic waves tend toward the Alfvén velocity

\[ U_A=\frac{H_0}{\sqrt{4\pi\rho}}, \tag{4} \]

obtained from (1) under the assumption that the magnetic pressure exceeds the gas pressure, that is, that the plasma is cold. Since, for a “frozen-in” magnetic field, the plasma density and the magnetic-field intensity vary proportionally, it follows from (4) that the Alfvén velocity \(U_A\) will increase somewhat more slowly than the magnetic-field intensity. Inside the core there acts a comparatively strong magnetic field created by a circular current. Therefore the propagation velocity of waves will differ from the propagation velocity of waves in plasma without a magnetic field.

It is assumed that at the boundary of the outer core there occurs not a decrease in the velocity of \(P\)-waves or a jumpwise increase in the velocity of \(S\)-waves, but that, under the action of longitudinal waves of type \(S\) or transverse waves of type \(P\), there arise

create in the core magnetosonic or magnetohydrodynamic waves, characteristic of plasma under certain conditions [9]. The propagation of magnetosonic waves is accompanied by the phenomenon of dispersion, that is, by an increase in the refractive index as a result of a decrease in the phase velocity of the waves. At a certain frequency the refractive index becomes equal to infinity, the phase velocity is zero, that is, the phenomenon of anomalous dispersion sets in. On passing through this frequency, \(n^2\)—the square of the refractive index—changes discontinuously from \(+\infty\) to \(-\infty\) and in the region of higher frequencies becomes imaginary. Consequently, magnetosonic waves with a frequency higher than the electron-ion plasma frequency cannot penetrate into the plasma across the magnetic field, and the wave is reflected from the plasma boundary. At still higher frequencies, the propagation of transverse waves again becomes possible.

In the region of anomalous dispersion and reflection, magnetosonic waves may propagate in the form of oblique waves, whose front is directed at an angle \(\Theta^\circ\) to the magnetic field. If the magnetic pressure in the plasma is taken into account, new types of waves appear, and their properties become more complicated. Consideration of the propagation of small oscillations in a conducting compressible medium with a magnetic field, which is composed of a strong uniform external field \(H\) and a weak wave field \(h\), neglecting wave damping under adiabatic compression, led to the following interesting results [7].

The wave velocity is determined by the condition:

\[ U_{1,3}^{2}=\frac{1}{2}\left(V_A^2+C^2\right)\pm \frac{1}{2}\sqrt{V_A^4+C^4-2V_A^2C^2\cos\Theta}, \tag{5} \]

where

\[ V=\pm \frac{H_0}{\sqrt{4\pi\rho_0}}, \]

\(V_A\) — the Alfvén wave velocity,
\(C\) — the speed of sound,
\(\rho_0\) — density,
\(\Theta^\circ\) — the angle between \(\vec H\) and the velocity \(C\).

In the general case, these waves correspond to the motion of matter in the plane \((\vec K,\vec H)\), in which a change in density occurs, where \(K\) is the wave vector.

In the particular case when \(\Theta \ne 0\), when wave propagation occurs along the magnetic field:

\[ U_{1,3}^{2}=\frac{1}{2}\left(U_A^2+C^2\right), \tag{6} \]

if \(V_A>C\), then \(U_1=V_A;\quad U_3=C;\)
\[ \tag{7} \]

for \(V_A<C,\quad U_1=C\quad \text{and}\quad U_3=V_A.\)
\[ \tag{8} \]

The motion of the plasma along \(\vec H_0\) does not produce electromagnetic effects, and therefore electromagnetic waves do not arise.

In the limiting case considered, the ordinary Alfvén, magnetohydrodynamic, and sound waves propagate. In a weak field \(H_0\), the sound wave is the one that propagates with velocity \(U_1\), and the Alfvén wave with velocity \(U_3\). In a strong field the reverse relation is obtained. Consequently, during propagation in an inhomogeneous medium, such as plasma in a magnetic field, an incident seismic wave may propagate either in the form of a magnetosonic wave, that is, the same seismic wave, or in the form of a magnetohydrodynamic wave. The latter is essentially an electromagnetic wave, not

despite the fact that its velocity is many orders of magnitude lower than the speed of light. The transition of a wave from one type to another occurs when the sign of the inequality between \(C\) and \(V_A\) changes. For

\[ \Theta^\circ=\frac{\pi}{2}; \qquad U_1=\pm\sqrt{V_A^2+C^2}; \qquad U_3=0. \tag{9} \]

The motion of the substance in the particular case under consideration occurs along the direction of propagation; therefore the wave in the plasma is longitudinal, as is a sound wave.

Of interest is the general case of the passage of elastic oscillations through a dense plasma located in a magnetic field, under the condition that the wave moves in any direction, when the angle \(|\vec H\cdot \vec C|=\Theta^\circ\). In this case the degree of compression of the plasma

\[ \frac{P'}{P_0}=\frac{1}{U_1}V_z \tag{10} \]

will be smaller than in the propagation of a sound wave with velocity \(V_z\) in the absence of a magnetic field, since \(U_1>C\). This phenomenon occurs because the transmission of momentum involves the intrinsic elasticity of the medium and the additional elasticity of the form of the medium, arising from the magnetic field. For this reason, with a smaller compression there arises a quasi-elastic force sufficient to transmit the oscillations further.

As the value of \(\Theta^\circ\) decreases, \(U_1\) also decreases; the wave passes into the faster of the two possible types of waves: the Alfvén wave or the sound wave, which is called the accelerated magnetosonic wave \((U_1>C)\). The accelerated wave is formed as a result of the action of the more powerful of two factors—pressure and magnetic force—which affect the oscillations in one and the same direction. The value \(U_3\) increases as \(\Theta^\circ\) decreases, and the wave passes into the slower of the two waves mentioned. Since \(U_3\leq C\), such a wave is called a retarded magnetosonic wave. It propagates as a result of the action of the less powerful of the two factors mentioned above, while the other factor acts against the first. It is interesting to note that in magnetosonic waves the substance moves in the plane \((\vec K,\vec H_0)\) under the action of electromagnetic forces and the elastic forces of the medium (plasma). When these forces add, the wave moves faster than the speed of sound in the medium in the absence of a magnetic field; if they subtract, it moves more slowly. In the general case, when the wave moves at an angle to the magnetic field, the motions of the substance themselves are neither longitudinal nor transverse; rather, there is one general motion and one general wave. For the case when the magnetic pressure exceeds the pressure of the medium (the low-temperature case) and \(V_A\gg C\), then \(U_1=V_A,\ U_3=0\). Thus, for a “cold” plasma, in which the thermal motions of particles may be neglected, only the accelerated magnetosonic wave remains, whose velocity is equal to the Alfvén velocity. In contrast to the ordinary magnetohydrodynamic Alfvén wave, the velocity of such a wave does not depend on direction, since it is not multiplied by \(\cos\Theta^\circ\), but depends linearly on the magnetic-field strength according to (4), which explains the observational results presented in Fig. 2 on the linear increase of the wave velocity in the region of the outer core [7].

The hypothesis of the existence of the Earth’s inner solid core can also be examined using the conclusions of the theory of propagation of magnetohydrodynamic waves. At the interface between two media in which the wave velocities are different, partial reflection and partial refraction of the incident wave will occur.

In the case of simple waves free of dissipation, when the boundary

between conducting media \(Z=0\) and perpendicular to the undisturbed magnetic field, the magnetohydrodynamic velocities will be equal to \(V_1\) in the region \(Z<0\) and \(V_2\) in the region \(Z>0\). Upon reflection from the surface of a solid conducting body, the velocity of the refracted wave is shifted in phase by \(180^\circ\) relative to the incident wave. The induced magnetic field of the refracted wave has no phase shift. Consequently, at the boundary of a solid body total internal reflection of the wave must occur. This conclusion is also consistent with the fact that the induced magnetic field has no phase shift. In Fig. 2, under the assumption of a solid inner core, reflection of waves at its boundary should have been observed. From the observational data presented in Fig. 2 it follows that the waves pass through the core. It is usually assumed that these are primary waves \(P\), and not secondary waves \(S\). Consequently, according to the plasma hypothesis the inner core cannot be in a solid state.

Upon reflection from a free surface, on the contrary, a phase shift of \(180^\circ\) is observed for the magnetic field, while no phase shift is observed for the wave velocity.

In the case where \(\rho\) and \(V\) vary continuously along a magnetic field line, then, just as in the passage of electromagnetic or sound waves, reflection from successively arranged layers is insignificant. The amplitude of the wave will vary as \(A \simeq \rho^{1/4}\), and the velocity as \(V \simeq \rho^{-1/4}\) (10). For the Earth’s core, an increase in \(\rho\) is observed as one approaches the center of the planet. Therefore one should expect an increase in the amplitude of oscillations, which has not been observed, and a decrease in the propagation velocity of the wave in accordance with the dependence (10) of the velocity on the density of the medium, which is not confirmed by the observational results presented in Fig. 2.

The data shown in Fig. 1 agree satisfactorily with the conclusions of the theory of propagation of magnetohydrodynamic waves in a plasma whose density increases as one approaches the center, as shown in Fig. 3. If it is assumed that at the boundary of the outer core there is a positive charge formed by heavy charged particles that have been displaced to this distance as a result of the centrifugal force, then the magnetic field \(H\) of the circular current formed during the Earth’s rotation determines the magnetic conditions, while the density distribution determines the hydrodynamic conditions for the occurrence of magnetohydrodynamic waves and the linear variation of their velocity in this field. The jump in the density of the medium in the region enriched with heavy particles increases abruptly. The change in the velocity of seismic waves at the boundary of the geosphere \(E\) makes it possible to determine the value of the magnetic-field intensity and to carry out certain calculations according to the inertial-plasma hypothesis of the Earth’s intrinsic magnetic field.

In an analogous manner, the jump in the change of velocity at the second boundary, closer to the center, can be explained by the influence of the magnetic field of the electronic circular current and by the distribution of the density of matter. As follows—

Fig. 3. Distribution of the density of matter as a function of depth.

follows from formula (10): with an increase in the density of matter the wave velocity decreases in proportion to $\rho^{-1/4}$; with an increase in the field strength $H$ the velocity must increase linearly. As a result of the action of these two opposing factors, the velocity retains a constant value. These relations also make it possible to carry out certain determinations of the parameters of the inertial-plasma hypothesis, which qualitatively explains the course of the dependence presented in Fig. 2. In determining the velocity of rotation of the core $E$, one should take into account the change in plasma viscosity in a magnetic field.

§ 3. The inertial-plasma hypothesis of the existence and preservation of the planet’s intrinsic external magnetic and electric fields

Various models of magnetohydrodynamic generators have been considered under the condition of plasma filling of the geosphere. The proposed inertial-plasma hypothesis is based on taking into account continuously acting factors: the centripetal force of gravitation acting on particles in the plasma; the rotation of the Earth and the emergence of centrifugal forces; the plasma filling of the Earth’s core and the formation of a magnetic field by the currents of particles moving in the equatorial region along a circle together with the geosphere including the core; and the action of Coulomb forces.

After a certain separation of charges by mass, as well as by the energy of their carriers, a separation electric field arises, formed by positive charges and electrons concentrated in geospheres of different radius. The field between charges arranged in this way will hinder further separation of charges, which would occur under the action of inertial and gravitational forces. As a result of the joint action of the forces separating the charges and the force of the electric field attracting the charges, as well as the influence of the viscosity of the medium and diffusion processes, a certain constant elevated difference will be established in the concentrations of electrons and positive charges in the inner part of the zone and in its outer part.

In the example of calculation given below, we shall neglect the action of gravitational forces, since, when the latter are taken into account, it is apparently always possible to choose the character of the Boltzmann distribution that ensures agreement of the calculations with the principal phenomena known in geomagnetism.

The rotation of plasma particles occurs with a linear velocity whose magnitude increases with increasing radius of the sphere, which gives a certain effect of centrifugal separation of particles by mass, energy, and charge. Heavy positively charged residues of atoms in the plasma of the core will be driven to the periphery of zone $E$. Thus, as a consequence of the Earth’s rotation one may expect separation of charges in the plasma with depth in layer $E$, the emergence of electrostatic charges and oscillations. After the centrifugal separation of charges in the plasma in layer $E$ and a certain scattering of electrons on atomic residues, an electronic charge rotating in the Earth’s axial magnetic field is created on the inner circular orbit. The axial symmetry of the magnetic field, in turn, stabilizes the presence of ions and electrons on circular orbits and promotes their displacement toward the equatorial plane. If there is an accelerating voltage along such an orbit, then acceleration of the charges and an increase of the current in the orbit will occur, and consequently also an increase in the strength of the magnetic field of axial symmetry [11].

The magnetic fields of the circular currents of positive and negative charges, adding together, give the resultant field of a linear magnet

(dipole). Let us assume that the velocity of the relative displacement of the geospheres is commensurate with the angular velocity \(\omega=73\cdot 10^{-6}\) rad/sec with which the Earth rotates about its axis. The linear velocities of charges located at distances \(R_1=1400\) km from the center and \(R_2=3500\) km, i.e., at the boundaries of layer \(E\), are respectively \(V_1=102\) m/sec and \(V_2=255\) m/sec; here the current \(i_1\) is formed by light charges—electrons—and flows along the inner sphere of smaller radius \(R_1\), while the current \(i_2\) flows along the outer sphere of zone \(E\), whose radius is \(R_2\), and is formed by positive charges associated with the larger mass.

The density of the convection current is \(\delta=\rho V\), where \(\rho\) is the volume charge density and \(V\) is their linear velocity.

Assuming that numerically equal charges move along orbits of radii \(R_1\) and \(R_2\), and that the current channels have equal cross section \(S\) of the turns, one may write

\[ q_1=\rho_1\cdot 2\pi R_1S=q_2=\rho_2\cdot 2\pi R_2S. \tag{1} \]

Whence

\[ R_1\rho_1=R_2\rho_2. \tag{2} \]

Taking into account that the linear velocity is proportional to the radius, we obtain

\[ \delta_1=\rho_1V_1=\delta_2=\rho_2V_2, \tag{3} \]

i.e., the currents \(i_1=i_2=i\) turn out to be equal. Consequently,

\[ i=\delta_1\cdot S=\rho V\pi r^2, \]

where \(r\) is the radius of the cross section, taken to be the same for both turns. Only the radii of the turns along which they flow will differ.

The magnetic flux created by the currents \(i_1\) and \(i_2\) is

\[ \Phi=L_2i_2-L_1i_1=(L_2-L_1)i, \tag{4} \]

where \(L_1\) and \(L_2\) are the inductances of circular circuits with radii \(R_1\) and \(R_2\). Taking into account only the external inductance, we obtain

\[ L_1=\mu_0R_1\left(\ln\frac{8R_1}{r}-2\right);\quad L_2=\mu_0R_2\left(\ln\frac{8R_2}{r}-2\right). \]

The flux of magnetic induction is formed as a result of the superposition of the fluxes due to the currents \(i_1\) and \(i_2\):

\[ \Phi=i(L_2-L_1)=\mu_0 i\left[R_2\ln 8R_2-R_1\ln R_1-(R_2-R_1)\ln r- 2(R_2-R_1)\right]. \tag{5} \]

Substitution of the numerical values gives

\[ \Phi=i(4r-6.08\lg r)\ \text{weber}. \tag{6} \]

For \(r=1000\) m one obtains \(\Phi=23.76\, i\) Wb.

The model of a magnetohydrodynamic generator considered is self-exciting.

Assuming, in accordance with Boltzmann’s principle, that the number of particles of a system located in force fields is in accordance with the energy and proportional to \(e^{-U/kT}\), for different distributions \(U/T\) one may obtain any distribution of volume charge of the form

\[ n=Ae^{-\frac{U_+}{kT}}+Be^{-\frac{U_-}{kT}}, \]

where \(U_+\) and \(U_-\) refer to charges of different sign.

The constants \(A\) and \(B\) are determined by the conditions of ionization and recombination. The quantity \(U\) is composed of three terms

\[ U=mV_g+eV_e+mV_i, \]

where \(e, m\) are the charge and mass of the particle,

\(V_g, V_e, V_i\) are the potentials, respectively, of the gravitational, electrostatic, and inertial fields.

Electrodynamic considerations may be neglected for small intervals of time.

By assigning different values to the quantities \(V_{e,g,i}\) and choosing the corresponding velocities of displacement of the geospheres, one can calculate any values of the field strength. The example given shows that, if certain kinds of forces are neglected (in our case, gravitational ones), one can calculate a field commensurable with the observed one, as, for example, occurs in the drift-current hypothesis.

The restrictions on the actual magnitude of the expected field strength are imposed not by arbitrary estimates of force fields, but by experimental data on the velocity of displacement of the geospheres relative to one another. For example, if in the above calculation one takes angular velocities commensurable with their values for westward drift of up to \(3\)—\(5^\circ\) per century, or linear velocities according to [12], one obtains estimates \(6\)—\(8\) orders of magnitude lower. Even in this case, however, the calculated fields turn out to be \(100\)—\(10000\) times greater than those due to the hydromagnetic effect. This means that it is a permanently acting and fairly intense effect.

In modern magnetohydrodynamic hypotheses, self-excitation of the terrestrial dynamo in a weak magnetic field is assumed. Ya. I. Frenkel’ believed that the source of such a field does not merit physical consideration [13]. It should be supposed that the probability of excitation of the dynamo and the duration of the establishment of its regime are proportional to the intensity of the field. Elucidation of the nature of this field is regarded as one of the cardinal tasks of the theory [12]. Such fields may apparently be produced by fluctuations of currents in the plasma, disturbances of cosmic origin, the Einstein–de Haas gyromagnetic effect, and, finally, differentiation of plasma particles in a force field.

Fluctuation currents have very short relaxation times, which leads to an inevitable contradiction with the durations of the establishment processes. Moreover, their mean densities and magnetic moments (for a Gaussian distribution) in macroscopic volumes and time intervals are zero. This creates enormous difficulties in constructing a correct theory on the basis of fluctuation phenomena.

The hydromagnetic effect, on the contrary, produces a constant magnetization; however, the strength of the corresponding field is considerably smaller (by a factor of \(10^{10}\)) than the observed one, and this field should simply be neglected in comparison with the field generated by charge differentiation in the plasma.

It is tempting to associate the self-excitation of the dynamo with cosmic factors. Fields of this origin may be sufficiently intense and remain stationary for a long time. In this case, however, we knowingly renounce the study of the history of changes in magnetic fields, since there are no ways of reconstructing the sequence of changes of cosmic fields in the past. It was apparently precisely this consideration that gave rise to the above-mentioned view of Ya. I. Frenkel’.

Thus, differentiation in the plasma remains at present the most probable source of the exciting field for the Herzenberg–Bullard dynamo; with its variations, in variants of the velocities of the geospheres, the phenomena of geomagnetism (variations of the dipole moment, inversions, etc.) should be associated. It is not excluded, although unlikely,

that the magnetic effect of differentiation by itself forms the Earth's principal dipole moment. However, it is quite improbable to assume that the plasma in the core remains undifferentiated. This would at least contradict theoretical and experimental data on the state of plasma in the outer magnetosphere.

In the proposed MHD model, motion both along the radius and tangentially is used, both being determined by constantly acting factors: the Earth's rotation and the action of centrifugal gravity. The example considered leads to a conclusion about the direction of the Earth's magnetic field in near-Earth space that is opposite to the observed one. This contradiction is removed by introducing a second hypothesis, following from the adopted position that the near-Earth magnetic field is created by the magnetic materials of the crust, which are magnetized in the field of currents flowing in the Earth's core. Under these conditions, the magnetic flux of the core will close in the Earth's crust. The magnetic field in near-Earth space will have the direction of the flux opposite to the flux closing in the mantle and crust, and will correspond to that observed in nature.

Some consequences follow from the hypothesis, allowing comparison with observations and having theoretical and applied significance. We shall discuss them in the next paragraph.

It can be seen that including gravitational forces in the consideration, differing from inertial forces only in direction, can yield two charge separations along the radius that are opposite in polarity; moreover, if one assumes their predominance over the inertial ones (as occurs, for example, on the Earth's surface), one can avoid introducing the hypothesis of the role of magnetization of the Earth's crust in the formation of the geomagnetic field. In the hypotheses proposed earlier, possibilities were considered for the formation of the Earth's magnetic field due to superposition of the magnetic fields of currents flowing either along the radius or around the Earth's circumference. A third possibility is the superposition of the magnetic fields of currents flowing both along the radius and around the circumference.

In the generator model under consideration, there is an internal magnetic system (the core)—the armature—and an external system (the mantle and crust)—the stator, on which the flux from the armature is closed. In such a system its own internal processes are possible, associated with energy consumption; with armature reaction; with the influence of these processes on the angular velocity of the armature; and various other transient processes.

The materials of the mantle are semiconductors \[14, 13\]. At the boundary of the semiconducting mantle and the overlying dielectric layers of the Earth, electric charges may accumulate and an electric field may arise in the dielectric, where an electric discharge may also begin. In this way it may be possible to estimate the depth at which electric discharges form in the Earth's interior and possible thunderstorm phenomena in rocks.

There is a connection between the Earth's rotation and its magnetic field \[16\]. The change in the length of day, measured astronomically as the drift of the centers of magnetic-field variations, as well as the corresponding accelerations in the mantle, cannot be explained only by changes in sea level, electric currents in the atmosphere, or mountain-building processes. These phenomena may be associated with the exchange of angular momenta between the mantle and the Earth's core. Such an explanation presupposes the existence of a connection between the core and the mantle, accomplished by means of electromagnetic induction, which does not contradict our model of an armature (core)—stator (mantle and crust) and the presence of different angular velocities of rotation of the geospheres. The magnitude of the induction depends on the electrical conductivity of the materials of the mantle and core and on the extent of the toroidal magnetic field in

in the core. These phenomena may be brought into agreement with the model set out above, which treats the core as an internal generator of magnetic fields, and the mantle and crust as a body that receives the action of magnetic fluxes from the core.

During periods of increased solar activity, a decrease in the Earth’s rotation rate is observed. It is known that at the same time there is also an increase in the concentration of charges in the ionosphere, a significant increase in the magnitudes of currents flowing in the atmosphere, and the occurrence of magnetic storms. These phenomena can be linked with one another if one considers the circuit formed by currents in the ionosphere (a low-pressure plasma) and currents in the sphere \(E\), filled with dense plasma at high pressure. Since plasma in the Earth’s core is formed as a consequence of high pressure, it should be assumed that the Earth’s magnetic field formed after the compression of the Earth and the emergence of plasma.

The sources of energy maintaining the necessary motion in the Earth’s core have been regarded as gravitational and flotation-related. In the hypothesis we propose, the sources of energy are gravity and the Earth’s rotation.

B. Gutenberg [16] believed that the displacement of the Earth’s magnetic poles relative to the continents could have occurred either as a result of drift of the Earth’s axis inside the Earth, or as a consequence of the motion of large blocks of the crust and parts of the upper mantle relative to the main part of the Earth’s internal body, or under the action of both these causes. The influence of motions in the Earth’s core on the displacement of the poles is considered negligibly small.

One may also put forward another possible hypothesis concerning the displacement of the Earth’s axis and the magnetic poles, which in general, according to the considerations set out above, should coincide. The interaction of the magnetic fields of orbital currents in the plasma with the magnetic fields in near-Earth space may shift the orbital turn with current without changing the position of the Earth’s axis. The proposed inertial-plasma hypothesis introduces into consideration a large number of parameters whose variation may be accompanied by changes in the values of the circular ionic and electronic currents even at a constant rotation rate \(\omega\). Among them we note changes in the linear velocity, in the concentration and magnitude of the charges of the ions, in the concentration of electrons in the orbit, etc. A large number of parameters makes it possible to explain more fully the observed phenomena of displacement of the magnetic poles relative to the geographic ones.

According to the principal equation of our hypothesis, the Earth’s magnetic field is formed as a result of magnetization by the difference of magnetic fluxes created by the circular current of ions along an orbit of larger (smaller) radius and by the opposing flux of a circular electron current along an orbit of smaller (larger) radius. A change in the sign of this difference of fluxes may occur as a result of a change in the magnitude of the circular currents, whose value is determined by the magnitude and direction of the velocity of rotation of the charges and by the ratio of gravitational and centrifugal forces. The observed displacement of the position of the magnetic poles within \(30^\circ\) is explicable when one takes into account the known displacement of the Earth’s geographic poles and the position of the Earth’s axis of rotation in space. The interchange of the geographic locations of the Earth’s northern and southern magnetic poles, which has occurred over its geological evolution, is in this case connected with a change in the direction of the Earth’s rotation or in the ratio between the centrifugal and centripetal forces of orientation of the geographic poles and the Earth’s axis of rotation, and not with convection of matter flows in the mantle, which account for local linear anomalies of the magnetic field, discovered, for example, in the eastern part of the Pacific Ocean.

As a cause of changes in the position of the Earth’s magnetic poles one may consider its collisions with other bodies. The mechanical and electromagnetic effects that arise in this case may disturb the hydrodynamic conditions and affect the Earth’s magnetic field.

The hypothesis of the existence of plasma in the zone of the Earth’s outer core makes it possible to consider and explain the following questions: the existence of the Earth’s magnetic field, the nonconstant rate of the Earth’s rotation during magnetic storms and increased solar activity, and other phenomena. Planets whose dimensions are insufficient to ensure the above-mentioned pressure values of 1.4 megabars and higher in their interiors will not have a plasma core.

Celestial bodies of very large mass, having a cold envelope at an internal pressure of many millions of bars, will have plasma cores, within which nuclear processes under the influence of pressure are also possible. As a result of nuclear processes, especially with a high content of active nuclei, the temperature inside a body of large mass rises to a value at which the occurrence of thermonuclear reactions, the heating of the body, and the transition of matter into the plasma state throughout the entire volume become possible.

The high pressure and radioactive radiation that cause ionization and the formation of plasma in the core are permanently acting factors. The conditions for recombination also, probably, remain constant; therefore it may be assumed that in the zone under consideration a high constant concentration of charges in the plasma will be maintained. In the scheme considered, a layer arises in the plasma whose outer surface is charged, for example, positively, and whose inner surface is charged negatively. The polarized layer of plasma, located in the equatorial region, forms a kind of large electret. In the polarized layer thus formed—the electret—there are electric forces of attraction; therefore transverse seismic oscillations are possible in such a layer, as on the surface of water with the participation of surface tension.

The constancy of the Earth’s magnetic field is determined by the fact that the separation of charges in the plasma proceeds until the electric field formed by the positive charge at the periphery of the core and by the negative electric charge in the central parts balances the centrifugal forces. When this condition is fulfilled, the separation of charges in the plasma will cease. Thus the constant charge in the orbit, the constant magnitude of the current of rotating charges, and the intensity of the Earth’s magnetic field are determined. Between the negative charge at the center of the Earth and the positive charge at the periphery, lines of a strong electric field will be established through the plasma. Considering the mantle as a conductor and the crust as a dielectric, we arrive at the consideration of a two-layer capacitor and double layers at the surfaces of the plates. If on the inner side of the boundary between the core and the mantle (in zone E) the positive charge is regarded as concentrated, then consideration of the phenomena of electrostatic induction in the conductor and dielectric polarization leads to a conclusion concerning the sign of the charge at the crust–atmosphere boundary that is in contradiction with practice. This difficulty is removed when account is taken of the predominant influence on the process of differentiation of the core plasma by gravitational forces and of the formation of a peripheral electric charge.

Another path, oriented toward purely experimental verification of the results, consists in abandoning the consideration of electric double layers and taking into account the real relationships of the dielectric properties and conductivity of the geospheres accessible to study (the upper horizons of the crust and mantle, and the atmosphere).

The state of the plasma in the core considered above will not be characterized by thermal equilibrium at the given temperature and equal concentration of positive and negative charges, as is normally inherent in an unperturbed plasma. The periphery of the Earth’s core is enriched with positive charges, and its central regions—with electrons. Equilibrium in the system, for a given temperature and distribution of concentration within the volume, is attained at a definite ratio of the electrostatic, gravitational, centrifugal, and magnetic forces acting on the particles. A volume negative, uncompensated charge at the center of the Earth in the equatorial region creates an external electric field, the lines of force of which extend through the semiconducting, magnetic, and dielectric crust of the Earth, forming an external electric field. In the scheme under consideration, on the basis of the plasma core of the Earth and centrifugal separation of charges, the preservation of the Earth’s residual negative charge is also explained. The shielding action of a strong positive electric charge rotating in the equatorial plane must considerably weaken or extinguish the electric field of the volume negative charge. On the Earth’s surface, in the plane of the equator, there should be a shadow from this screen. Therefore one may expect that the constant electric field of the Earth in the equatorial region should normally be smaller than in the polar regions. Since the Boltzmann distribution of particles mentioned above need not necessarily be symmetric, in the general case one should assume the presence of shadows of similar origin.

§ 4. Theoretical and Applied Significance, Ways of Substantiating and Testing the Hypothesis

A theory of the origin of the Earth’s magnetic field must describe the mechanism by which charges arise and the system of their motion in the Earth’s core, proceeding from the properties of its matter. A correct theory of geomagnetism makes it possible to draw conclusions about processes in the core, its composition, and the physical state of matter.

The inertial-plasma hypothesis satisfies these requirements. At present, within its framework, it has proved possible to explain qualitatively the origin of the main dipole source of the Earth’s magnetic field either directly by the magnetic effect of plasma differentiation in a force field, or by considering this effect as a source of the magnetic field in which self-excitation of a Herzenberg–Bullard dynamo occurs [3]. It has also proved possible to explain qualitatively such phenomena as the drift of the magnetic poles, the westward drift of the centers of secular variations, and reversals of origin of the nondipole component.

As a result of the interaction of the interior and space, energy is transferred from the region of near-Earth space into the Earth’s interior, the plasma in zone E is heated, and, ultimately, our planet is warmed by the energy of the Sun and the energy from near-Earth space.

It should be thought that the plasma ratio of matter in the outer core E and the transitional layer F will be characterized by plasma oscillations with a frequency determined by the electron concentration. These layers must also possess radio-waveguide properties. Therefore sounding of the plasma layers E and F would be possible with the aid of electromagnetic waves. Under the influence of oscillatory motions of the plasma, particles in the plasma can form internal electric fields. Under the action of currents flowing along the boundary of the plasma, internal and external magnetic fields will arise. The incidence of elastic longitudinal waves of type P on layer E, filled with plasma, must be accompanied by

with the occurrence of the magnetohydrodynamic low-frequency oscillations considered above, which are weakly absorbed in rocks. Experiments may be arranged to detect such electromagnetic waves emitted by the plasma from layer E when elastic waves impinge on it. This also constitutes one of the ways of testing the hypothesis.

Measurements of the magnetic-field intensity near the Moon by means of the Soviet automatic stations of the “Luna” series made it possible to conclude that the Moon has no intrinsic magnetic field or magnetic poles. For this reason, no changes in magnetic intensity with distance near this body were observed. By its nature, the Moon’s weak magnetic field, which amounts to 24–38 gammas, whereas that of the Earth varies from 30,000 to 74,000 gammas, may be regarded as an interplanetary field deformed by the Moon [18].

As a result of studies of the circumplanetary space of the planet Venus by means of the automatic station “Venera-4,” it was established that the planet Venus has practically no intrinsic magnetic field. For this reason, Venus also has no radiation belts [19]. The absence of an intrinsic magnetic field in small celestial bodies—for example, the Moon—permits the conclusion that these celestial bodies lack a plasma core. For this reason one should expect that the planet Mercury, which has a small mass, will also have no intrinsic electric and magnetic field.

In the crystalline rocks and breccias delivered by “Apollo-11,” natural remanent magnetization was discovered. These data indicate that in past epochs the Moon could have had a magnetic field with an intensity amounting to several percent of the terrestrial field. The Moon’s magnetic field, which existed 3.7 billion years ago, could have arisen as a result of currents accompanying the motion of the Moon’s liquid interior, and of the action of the Earth’s magnetic field at those times when the Moon was closer to the Earth [20]. The absence of an intrinsic magnetic field probably does not exclude the presence of a plasma core in larger celestial bodies. It does not contradict the inertial-plasma hypothesis, for example, that the planet Venus, whose dimensions and mass are almost equal to the Earth’s, lacks a magnetic field. In fact, according to our hypothesis, the Earth’s external magnetic field is created by the magnetized rocks of the crust. On Venus the crust is hot: it is at a temperature above the Curie point. The second circumstance determining the small value of Venus’s magnetic field is that this planet rotates almost two hundred times more slowly than the Earth. This accordingly determines a decrease in the values of the current and of the magnetic flux along the axis of this planet by no less than two orders of magnitude in comparison with terrestrial values. The value of the magnetic flux obtained under these conditions is small and, probably, difficult to measure with instruments designed for these purposes.

With the aid of the spacecraft “Venera-4” and “Mariner-5,” launched toward Venus in 1967, it was established that this planet has no noticeable magnetic field of a dipole nature [21]. The presence of the Sun’s intrinsic magnetic field is also a consequence of the emergence of a magnetic field during the regular circular motion of plasma particles and of the superposition of the magnetic fields of irregular currents in the body of the Sun. One should expect the presence of strong intrinsic electric and magnetic fields in Jupiter, whose large mass provides conditions for the possible existence of a plasma core of a planet of large radius.

It is probably possible to state the converse proposition as well: the presence of a planet’s intrinsic electric and magnetic fields permits one to think that the body consists of plasma or that such a celestial body has a plasma core rotating with high velocity.

There are two principal cosmological hypotheses for the evolution of celestial bodies. One of them proceeds from the gravitational compression and heating of bodies, the other from the expansion and cooling of bodies. In the proposed hypothesis one considers the initial compression and heating to temperatures at which thermonuclear reactions on atomic nuclei begin, the course of reactions, and the transition of matter into the plasma state. Thus, both hypotheses may be applied to explain certain stages in the development of a celestial body.

Small celestial bodies that do not have a plasma core will cool and contract. Bodies of large mass that have a plasma core will develop according to a more complex law, determined by the mass of the body and by the reserves of gravitational energy in the system.

Under the action of high pressure, nuclear processes are possible—for example, \(K\)-capture [22]—and the formation of radioactive nuclei in the plasma center of a planet. The nuclei of radioactive atoms migrate to the periphery, capturing at the plasma boundary the number of electrons necessary for the equilibrium state of the system and forming an atom. By flows of matter in the mantle, radical atoms are carried throughout the volume of the celestial body. The radioactive decay of these atoms maintains the heat balance of the celestial body at a certain level. It is assumed that the formation of radioactive atomic nuclei is a continuous process until the mass of the body creates, at the center, pressures of millions of atmospheres, necessary for the formation of plasma and the occurrence of intranuclear processes.

A hypothesis on the evolution of a planet must answer many questions, but the chief one is the heat balance of the celestial body. The heat balance explains the physical properties of the body, its structure and chemical composition, and the further evolution of the cooling and heating of the body. The hypothesis described proceeds only from the objective prerequisites for the existence of the planet’s mass and of gravitation as a property of matter.

It has been shown that the energy released during compression is insufficient to explain the thermal evolution of the Earth. This quantity must be supplemented by the energy of nuclear fission and thermonuclear energy, which is released during compression. One may speak of density fluctuations in the plasma. At a high local plasma density such as on the Sun, thermonuclear processes occur and energy is released in this volume. Pressure and temperature alter the chemical properties of elements and may bring about nuclear and thermonuclear processes, which change the chemical composition of the planet and maintain the high temperature of the celestial body. These processes are possible under the necessary condition that the mass of the planet be not less than a certain value \(M_x\). If the mass of the planet is less than \(M_x\), then the body cools when the processes of radioactive decay in it come to an end.

When the mass of the body is greater than \(M_x\), but less than \(M_y\), nuclear processes and the formation of new chemical elements migrating to the periphery will proceed in the planet’s plasma core. When the mass of the body is very large, greater than \(M_y\), as in the Sun or Jupiter, vigorous heating processes will proceed in the plasma core of the body.

We have developed a connection between ideas about the plasma structure of the core and the doctrine of the origin of electrification of the Earth’s interior, of electric discharges in the Earth, of the distribution of radioactive isotopes and radiation, and also of the planet’s thermal fields. The applied significance of these problems and the ways of substantiating and verifying the hypothesis on this basis have been indicated.

In the future it is necessary to consider a rigorous quantitative description of the processes in the core of a celestial body on the basis of plasma concepts. Experimental confirmation of these concepts is also necessary.

The plasma core, owing to the nonuniformity of the magnetic fields localized in it, is a medium that is nonuniform and anisotropic with respect to the propagation velocities of seismic (magnetohydrodynamic and magnetosonic) waves. The latter should manifest itself, for large epicentral distances, in a dependence of the wave travel time on the path, the emergence angle of the rays, and the apparent velocity, as well as on the geomagnetic latitudes and longitudes of the earthquake focus and the observation point. The existence of such a dependence is highly probable, since it is known that, for large epicentral distances, these quantities undergo significant variations [3].

If, on the basis of inertial-plasma concepts, it were possible to introduce into the seismic-ray equation for a coaxially spherically inhomogeneous medium magnetohydrodynamic corrections that would reduce the above-mentioned scatter in the experimental data and, accordingly, reduce the errors in determining the locations of the foci of distant earthquakes, this would be the most reliable proof of the hypothesis. Such work would have applied significance. The direct ray of a wave propagating through the core at large epicentral distances will be brachistochronic. The use of these waves has advantages over work with surface waves, since in this case a large gain is obtained in the arrival time of the signal and in the promptness of accounting for seismic information. The latter is very important in designing automatic systems for the registration and processing of seismic signals, in particular “large seismic arrays.”

In one of the recent studies, five million models of the Earth were considered with the aid of a computer [23]. The results obtained were compared with the parameters of the planet: the moment of inertia, the mass of the Earth, the velocities of longitudinal and transverse seismic waves, the density distribution in the mantle, the density of the core, and so on, which made it possible to select three plausible models. According to these three models, the radius of the core is determined to be 1280 km, i.e., 18–22 km greater than the generally accepted value. The density of the inner core reaches \(13.3\text{–}13.7\ \mathrm{g/cm^3}\), instead of the accepted \(12\ \mathrm{g/cm^3}\).

The value of the density of matter in the outer core, which the investigator F. Press considers liquid, lies within the range \(9.4\text{–}10.0\ \mathrm{g/cm^3}\). According to these results, the upper mantle is strongly inhomogeneous both in the vertical and in the horizontal directions, which, in F. Press’s opinion, is a consequence of instability caused by volcanism, seismic waves, and variations in heat and magnetic fluxes. A model of the Earth with a plasma core was apparently not considered. The plasma hypothesis of the core requires further theoretical substantiation, a quantitative description of phenomena that have thus far been explained only qualitatively, and experimental verification of its consequences by comparison with seismological data and observations of the Earth’s electromagnetic field.

The author is grateful to T. Yu. Mopilevskaya for assistance in carrying out the mathematical calculations, and to Associate Professor L. A. Zashchinskii for discussion of the materials and suggestions concerning the work, some of which are reflected in this article.

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