LIGHTNING AND ITS PHYSICAL NATURE

M. A. Bak and N. N. Nikolaevskaya, Leningrad

Introduction

The electrical state of the Earth has from ancient times been the subject of numerous observations and investigations by a wide circle of scholars. However, serious and systematic study of this question began only in the last twenty years, in connection with the solution of a number of major scientific and technical problems. The constant presence of an electric field in the terrestrial atmosphere is well known, as is the existence of two electrical states of the atmosphere—the so-called fair-weather state and the thunderstorm state. Systematic observations of the gradient of the electric field in fair weather, in the most varied regions of the Earth’s surface, show that statistically, in each given region of the atmosphere, there is its own characteristic course of the diurnal and annual variation of this gradient. Near the surface of the Earth, the magnitude of the field gradient in clear weather usually does not go beyond the interval 50–300 V/m, with the gradient directed toward the Earth’s surface[^1]. The most frequently occurring field gradient—about 100 V/m—gives an average density of negative electric charge on the Earth’s surface of the order of 3 electrostatic units per 1 m². With such an average density, the total negative charge of the Earth is expressed by the value 0.6 megacoulomb. From this it is easy to calculate the potential of the Earth relative to an infinitely distant point:

\[ V \simeq -10^9\ \mathrm{V}. \]

The constant presence of ions of both signs in the atmosphere con-

negative charge of the Earth within 10 min. However, the electric field in the atmosphere exists constantly, and the negative charge of the Earth does not disappear. The maintenance of the existing, quite definite field gradient is due to the compensating processes that take place. Attempts to detect the agents producing this compensating process have been made repeatedly, but the results obtained cannot be considered sufficiently convincing (see Ch. 1). The fundamental problem of the circulation of electricity in the atmosphere remains open for the time being.

The state of atmospheric electricity during a thunderstorm is, therefore, of great interest not only from a practical, but also from a purely physical point of view. The study of the process of thunderstorm formation, i.e., the elucidation of the mechanism of the additional formation of ions in the atmosphere, the separation of these ions over large distances, and the concentration of ions of like signs in certain volumes of a thundercloud, is the subject of many experimental works and theories. The majestic and grandiose natural phenomenon—lightning, representing an electrical breakdown of an enormous natural and very peculiar capacitor—turns out in reality to be a very complex phenomenon, the nature of which has essentially not yet been clarified, despite the abundance of relevant works (see Ch. 3). The nature of ball lightning and of so-called bead (or string-of-beads) lightning is also a mystery.

We shall not dwell at length on the entirely obvious practical importance for everyone of the scientific study of electrical processes near the Earth’s surface in the atmosphere. We shall merely point out that almost 50% of all accidents at the largest power stations and transmission lines are accidents due to lightning strikes; thousands of people perish every year as a result of thunderstorm discharges. Protective means against thunderstorm discharges are almost always created from purely empirical considerations and often do not justify their purpose².

It will not be superfluous to cite general statistical data concerning the number of thunderstorms occurring over the entire globe. Simultaneously in the atmosphere of the whole globe there occur on average about 1800 thunderstorms³, which gives about 100 lightning flashes per 1 sec. The number of thunderstorms in different places on the Earth’s surface varies; thus, for example, the greatest number of them occurs in equatorial Africa and in the tropics in general, where for each given point of the indicated latitudes it reaches about 200 per year, whereas in the regions of the Caspian Sea coast only 5–10 thunderstorms per year³ are observed. In some regions with few thunderstorms, thunderstorms sometimes do not occur even every year. In general, the number of thunderstorms in one region or another is not determined by its geographical latitude—despite the absence of thunderstorms in the polar regions and their maximum number in the tropics—but depends, apparently, only on local climatic and other conditions⁴. The conditions for the formation of a thunderstorm in a given place are very diverse, and accordingly this or that

a different type of thunderstorm. Despite the diversity of types of thunderstorms, ordinarily all investigations connected with the study of a cloud are carried out for the thermal or frontal type of thunderstorm. These two types of thunderstorms occur in the overwhelming majority of cases and, moreover, are the simplest for the experimental study of processes connected with a thunderstorm, such as: the distribution of potentials in a thundercloud, the measurement of currents, the study of the polarity of individual parts of the cloud, etc. The thermal type of thunderstorm is produced as a result of intense local heating of an area by the rays of the Sun. The frontal type of thunderstorm is produced when a heated moist air current rises along the slope of an advancing descending cold air current (Figs. 1 and 2).

Fig. 1. Diagram of the formation of a thermal thunderstorm

Fig. 2. Diagram of the formation of a frontal thunderstorm

In constructing a theory of thunderstorm formation, the thermal type of thunderstorm is likewise considered (see Ch. 1).

The specificity of the conditions for studying thunderstorms, and especially lightning, has required the development of several special research methods. The creation under laboratory conditions of an environment more or less correctly reflecting the naturally occurring phenomenon is extremely difficult and, in essence, has not yet been achieved. All this, of course, has affected the degree of knowledge of questions of thunderstorm formation and the nature of the thunderstorm discharge. This apparently explains the insufficient systematization of the experimental material that exists at present on this question.

The principal aim of the present article is the desire to set forth more or less systematically the questions concerning thunderstorm formation, thunderstorm discharges, and the mechanism and nature of lightning, on the basis of the available original works in this field.

The present review is divided into four separate parts in the following order: I. Theories of the formation of thunderclouds. II. Methods for studying the thunderstorm discharge. III. Lightning and its physical nature. IV. Basic parameters of lightning.

I. THEORIES OF THE FORMATION OF THUNDERCLOUDS

The study of various thunderstorm phenomena must begin with an explanation of the processes by which the electric fields associated with a thunderstorm are formed. The electric fields existing during a thunderstorm in clouds, and consequently also between clouds or between a cloud and the earth, are the result of the formation and concentration of an enormous quantity of electric charges in different parts of the cloud. The electrification of thunderclouds evidently occurs because of: 1) the creation of ions of both signs from electrically neutral molecules of water and of the gases composing the air, 2) the separation of these ions over comparatively large distances (the bulk of the ions therefore has no opportunity to recombine), and, moreover, 3) the concentration of charges of like sign in different parts of the cloud; all this requires the expenditure of a certain amount of energy. The discovery of the agent at whose expense the indicated work is performed, and the clarification of the actual mechanism for obtaining the required energy—this, in essence, is what a theory of the formation of thunderclouds must explain. A sufficiently large body of experimental material on the study of meteorological and electrical phenomena in the atmosphere will be a reliable criterion of the validity of one theory or another.

Let us turn to the consideration of theories of thunderstorm formation; we shall note that all theories consider, out of the general variety of thunderstorms, only the thermal type of thunderstorm, assuming that in all other cases the principal processes are the same and are only somewhat complicated by a number of external factors, so that the conclusions obtained are easily extended to other types of thunderstorms.

1. Simpson’s theory—the theory of “drop breakup”⁵

Rapidly ascending currents of heated and moist air and the force of gravity are, according to this theory, the principal agents creating large stores of electrical energy in a thundercloud. The theory is based on the well-known experimental fact of the electrification of water drops when they are broken up by a sufficiently rapid air current, the positive charge being acquired by the large drops, while the negative charge is carried away by the small drops and by the air. Simpson’s theory therefore received the name “the theory of drop breakup.” The final formulation of the theory took place by 1927, although its initial propositions had been published as early as 1909.

It is known that water drops of any diameter falling in air under the action of gravity (in the general case—any objects falling in any medium) rather soon after the beginning of the fall acquire a constant velocity relative to the air. Such a “terminal” velocity depends, of course, on the size of the drop; thus, for example, according to Lenard’s data,⁶ a water drop with a diameter of 0.1 cm, in free fall in air, acquires a “terminal” velocity of 4.4 m in 1 sec., while a drop with a diameter of about 0.5 cm—8 m in 1 sec. Velocities greater than the latter are observed in ...

under the given conditions is not successful. Larger drops are not stable; if, however, they are preserved while falling, then, encountering sufficiently strong air resistance, they probably become slightly flattened, which causes increased resistance to the motion and therefore a lower velocity.

Water drops condensing in the cloud fall downward under the action of the gravitational field, encountering a fairly strong air current that always accompanies thunderstorm formation. The vertical component of the current velocity often reaches a value on the order of 8 m per 1 sec. At such relative velocities, large drops are broken up and, consequently, become electrified. The fragmented drops suspended in the air current rise upward, with the smaller drops being carried by the current at relatively higher velocities. The decrease in the velocity of the air current with height and repeated condensation in the upper, colder layers of the atmosphere cause the subsequent fall of water drops. Large drops, already having acquired a small charge, are again broken up, and the process is again repeated. Such, in general outline, is the mechanism of creation, separation, and concentration of electric charges, producing as a result large stores of positive charge in the thunderstorm center of the cloud and negative charge in the upper part of the cloud and in places remote from the thunderstorm center.

The described mechanism of thunderstorm formation is well illustrated in Fig. 3, belonging to Simpson⁵. This structure of a thundercloud, given by Simpson in 1927, underwent substantial changes in connection with his later experimental work⁷.

Such a structure of a thundercloud leads to two important conclusions which, for the overwhelming majority of cases, proved not to correspond to reality (which also served as the reason for the creation of new theories of the process of thunderstorm formation). The first conclusion is that the concentration of charges is extremely large in the region of the thunderstorm center (B), which is positively charged. The greatest gradients are formed in this part of the cloud; therefore lightning discharges occur mainly from this region; these discharges must be positive, i.e., in a discharge to the ground the form of the lightning stroke will be: cloud—plus, ground—minus. The second conclusion is that the negative charge of the thundercloud (A) lies above the positively charged thunderstorm center (see Fig. 3).

In his time Simpson obtained confirmation of his theory by comparing the direction of the branches of lightning with the branches of a spark obtained from an ordinary induction machine. Simpson’s initial experiments on the study of the branching of a spark discharge in the laboratory showed branching of the spark only in a discharge from a positive electrode to the ground⁸. Since photographs of a lightning stroke from a cloud to the ground almost always show branches directed toward the ground, consequently, according to Simpson, lightning originates at the location of the positive charge. Hence follows the positive polarity of the thunderstorm center required by the theory.

However, the experiments of Allibone and Shonland9 rather soon proved the possibility of the propagation of spark branches when the spark passes from a negative center. Moreover, most investigations of the polarity of lightning, especially in discharges to a transmission line10,11,12, showed the presence, and even predominance,

Fig. 3. Structure of a thundercloud (after Simpson).
1—negative rain, 2—positive rain

of a negative polarity of the lightning stroke, which seriously contradicts Simpson’s theory.

The last point that should be cited as evidence of the untenability of certain propositions of Simpson’s theory is the question of the distribution of charges through the thickness of clouds. Leaving aside Simpson’s own investigations of this question, on which we shall dwell in detail somewhat below, it should be noted that the quite careful measurements of Wilson and his school showed that the upper part of a cloud, as a rule, is charged positively, whereas the base of the cloud is endowed with a negative charge12.

Such, in general outline, are the experimental contradictions of the theory which subsequently compelled Simpson (by 1936)7 to carry out a number of additional experiments and to revise certain parts of his theory. Before examining the present state of the question of the structure of a thundercloud, on the basis of the work done by Simpson himself and by a number of other investigators, we shall dwell on the parallel theory of thunderstorm formation that existed alongside it, that of Elster and Geitel, as well as on Wilson’s theory.

2. Elster and Geitel’s Theory13—the “Influence” Theory

As the agent performing the work of electrifying clouds there is taken, along with the strong air current and the force of gravity, the Earth’s normal electric field, directed, as is known, from above downward. This additional factor is very substantial in the theory and makes it possible to explain a number of experimental data that were in principle insoluble in the preceding theory. The Earth’s electric field polarizes water droplets, producing in

...field in them, opposite to the normal fair-weather terrestrial field, independently of the direction of motion of the drops (downward or upward). Large falling drops encounter a multitude of the smallest drops, rapidly carried by the air current. In collisions of large falling drops with small ones flying upward, a redistribution of the charges of the drops occurs, in which the large drops acquire a negative charge, and the small ones a positive one. The reason for such a distribution must be sought in the following: contact of polarized drops very often does not lead to coalescence^14. Small drops slide along the surface of large ones and, separating, continue their path in the air current. In a polarized drop the bottom is positively charged and the top negatively, so that upon collision of oppositely moving drops the negative charge moving upward on the small drop is compensated by the positive charge of the large drop. Thus, after the collision the small drop will be positively charged by the amount of charge lost by the large drop. As a result of the described process, the statistical distribution of charges in the cloud is such that the base of the cloud becomes negative, and its top positive.

This very successful interpretation of the charge distribution within the body of a thundercloud was in its time (1929) used by Wilson^12, who introduced much that was fundamentally new into this theory of thunderstorm formation and constructed a consistently developed theory, assigning an active role in the explanation of the process to air ions of both signs. In connection with this it is appropriate to set forth in detail Wilson’s theory and the criticism of this theory, which will apply entirely also to the theory of Elster and Geitel just presented.

3. Wilson’s Theory^12, ^15 — “the theory of influence and selective collision of drops”

The process of electrification of a thundercloud occurs as a result of the selective contact of polarized raindrops with air ions ordinarily present in the atmosphere.

The mechanism of formation of a thundercloud, in general outline, is as follows. Water vapor, condensing at a certain height, forms water drops, which under the action of gravity fall in the direction of the Earth. A strong air current, always accompanying thunderstorm formation, prevents the free fall of the drops. Small drops are carried upward, some drops are in a suspended state, and large drops, overcoming the force of the air current, fall downward. The ever-present normal electric field of the atmosphere acts on all the forming drops, polarizing them. Ionized air molecules, moving according to their signs in the electric field of the atmosphere, encounter polarized water drops on their path. The number of collisions of a drop with air ions is large, taking into account the size of the drop and the number of ions (\(\sim 1000\) per \(\text{cm}^3\)).

The velocities of motion of air ions do not exceed 3 cm in 1 sec., since the ions possess their maximum velocity only inside the cloud, where the field gradient reaches \(\sim 10\,000\) V/cm, which corresponds, approximately, to a velocity of 3 cm/sec. for an ion mobility of \(0.0003\ \text{cm}^2/\text{V}/\text{sec}\). Such velocities, according to Stokes’ law and the corresponding measurements of Lenard\(^6\), tear away drops freely falling in the field of gravity with a diameter greater than 0.01 cm. An enormous number of drops with a diameter greater than 0.01 cm will therefore fall faster than the positive ions moving downward. The number of such drops is considerably greater than the total number of Simpson’s “half-centimeter” drops.

As a result of the interaction of large and very small polarized drops with air ions, in the presence of a strong upward air current, we obtain negatively charged large drops located at the base of the cloud, and positively charged small and very small water drops at the top of the cloud, for the following quite obvious reasons: a falling polarized drop will attract positive ions coming from behind; but, owing to the difference in velocities, these ions will not catch up with the large drop. The positive ions which are overtaken by the drop will, roughly speaking, avoid it, since the lower part of the polarized drop has an induced positive charge. Negative ions moving toward the large drops will be attracted by them. Depending on the magnitudes of the velocities of the negative ions and of the drops (the directions of the velocities being opposite), the total charge of the drop will become more and more negative, as the positive charge at the bottom of the drop is compensated. Something analogous will occur with drops whose diameter is less than 0.01 cm. These drops will be overtaken by positive ions and will accordingly become positively charged. The air current will filter the large drops from the small ones, forming a cloud with a negatively charged base and a positively charged top. Such a dipole-like distribution of charges in the cloud will further increase the polarization of the drops which have not yet been separated, and this will promote greater electrification of drops newly arriving at the base of the cloud. As a result of considering thunderstorm formation according to Wilson, one obtains a rapidly developing process of charge separation in a cloud, accelerating with time and usually leading subsequently to a thunderstorm discharge—to lightning.

Experimental confirmation of the described mechanism for the acquisition of charges by water drops moving in the electric field of a plane condenser was carried out by Gott\(^16\).

Measurements of the distribution of charges in a cloud made by Wilson agree with the conclusions of his theory. However, experiments of recent years (see below) do not always give the Wilson distribution, in which the base of the cloud is negatively charged and the top positively.

The gradients of the electric field in a cloud of the described type, theo-

...theoretically be relatively large, so that, for example, despite the negative surface charge density on the earth in fair weather, the gradient beneath a thundercloud must have the opposite direction. The same may be said of the region located above the cloud. Hypothetically, in these regions the field gradient must have a direction opposite to that of the gradient in fair weather, i.e., from below upward.

On the basis of the foregoing, one can, according to Wilson, explain the commonly observed positively charged rains that occur at the beginning of thunderstorms. The first batch of large falling raindrops has collisions predominantly with positive ions, which under the thundercloud move from below upward. Therefore the drop becomes positively charged while falling.

Without for the moment entering into criticism of the fundamental propositions of Wilson’s theory, let us point out that a number of investigators, and in particular Wilson himself, consider this theory capable of explaining the maintenance of the Earth’s negative charge and of the positive charge of the upper conducting layers of the atmosphere. The existing Wigand—Wilson hypothesis, which assumes that the electric current of fair weather is compensated by currents during thunderstorm phenomena, takes its origin from this theory of thunderstorm formation.

As was indicated in the introduction, the normal electric current from the atmosphere to the Earth is capable, in the course of 10 minutes, of neutralizing the entire negative charge of the Earth. The absence of this fact is explained, according to the Wigand—Wilson hypothesis, by the large electric fields in thunderclouds of the type: base—minus, top—plus. The reverse direction of the field gradients beneath a thundercloud and above it gives rise to compensating processes. Strong electric fields in the region of an occurring thunderstorm extraordinarily increase the densities of the reverse current, which sometimes reach values thousands and tens of thousands of times greater than the current density of fair weather. By way of example, let us note that currents of such great densities do in fact occur during a thunderstorm near the tops of trees, the masts of ships, and generally above protrusions on the earth’s surface. These discharge points beneath thunderclouds sometimes even glow, which is accompanied by a slight crackling (corona). The phenomenon itself is traditionally called St. Elmo’s fire.

However, the relatively large current densities existing beneath thunderclouds do not always correspond in sign to Wilson’s theory. For example, St. Elmo’s fire is known to occur with a positively charged base of the cloud, often in mountains during snowfall. In this case the Earth is the cathode, and the glow itself is usually narrower and weaker. How rare these cases are in comparison with cases confirming Wilson’s theory is not statistically known, but there are grounds for considering them not so very rare.

The predominance of negative lightning strokes as compared with positive ones will also contribute to the maintenance of the Earth’s negative charge in accordance with the Wigand—Wilson theory.

The maintenance of a positive charge in the upper layers of the atmosphere is carried out, according to this theory, by the upper positive layer of the cloud, which theoretically should have a density of electric charges greater than the density of the charges located above it in the atmosphere. The field gradient is large and directed from the top of the cloud upward, toward the upper layers of the atmosphere; this gradient redistributes charges in the opposite way to what occurs in fair weather.

Let us note that the understanding just presented of the maintenance of the fair-weather field according to Wilson is supported by the fact that the daily variation of the mean fair-weather field gradient follows rather accurately the daily variation of thunderstorm activity[^17].

The general statistical distribution of thunderstorms over the whole earth and an approximate calculation of the total amount of electricity redistributed with time quantitatively confirm what has been said, if, of course, the theory and its conclusions are considered valid. Here, however, much additional experimental material is required, which will help decide to what extent thunderstorms perform the function of maintaining the negative charge of the Earth, and to what extent the number of negative lightning strokes predominates over positive ones. Part of such material has in recent years been obtained by opponents of Wilson’s theory, and it has turned out that these data (see below) quite convincingly refute not only the conclusions of the theory, but also the foundations of the theory itself[^7],[^11],[^12].

Thus, for example, experimental data rather often give charge distributions in a cloud different from Wilson’s—namely, such as lead to the appearance of positive lightning. Moreover, although the number of lightning strokes by polarity is not equiprobable, the percentage of positive discharges is sufficiently large (see Chapter 4).

Experimental material on the distribution of temperatures in a cloud, to a considerable degree, authoritatively refutes the fundamental propositions of Wilson’s theory (see below). In this connection, before proceeding to a discussion of other existing theories of thunderstorm formation, it is necessary to give an account of the state of the Simpson and Wilson theories up to the present period, 1939. This is all the more necessary because these two theories enjoy the greatest popularity.

The scientific polemic conducted over a number of years between these two schools still has not led to a definite result sufficiently confirming either theory. A number of conclusions from the experiments of one school at times confirm some part of the views of the other theory, and so on. The latest major work by Simpson and Scrase[^7] deals rather sharply with Wilson’s theory, but by no means with “the same sharpness” confirms the theory of “drop fragmentation.”

Most measurements were usually made from the surface of the Earth and therefore could not be considered controls for resolving the question of the arrangement of charges in a thundercloud. Therefore, in 1937 Simpson carried out extensive investigations of the actual

of the distribution of polarity in different parts of a thundercloud. For this purpose, balloons—sondes—were used, which made it possible to record polarities, changes in polarity, magnitudes of electric-field gradients, temperature, etc., starting from the Earth’s surface up to regions situated above the tops of thunderclouds, i.e., up to 8–10 km above sea level. The instrument that records the field is called an altielectrograph and is based on the principle of the leakage of charges from a point conductor in the form of a luminous discharge in a sufficiently strong electric field. This instrument was used in its time [Whipple and Scrase, 1936] for measurements of potential gradients at the Earth’s surface during fair weather and thunderstorms.

Let us briefly summarize the main results of Simpson’s investigations. Measurements of field gradients showed that near the Earth’s surface the gradients are comparatively small—rarely exceeding 300 V/cm (apart from the moments following a lightning stroke). There is no appreciable increase in the gradient when the cloud base is reached. Large gradients were observed at altitudes of 5 km and were not encountered at altitudes below 2 km. At these altitudes (5 km) the air temperature was below zero, so that the water droplets present were probably in a frozen state.

The polarity in the cloud was found in most cases to be “compromise” (Fig. 4), i.e., at first glance seeming to confirm both Simpson’s distribution and Wilson’s distribution. The main body of the cloud is negatively charged; the upper part of the cloud is usually positively charged. A local concentration of positive charges has been found rather often at the base of the cloud. Usually a heavy, large-drop rain is produced at this place. There are sometimes several centers or regions with a positive concentrated charge. Thus a negative field is obtained beneath the cloud, except in the regions of the thunderstorm center. Such, in general outline, are the conclusions from Simpson’s latest work, which are well illustrated in Fig. 4, where the polarities of the separate parts of a thundercloud and the distribution of temperature through the thickness of the cloud are given correspondingly.

Summarizing these investigations, Simpson^7 gives three propositions confirming his theory:

a) the presence of regions of concentration of positive charges in the lower parts of the cloud;

b) these regions of positive electricity are closely connected with the active regions of thunderstorms, where ascending air currents are strongly developed and from which the greatest fall of rain occurs;

c) this accumulation of positive charges has been found in those parts of the cloud where the temperature is above the freezing point.

The data concerning the remaining mass of the cloud, its upper part, remain outside the scope of the theory. The theory of “drop breakup” cannot explain the reason for the presence of positive charges in the upper part of a thundercloud.

Criticism of Wilson’s theory of thunderstorm formation from the point of view of Simpson’s recent investigations follows clearly from the conclusions presented above. The distribution of gradients, and especially of temperatures, in the cloud contradicts Wilson’s “influence” theory to a very great extent. Indeed, in considering the temperature characteristic of the cloud (Fig. 4), Simpson notes that the boundary between the positively charged top of the cloud and the underlying negatively charged region is located at altitudes of 4–6 km, where the tem-

Fig. 4. Structure of a thunderstorm cloud (after Simpson and Scrase). 1—positive rain, 2—negative rain

perature is of the order of \(-10^\circ\text{C}\), i.e., considerably below the freezing point of water. Consequently, in this part raindrops do not exist, whereas according to Wilson it is precisely here, at the boundary, that raindrops become charged and are distributed. True, supercooling of water may occur, but when drops coalesce freezing will occur immediately. Thus, the water in the upper part of the cloud and in its middle is in a crystalline state, in the form of ice needles and plates, tending to arrange themselves horizontally while falling under the action of gravity.

It is known that ice is a poor conductor and does not polarize; moreover, the shape of the hailstones, their orientation, and their rate of fall cannot lead to the formation of induced charges and, consequently, they will not become charged at all. All this gives a clear idea that Wilson’s theory does not explain even the process of separation of charges found by Simpson.

As regards the role of thunderstorms as the principal factor maintaining the negative charge of the Earth and, consequently, maintaining the general circulation of electricity in the atmosphere, Simpson’s investigations of potential gradients throughout the entire thickness of the cloud do not confirm the corresponding conclusion of the adherents of Wilson’s school. Indeed, although a positively charged summit of the cloud was found, the magnitude of the gradients proved extremely small. The greatest field turned out to be of the order of \(-300\ \text{V}/\text{cm}\).

Of course, additional and more precise measurements will be able to answer this question more clearly, although everything done by Simp-

is not, very strongly convinces one that thunderstorms apparently do not determine the relative constancy of the Earth’s charge.

The detailed analysis given above of the two principal theories of thunderstorm formation shows that in reality the phenomenon under consideration cannot be modeled so simply. Although each of the theories seems quite simple and complete, the experimental material is not explained by either of them. It is doubtful that any fortunate combination of Simpson’s and Wilson’s theories will give the correct answer.

4. The theory of “evaporation and condensation.”

The theory given by Gunn^17,18 is based on the long-known experimental fact of the electrification of drops during condensation and evaporation. At the end of the eighteenth century Laplace expressed the possibility of a concentration of electric charges during thunderstorms as a consequence of the electrification of water droplets associated with condensation and evaporation. It turns out that the electrification of a water drop that takes place is positive during evaporation and negative during condensation. The equilibrium charge of each drop is determined by its radius and is proportional to it. Thus each drop and the ionized water vapor surrounding it is regarded as an “electrical concentration cell.” All earlier investigations ignored the fact of the successive change of states of a raindrop and the importance of this change, which affects the electrical properties of rain and thunderclouds. In fact, in thunderclouds and during their formation, moist air is subjected to various temperature effects before the raindrops that fall to the Earth’s surface are finally formed. In Gunn’s opinion, an entirely natural dynamic equilibrium is obtained in the cloud, in each individual cell of it, instead of the static distribution that is usually discussed in the preceding theories. It is thought that the process of thunderstorm formation according to Simpson and Wilson cannot be considered a completely static equilibrium, but from Gunn’s point of view this is perhaps indeed so.

The essence of the theory is that the interaction of various factors, such as pressure, temperature change, air currents, the amount of water vapor, etc., creates a definite dynamic process in the atmosphere. As a result of such interaction, a thundercloud with a negative charge at its base is obtained.

However, it is probable that the presence of a low warm air current can also create a positive charge at the base. All approximate calculations of a number of quantities, such as, for example, potential differences, electric field, electric moments, currents, etc., agree well with observations. Nevertheless, in a number of review articles that appeared after 1935, i.e. after the publication of this theory, and also in Simpson, Schonland, Allibone, and others, there is a complete absence of a description of this theory and criticism of it

Recent temperature studies by Simpson (see above) seriously refute the fundamental propositions of this theory. The main part of the cloud is at a temperature below zero, and therefore one can regard, in Gunn’s sense, only the lower part of the cloud, which also includes positively charged thunderstorm centers with large gradients. Gunn’s theory cannot yield such a distribution of gradients.

Equally little known is the theory of thunderstorm formation whose author is considered to be Dossere.

5. Dossere’s Theory^19,20^—the “Photoelectric Theory”

The author believes that the action of the Sun’s ultraviolet rays on the cloud that has formed causes positive electrification of the cloud top, where crystals of “dry” ice are located. Indeed, the photoeffect from “dry” ice under the action of ultraviolet radiation is relatively large; on the other hand, the distribution of temperatures in the cloud likewise corresponds to the presence of ice at its top, but no especially convincing calculations are given in this regard. Lightning is regarded by the author as a means of rapid and direct transfer of charges, occurring between clouds or between a cloud and the Earth. The polarity of the lightning depends on the part of the cloud in which the lightning is ignited. Rain is represented as melting hail. All this the author of the theory considers to confirm the theory of positive photoelectrification of ice at the cloud top by the Sun’s rays. Simpson’s investigations did not reveal, as has already been indicated, large field gradients at the cloud top, and therefore there is no reason for thunderstorm discharges to arise. On the other hand, the presence of regions of large positive charge in the middle and at the base of the cloud can hardly be explained by this theory.

The brief account given of the existing theories of thunderstorm formation is illustrated quite well in Table 1, where a comparison of these theories with one another is presented clearly.

As was indicated, experimental investigations of recent years have shown a negative charge at the base of the cloud and a positive charge at the top. In addition, regions with a positive charge have been found at the base, which Simpson calls thunderstorm centers. It is quite possible that negative centers are equally present at the base of the cloud.

Concluding the account of the theories of the formation of thunderclouds, it is necessary to note the insufficiently satisfactory state of the theory of thunderstorms. This in turn is seriously reflected in the understanding of the mechanism of the thunderstorm discharge—lightning. The subsequent presentation of questions connected with the mechanism and nature of lightning will fully confirm this conclusion.

Table 1

Name of theory	Author	Electrification process	Agents	Charge distribution in the cloud: base	Charge distribution in the cloud: top
Theory of “droplet breakup”	Simpson	Breakup of raindrops	Air current and gravity	+	−
Theory of “influence”	Elster and Geitel	Collision of polarized drops	Air current, gravity, and the electric field in the atmosphere	−	+
Theory of “influence and selective collision”	Wilson	Selective collision of polarized drops with air ions	Electric field in the atmosphere, charges of ions, air current, and gravity	−	+
Theory of “evaporation and condensation”	Gunn	Electrification of drops during evaporation and condensation	Temperature, pressure, air current, and gravity	−	+
Theory of the photoelectric effect	Doseré	Photoeffect from “dry” ice	Ultraviolet radiation of the Sun, temperature, air current, and gravity	−	+

II. METHOD FOR STUDYING A THUNDERSTORM DISCHARGE

Alongside the usual methods for studying impulse voltage that are employed in laboratory practice, the study of the thunderstorm discharge required the development of an entirely new measurement technique. The specificity of the setting in which the thunderstorm discharge occurs, and the conditions accompanying the registration of the effect in the field—spontaneity of lightning and large fluctuations of the discharge parameters (see Ch. IV); the comparatively large spatial scatter of the phenomenon and its relative rarity and short duration; the variety of types of thunderstorm discharge and the complexity of each individual type (see below)—all this substantially complicates the process of measuring lightning parameters. The statistical value of one or another measurement is very often rather small in connection with the listed conditions under which one has to observe and record a thunderstorm discharge in nature.

All existing methods of recording lightning can be roughly divided into two groups. The first group includes methods for recording the time sequence of the development of a thunderstorm discharge, with all the measurements that follow from this, whereas the second group may include general integral measurements of lightning parameters. Accordingly, let us list the principal existing methods and techniques for recording lightning and its parameters, giving brief descriptions and characteristics of the instruments and installations that carry them out.

Photographing lightning with an ordinary camera was probably begun soon after the discovery of photography. A stereoscopic photograph can give a spatial picture of the general luminosity of the channel through which the thunderstorm discharge has passed. Of course, it is not possible to obtain in this way any process of lightning development. A spatiotemporal scanning of the phenomenon can evidently be carried out by creating relative motion between the object and the photographic film. This, in essence, is the basis of the fundamental arrangement of the so-called Boys camera, proposed by him at the end of the last century.^(21, 22)

The Boys camera is at present the principal instrument with which the process of development of a thunderstorm discharge is photographed. It is true that this camera, in its modern version, differs very greatly from the original one, but the fundamental idea of the relative displacement of the object and the film remains unchanged in the corresponding measurements.

The motion of the object relative to the photographic film

Fig. 5. Schematic arrangement of a two-lens Boys camera. 1, 3—lenses, 2—prisms, 4—film

can be obtained by rotating the lens while the film is at rest, or by rotating the film; in the general case, the lens and the film may be rotated (or moved) at different speeds. Fig. 5 schematically shows the arrangement of a Boys camera with two lenses.

As an example of photographing lightning with a Boys camera, one may cite the excellent photographs obtained by Schonland. Figs. 6a and 6b show photographs of one and the same lightning discharge, taken with a rapidly rotating and a slowly rotating camera. In the photograph in Fig. 6a the character of the development of the lightning, consisting of a series of successive discharges—the so-called multiple discharge (see Chap. III)—is visible. The slow sweep (Fig. 6b) does not make it possible to trace the development of the thunderstorm discharge.

Fig. 6a. Photograph of lightning, obtained with the aid of a rapidly rotating camera. A series of successive discharges is clearly visible.

In addition to the useful distortion of the photograph due to the relative displacement of the lens and the film, there are various harmful factors that distort the photograph. To take the harmful distortions into account, and for additional control, a two-lens camera is sometimes used. The photographing is carried out by two diametrically arranged lenses on photographic film placed on the inner side of the drum (Fig. 5). The lenses in a two-lens camera can be rotated at different, but quite definite, speeds, thereby obtaining different time sweeps. There is no need to fear superposition of the photographs, since one lens gives an image on the upper part of the film, and the other on the lower part. The following very important practical point should be noted, which may occur when photographing lightning and may sometimes blur or distort the entire picture. A lightning stroke will be photographed in the best way if, during the discharge, the lens of the camera (or the film) has a direction of velocity close to perpendicular with respect to the path of propagation of the lightning. However,

Fig. 7. Photograph of lightning (McEachron). Left—a picture with a rotating plate. Right—an ordinary photograph of the same discharge

Twelve lenses produced a sweep, five—a conventional photograph. A camera with this number of lenses covered the whole horizon. The motion of the film was effected by a motor, and not by hand, as in the experiments of Schonland \({}^{30,31}\) with a two-lens camera.

Concluding the description of the various cameras that give time sweeps, let us note that this method of recording the process of development of a thunderstorm discharge gives a two-dimensional picture. The third dimension here is time, calculated from the values of the displacement and the relative velocities of motion of the lenses and the film. Measurements of a number of linear parameters of lightning should, of course, be given with allowance for the three-dimensionality of space. The factor applied to take account of the third spatial dimension is usually obtained by comparing the two-dimensional image (photograph) with its projection on the axis connecting the beginning and end of the zigzag picture. Statistically, the correction for three-dimensionality usually does not exceed \(30\%\) relative to the total length of the two-dimensional image \({}^{31}\).

Despite the fact that thunderstorm discharges are photographed comparatively well under ordinary conditions, in sweeps some elements of the lightning are not recorded, owing to insufficient intensity. The use of quartz optics will, of course, increase the intensity; however, up to now quartz has not been used in photographing lightning, although the ultraviolet part of the total radiation of a lightning channel is probably fairly large.

All photographs of lightning refer to night thunderstorms. The development of methods for photographing lightning in daylight is of interest, increasing many times over the efficiency factor. In addition, spectral study of lightning may provide much interesting material from the point of view of elucidating the nature of the thunderstorm discharge.

Space-time registration of the discharge can be carried out not only by the method described above; oscillography also gives a sweep of the phenomenon in time. A peculiarity of this method of registration may be considered the following: along a series

far from always the case. At times the motion of the lens proves to be almost parallel to the direction of the lightning stroke. This often happens in discharges between clouds, if the camera has been set up to photograph a cloud–Earth type stroke. Thus, the time sweep may prove to be of the most varied kind, depending on the mutual orientation of the direction of motion of the thunderstorm discharge and the direction of rotation of the lenses (or film). In connection with this, in order to determine the angle of orientation, and also for certain other reasons, at present the camera is almost always mounted with both moving and stationary lenses (or films). In this case an ordinary photograph and a sweep are obtained (Fig. 7).

Field-experiment conditions require, in order to increase efficiency, the use of the largest solid angle in photographing.^23 For this purpose cameras with a large number of lenses are employed.

Work on the study of lightning, carried out at the Power Engineering Institute of the Academy of Sciences of the USSR and at the All-Union Electrotechnical Institute, deserves great attention in view of the broad scope it has recently assumed, and in view of the achievements that have been made in the construction of apparatus, systematic photography of thunderstorm discharges, interpretation of the discharge mechanism, etc.^24–29

In the study of lightning in the Bakuriani region (1938), a group of workers from the Power Engineering Institute of the Academy of Sciences of the USSR and the All-Union Electrotechnical Institute, under the direction of Prof. Stekolnikov, used a camera with 17 objectives.^27 Lightning was photographed on stationary and moving films with stationary lenses.

Fig. 6b. Photograph of lightning obtained with a slowly rotating camera.

The magnetic method of recording is usually used for measuring lightning currents, determining the polarity of the stroke, etc., and is very widely used in recording lightning overvoltages in transmission lines.

All the listed methods of recording lightning and, in general, impulse voltages, to one degree or another give an overall picture of the phenomenon taking place. However, each method taken separately is very one-sided and at times gives contradictory results. Therefore

Fig. 9. Klydonograms at different polarities of the recorded waves

Fig. 10. Klydonogram obtained on a rotating film. The drawing shows three consecutive discharges.

With time sweep, it becomes possible to quantitatively determine voltages, currents, and quantities of electricity during a discharge. Determining the polarity in the course of a multiple discharge by this method is possible, of course, taking into account the induction effects of the surrounding environment. Generally speaking, induction effects, which appear comparatively often in oscillographic recording, are very difficult to eliminate and at times strongly distort the effect. This circumstance considerably diminishes the value of the oscillographic method.

Simultaneous recording by oscillographs and Boys-type cameras was carried out by MacEachron \(^{33}\), Schonland \(^{32}\), and Stekolnikov \(^{29}\). It was shown that, with a well-adjusted system of oscillographing and photographing, the records obtained are correspondingly identical. A group of collaborators at the VEI, in order to obtain a more complete picture of the thunderstorm discharge, used two oscillographs: one recorded the entire wave, while the other recorded only the wave front.

Fig. 8. Schematic arrangement of an ordinary klydonograph

Let us proceed to a brief description of other instruments that register one or another parameter of lightning and of discharges in general. Among such instruments, first of all, is the klydonograph, invented by Peters \(^{34}\). The schematic diagram of the instrument is shown in Fig. 8. As a result of applying voltage to the electrode, a corona glow appears at its end, which is recorded on the film (the so-called Lichtenberg figures).

Reliable operating results for this instrument are usually obtained for voltages from 1.5 to 30 kV. For higher voltages a voltage divider is used \(^{35}\).

Klydonographs provide an answer regarding the polarity of the discharge from the appearance of the photograph (Fig. 9). There are klydonographs with rotating film \(^{25}\). By creating sufficiently rapid rotation, photographs of successive stages of the process can be obtained; Fig. 10 \(^{24}\) serves as an example. After each lightning stroke, the electrode of the klydonograph is automatically moved horizontally, thus using the remaining area of the film. This greatly facilitates photography under field-research conditions.

Alongside recording the phenomenon photographically and electrically, there exists the method of magnetic recording \(^{27}\). The magnitude of the electric current that has passed through a conductor can be obtained by measuring the residual magnetization of a ferromagnet placed near this conductor. This method of recording was first applied at the end of the last century by Pockels. The polarity of lightning can also be determined by this method. However, in the case of bipolar discharges (see Ch. III), the ferromagnet gives only a difference effect.

Advances in the Physical Sciences, Vol. XXII, No. 3

At present many investigators use all the above-listed methods of recording lightning simultaneously. Duplication of a number of instruments is also a reliable criterion of the correctness of the recording of the phenomenon, and therefore is often practiced. ^{29,32,33}

In conclusion, let us point out that the general methodology of lightning measurements is not always reliable in describing the phenomenon that actually occurs. The errors in determining the required parameters of lightning are almost always fairly large. All this, of course, has a substantial effect on the resolution of a whole series of questions connected with the mechanism of the thunderstorm discharge.

III. LIGHTNING AND ITS PHYSICAL NATURE

Lightning is an electrical discharge between clouds or between a cloud and the Earth. There are three types of lightning: 1) linear lightning, i.e., ordinary lightning, the most widespread kind of lightning, observed in all thunderstorms and consisting of a rectilinear or tortuous, brightly luminous electrical discharge; 2) ball lightning—a brightly luminous ball which flies through the air or remains motionless on some object; ball lightning is a comparatively rare phenomenon; 3) bead lightning, which is a discharge in the form of a chain consisting of separate luminous balls; this type of lightning is the rarest phenomenon.

Of all these types of lightning, linear lightning has been studied most fully, owing to the fact that it is observed in all thunderstorms and, moreover, may to some extent be reproduced under laboratory conditions.

The systematic study of the phenomenon of the thunderstorm discharge begins with the invention by Boys ^{21,22,36} (1900) of a special photographic camera. However, only during the last decade have there been serious achievements in the study of lightning which shed some light on the mechanism of the thunderstorm discharge. In this respect the investigations of Schonland (England) and McEachron (America) deserve great credit. In the USSR the beginning of the systematic study of the thunderstorm discharge dates to 1934–1935, when a comprehensive study of this phenomenon was begun in a field laboratory (under the direction of Prof. Stekolnikov), and at present quite valuable results have already been obtained.

Contrary to the earlier conception of lightning, formed on the basis of visual observations, it has now been established that the thunderstorm discharge is an extremely complex phenomenon. The development of a thunderstorm discharge is now pictured as follows: from a cloud charged for the most part negatively, there appears a weak, luminous discharge, the so-called leader, which moves in the direction of the Earth. When the leader reaches the Earth, an intense, brightly luminous discharge immediately appears, going in the opposite direction, i.e., from the earth to the cloud along the path laid down by the leader. This discharge is called the main or

of the return stroke. Figure 11 shows a photograph obtained in the Boys camera of the leader (on the right) and of the return stroke (on the left). Quite often it is observed that after the main discharge reaches the cloud, after some interval of time a second discharge appears (also consisting of a leader and a main discharge), proceeding along the path of the first discharge, then a third, etc. This multiplicity of lightning, i.e., the appearance of a whole series of successive discharges following one another along one and the same path with small time intervals, was noted long ago (1884). Subsequent investigations by Gaffert37, Walter38, Larson39 with the aid of rotating photographic cameras confirmed the existence of multiple lightning, and, finally, the investigations of Schonland31, 40, McEachron11, 41, Stekolnikov25, 29, and others with an improved Boys camera and oscillographs made it possible to determine the time between individual discharges, the velocity of propagation, and the number and character of their development.

Fig. 11. Discharge with a leader. The arrow indicates the direction of the time sweep.

Along with such leader discharges, discharges are sometimes observed that have no leader. Such discharges will be considered in detail in § 6.

As a result of numerous investigations in recent times, data have been obtained concerning the character of the development of the thunderstorm discharge and its principal parameters, although sufficiently accurate statistical material is not always yet available.

Let us consider all the successive stages of the thunderstorm discharge and their parameters.

1. Leader

a) Types of leaders. Schonland divides leaders into three types: 1) stepped leader, 2) dart-shaped, and 3) dart-stepped leader.

A stepped leader, according to Schonland, always precedes the first stroke of a multiple lightning flash and propagates from the cloud to the Earth in steps, i.e., after leaving the cloud, the discharge travels a certain distance and stops; after some interval of time the discharge appears again and travels along the same path, but a greater distance, then again stops, and so on, until it reaches the Earth, after which the return stroke appears. The length of a step of such a leader is about 50 m. A stepped leader often has branches propagating toward the ground, which terminate in the air without reaching the ground. In this case the return stroke, traveling along the path of such a leader, also gives rise to branches propagating along the paths of the leader branches.

In his latest work Schonland^32 gives data obtained by simultaneous photography and oscillography of lightning. Comparing the measurement results obtained by these two methods, Schonland concludes that the oscillograms of the first stroke of a multiple lightning flash likewise show the stepped character of the leader’s development. Voltage pulsations were found on the oscillograms which, in Schonland’s opinion, correspond to the steps of the leader. In Fig. 12a are shown: a schematic oscillogram (above) and a photograph on moving film (below) of one and the same discharge (the two diagrams are synchronized in time). The pulsations (a) at the beginning of the wave correspond to the steps of the leader in the lower photograph; the abrupt change of field (the peak b) corresponds to the appearance of the return stroke and, finally, the segment c on the oscillogram corresponds to the continued luminosity of the channel after the return stroke has reached the cloud. Fig. 12a also shows subsequent strokes with dart leaders (there are no pulsations). Schonland calls this type of stepped leader the α-type; this type of discharge occurs most often (65%). Another type of stepped leader, which he calls the β-type, is also represented schematically in Fig. 12b. Leaders of the β-type at first advance rapidly in bright and long steps, but as they advance toward the Earth the brightness of the luminosity, the length of the step, and the effective velocity of such a leader decrease. Leaders of the β-type have

Fig. 12a. Discharge of the α-type (according to Schonland)

a velocity of propagation significantly greater than that of the leaders of the $\alpha$-type. In Figs. 12a and 12b the difference between these two types of leaders is clearly visible.

In his latest work, McEachron\(^{33}\) gives new, extremely interesting data concerning stepped leaders. McEachron studied (by photographing and simultaneously oscillographing) lightning strokes to the Empire State Building (New York), whose height is 380 m. Of 55 recorded discharges, with a negatively charged cloud, 36 also had an initial stepped leader,

Fig. 12b. Discharge of the $\beta$-type (after Schonland)

but one that propagated from below upward, i.e. from the building to the cloud. Such a “stepped positive leader” was not accompanied by a return discharge. It should be noted that the “positive” leader, i.e. a leader propagating from a positively charged cloud, was first discovered by Stekolnikov\(^{27}\).

In contrast to the data of Schonland and McEachron, in Stekolnikov’s latest comprehensive investigations\(^{29}\) (at an altitude of 2000 m) the appearance of stepped leaders was not observed. In the photographs Stekolnikov could not detect leaders at all in the first discharges (possibly because of the weak intensity of such leaders), whereas the oscillograms showed a change in the field strength that may be attributed to a leader, but no voltage pulsations were observed. Stekolnikov concludes that the data he obtained do not confirm Schonland’s point of view regarding the obligatory existence of a stepped leader for the first discharges. Thus the question of the nature of the leader for the first discharge requires further investigation.

Another type of leader—the dart-shaped one—usually precedes subsequent discharges and advances continuously from the cloud to the Earth, in the form of a brightly luminous head leaving behind it a weakly luminous channel. A dart leader rarely gives branchings.

If a very large interval occurs between successive discharges, then the discharge after such an interval has a stepped-dart leader, i.e. a dart leader whose lower end has a stepped character. The length of the step of such a leader is only 8–10 m.

— In Fig. 13 the development of a thunderstorm discharge according to Schonland is schematically represented; it consists of several successive discharges (recorded on a moving film). At the left is shown the first stroke with a stepped leader and branches; the subsequent discharges have a dart leader.

Fig. 13. Scheme of the development of a multiple discharge (according to Schonland)

Schonland40 gives data characterizing the percentage occurrence of leaders for the first and subsequent discharges; these data are given in Table 2.

Table 2

Photographs	First discharges, number	First discharges, with leader	Subsequent discharges, number	Subsequent discharges, with leader	All discharges, number	All discharges, with leader
Good . . .	15	15	26	23	41	38
Satisfactory . . .	18	9	41	26	59	35
Total . . .	33	24	67	49	100	73

It follows from Table 2 that, of the total number of discharges photographed by Schonland, 73% have leaders; moreover, for both the first discharges and the subsequent ones, the percentage occurrence of leaders is approximately the same. In his first work Schonland31 indicated that, of 36 discharges, 26 had leaders, which amounts to 72%. The data presented show that the majority of discharges have leaders.

b) Velocity of propagation of leaders. The propagation of a stepped leader is characterized by a certain “effective” velocity, which is less than the actual velocity of advance of the step, since the effective velocity includes the time intervals between steps.

Table 3 collects data obtained by Schonland for the “effective” velocity of stepped leaders.

Table 3

Velocity in cm/sec · \(10^{7}\)	Number of stepped leaders of the first discharge	Velocity in cm/sec · \(10^{-7}\)	Number of stepped leaders of the first discharge
From 1.0 to 2.0	9	From 7.0 to 9.0	3
» 2.0 » 3.0	3	» 9.0 » 11.0	1
» 3.0 » 5.0	3	» 11.0 » 13.0	1
» 5.0 » 7.0	3	» 13.0 » 15.0	0

The average “effective” velocity is found to be \(3.8 \cdot 10^{7}\) cm/sec; most leaders have a velocity between \(1.0\)—\(3.0 \times 10^{7}\) cm/sec. The data of Table 3 represent the “two-dimensional” velocity of the leaders; in order to obtain the “three-dimensional” velocity (i.e., allowing for the spatial advance of the leader channel), Schonland increases these data by 30% (see Ch. II).

The velocities of upward-moving (positive) stepped leaders, measured by McEachron\({}^{33}\), lie in the interval from 0.17 to 2.09 ft/μ sec, i.e., from \(5.1 \cdot 10^{6}\) to \(6.3 \cdot 10^{7}\) cm/sec.

The velocities of propagation of dart-shaped leaders are considerably higher and are given in Table 4. The average velocity of a dart-shaped leader is \(5.5 \cdot 10^{8}\) cm/sec; the most probable velocity corresponds to \(2.0 \cdot 10^{8}\) cm/sec. The maximum velocity is \(2 \cdot 10^{9}\) cm/sec.

Table 4

Velocity in cm/sec · \(10^{8}\)	Number of dart-shaped leaders	Velocity in cm/sec · \(10^{-8}\)	Number of dart-shaped leaders
From 1.0 to 3.0	17	From 13.0 to 15.0	6
» 3.0 » 5.0	8	» 15.0 » 17.0	1
» 5.0 » 7.0	6	» 17.0 » 19.0	2
» 7.0 » 9.0	5	» 19.0 » 21.0	2
» 9.0 » 11.0	5	» 21.0 » 23.0	1
» 11.0 » 13.0	2

There exists a definite relationship between the velocity of a dart-shaped leader and the interval between this leader and the preceding discharge: namely, the greater this interval, the lower the velocity of the leader, and vice versa. There is no doubt that this is connected with recombination processes occurring in the ionized channel created by the preceding discharge. The dependence of the leader velocity on the interval is confirmed by the data of Table 5.

Table 5

Leaders	Discharge serial number	Interval between discharges, sec.	Speed of the dart-shaped leader · \(10^{-8}\) cm/sec
Fast	5	0.015	21.5
Fast	9	0.06	17.1
Fast	9	0.12	20.2
Fast	14	0.005	19.3
Fast	7	0.014	15.0
Slow	5	0.07	1.9
Slow	5	0.07	1.7
Slow	7	0.48	1.8
Slow	4	not measured	1.7
Slow	8	0.08	2.0
Slow	6	0.14	2.8
Slow	5	0.03	not measured

Sometimes a decrease in the speed of propagation of the leader is observed as it approaches the Earth; thus, for example, for one discharge the following change in speed was obtained (Schonland \(^{31}\)): for the first 700 m the speed of the leader was \(9.3 \cdot 10^{8}\) cm/sec, while for the last 600 m the speed decreased to \(5.3 \cdot 10^{8}\) cm/sec.

However, there are still too few data to assert the universality of this fact.

The three step-dart leaders recorded by Schonland \(^{40}\) had speeds of \(1.9 \cdot 10^{8}\), \(1.2 \cdot 10^{8}\), and \(1.0 \cdot 10^{8}\) cm/sec.

c) Relation between the length of a step and the interval. Usually the length of a step of a stepped leader is 50 m, and the interval between steps is of the order of 100 μsec. For a step-dart leader the step length is of the order of 10 m and the interval about 8 μsec. There is a definite dependence between the mean step length \(\bar l\) in the discharge and the mean interval \(\bar t\) between steps. The dependence obtained by Schonland is presented graphically in Fig. 14, where along the ordinate axis \(\bar t\) is plotted in microseconds, and along the abscissa axis \(\bar l\) in meters; each point corresponds to one

Fig. 14. Dependence of the mean length of a leader step
on the mean value of the time interval.

rank. The black circles are data from good photographs, where the accuracy of determining \(\bar l\) and \(\bar t\) is sufficient; the crosses correspond to stepped-arrow leaders. From Fig. 14 it follows that the larger the time interval, the longer the step appearing after this interval. The curve of Fig. 14 makes it possible to obtain the dependence between the “effective” velocity of the leader \(\left(\bar v=\dfrac{\bar l}{\bar t}\right)\) and the mean step length \(\bar l\). In Fig. 15 this dependence is given; the dashed straight line in Fig. 15, on which the points fall even somewhat

Fig. 15. Dependence between the effective velocity of the leader and the mean step length

better, intersects the abscissa axis at the point \(\bar v = 1.0 \cdot 10^7\) cm/sec. This velocity is a certain “limiting” velocity and has a definite physical meaning (see § 7).

§ 2. The main (return) discharge

As soon as the leader reaches the Earth, the main discharge immediately arises, propagating from the Earth to the cloud. The main discharge is considerably more intense in luminosity, and it was observed that as the main discharge moves upward this luminosity decreases, especially as it passes branching points. An increase in luminosity as the discharge moves upward was never observed.

a) Velocity of the return discharge. The velocity of propagation of the return discharge is considerably greater than the velocity of the leader; namely, the mean value of the velocity of the return discharge is \(\simeq 5.2 \cdot 10^9\) cm/sec, and the most frequently occurring value of the velocity is \(\simeq 3.5 \cdot 10^9\) cm/sec. Schonland \(^{40}\) gives the results of determining the velocities of return discharges for 48 cases. These results are presented in Fig. 16, where the first column of the graph gives the velocities of propagation of the channel of the return discharge; as is seen, the maximum velocity is \(14.4 \cdot 10^9\) cm/sec and the minimum is \(2.0 \cdot 10^9\) cm/sec. In the second column of the graph are given data for the velocity of propagation of the lower part of the channel (the more intense one), and in the third column—data on the velocity of propagation of the upper part of the channel (the less

intensity). As can be seen, bright luminosity occurs at high velocities of channel propagation. In the last fourth column are given the velocities of return strokes along a branch; unfortunately, there are too few data here.

In Fig. 17 one of the discharges is schematically represented, in which a considerable change in luminous intensity and a decrease in velocity were observed as it moved upward. In the figure, the numbers near the discharge give the time in microseconds from the beginning

Fig. 16. Distribution by velocities of main discharges (after Schonland)

of the discharge. For this discharge it was possible to determine the change in velocity as it advanced; the results were as follows:

Section of the channel	Velocity \(\times 10^{-9}\) cm/sec
From the Earth to branch 2	16.1
From branch 2 to branch 3	21.0
From branch 3 to branch 5	9.7
From branch 5 to the cloud	5.5

The total length of this discharge was about \(2.5\) km.

b) Luminosity. The luminosity of the main discharge continues for a comparatively long time; quite often the duration of the luminosity considerably exceeds the time required for the discharge to reach the cloud. Table 6 gives Schonland’s \(^{31}\) data on the duration of luminosity for four discharges.

MacEachron \(^{11}\) also states that he observed luminosity that continued considerably longer than the time required for the discharge to reach the cloud; for example, a case was recorded in which the luminosity continued for \(0.185\) sec.—right up to the appearance of the second discharge.

Fig. 17. Change in luminous intensity of the main lightning channel as the discharge moves upward (diagram)

Table 6

Discharge	Duration of glow at the base (in μ sec)	Time required to reach the cloud (in μ sec)	Time required to reach the end of the last branch (in μ sec)
4	125	44	96
8	162	50	61
9	150	65	145
7	12	49	40

Walter^42 suggested that such a duration of glow is due to the large resistance at the point of contact with the Earth. However, as MacEachron points out, prolonged glow was observed with very good contact (the discharges struck the steel frame of a building), and, moreover, for different discharges the time of glow was different, although the contact resistance was the same. MacEachron assumes that the duration of glow depends on the processes occurring in the cloud during the discharge.

As was already indicated above, a considerable change in the intensity of the glow is observed as the discharge advances upward and as the branching points are passed. This question was thoroughly investigated by Malan and Collens^43, who discovered the “fine structure” of the main discharge. It was established that the glow of the channel consists of a number of separate “components” following one after another. The appearance of these components depends mainly on the appearance of branches. Fig. 18 presents a diagram of such a main discharge (the discharge is idealized), in which the arrow indicates the direction of motion of the film in the camera. The branches are indicated by the symbols br 1, br 2, etc. In the diagram four glow components are visible at the bottom of the channel and only two at the top (one of them double); the intensity of the glow is characterized by the density of the hatching. These glow components are directly connected with the branches, since the second component appears at the moment when the first component reaches branch 2; the third component arises at the moment,

Fig. 18. Fine structure of the glow of the main channel

when the first component reaches branch 3. The fourth component is formed when the first component reaches the cloud and all branches terminate.

The most frequently encountered values for the duration of the glow of the individual components and the times of their occurrence are given in Table 7.

Table 7

Components	Duration, in μsec	Starting time, in μsec
1	< 10	0
2	20	25
3	50	70
4	100	(150—500)

Fig. 19 shows the distribution with respect to the time of occurrence and the duration of the glow components for 16 discharges (recorded by Malan and Collens^43). The lightly hatched rectangles (near the ordinate axis) give the transit time of the return stroke from the Earth to the cloud; the black bars refer to the glow components; the length of a bar gives the duration of the component, and its position along the abscissa gives the time of appearance of the component (the numbers on the left are the numbering of the discharges). As is evident from the graph, in almost all discharges the second component appears when

Fig. 19. Time distribution of the glow components of the main discharge

the discharge has not yet reached the cloud. The small black rectangles on the left (at the ordinate) characterize the first components of the glow.

Glow components may also occur in unbranched discharges, but the number of components for such discharges does not exceed two, and for the most part only one component is observed. The number of components of branched discharges is usually 4–6 (a discharge with twenty components was recorded).

As already noted, for branched discharges the appearance of glow components is connected with branchings. This connection is clearly visible in Fig. 20 (Malan and Collens[^43]), where the ordinate axis gives the time at which the component begins, and the abscissa axis gives the time at which the branch begins. The straight line drawn at an angle of 45° corresponds to equality of these times. As is evident from the graph, most of the experimental points lie above this straight line; this means that the components begin somewhat later in comparison with the appearance of the branch. However, this difference amounts to only \(10^{-5}\) sec/km, which lies within the limits of measurement error.

Fig. 20. Time dependence between glow components and branches. On the abscissa axis is the time at which the branch begins; on the ordinate axis is the time at which the components arise.

The propagation velocity of the glow components is very high, and therefore it is difficult to determine it; measurements show that the velocity of the components is greater than \(10^{10}\) cm/sec (this value is the limit of measurement in the cited work[^43]). The propagation velocity of components not connected with branches is considerably smaller (although not always). The direction of propagation of the components may be arbitrary (from the cloud to the earth and vice versa), although it has been noted that components with low velocity usually propagate from the cloud toward the Earth. It is very difficult to determine the direction of components connected with branches because of the great speed of motion of these components.

Photometric measurement of the photographs gives the change in the intensity of the channel glow with time. In Fig. 21 a photometric curve is given; along the ordinate axis is plotted the intensity (the glow intensity of the first component is taken as 100), and along the abscissa axis—the time from the moment the discharge begins. It is seen that at first the channel has a glow intensity of 100, then it falls to 45 and again rises to 115 (the second component appears). Maxima 18 and 2 correspond to the appearance of components 3 and 4.

The physical nature of such a “fine structure” of the return discharge is not at all clear, and there are still too few experimental data on this question.

Fig. 21. Change in the luminosity of the discharge with time

§ 3. Branches

Usually, the first discharges have quite many branches; thus, of the first 57 discharges investigated by Schonland^40, 54 had branches, which amounts to 95%. Subsequent discharges have branches comparatively rarely; thus, of 33 subsequent discharges only 14 had branches, which amounts to 42%. On average, each first discharge gives 5 branches (198 branches in 40 discharges), whereas in subsequent discharges there is on average 1 branch per discharge. The branches of subsequent discharges are considerably weaker in intensity than the branches of the first discharge, and they always develop along the paths of the branches of the preceding discharge. The rate of development of such a branch is of the same order as the rate of development of the entire discharge (the leader branches develop with a velocity of \(\sim 10^7\ \text{cm/sec}\), and the branches of the main discharge with a velocity of \(\sim 10^9\ \text{cm/sec}\)). In Fig. 22 a “time diagram” of a branched discharge is given, taken with a moving camera. The dashed line on the diagram is the path of the leader; the heavy line is the return discharge. The small numerals are the times in milliseconds for li-

Fig. 22. Time diagram of a branched discharge (the arrow indicates the motion of the camera). Dashed line—the leader, solid line—the main discharge

letters; bold numerals—the time in microseconds for the principal discharge. The arrow indicates the direction of motion of the lens of the photographic camera.

§ 4. Multiplicity of Lightning

The most complete investigation of the phenomenon of lightning multiplicity was carried out by Schonland ^40 and McEachron ^11,41.

a) Number of successive discharges. The maximum number of successive discharges—up to 40—was recorded by Larsen ^39. Schonland observed up to 27 successive discharges, McEachron only 12, and Stekol’nikov 11 (1936).

The number of multiple lightning flashes out of the total number of recorded cases amounts to 30–50%. Table 8 gives McEachron’s data ^44, characterizing the percentage occurrence of multiple lightning flashes.

Table 8

Year	Total number of lightning flashes	Single lightning flashes	Multiple lightning flashes: number of multiple lightning flashes	Multiple lightning flashes: %	Multiple lightning flashes: total number of discharges	Number of thunderstorms: only with single lightning flashes	Number of thunderstorms: only with multiple lightning flashes	Number of thunderstorms: both
1934	42	32	10	24	44	11	3	2
1935	21	19	2	9	4	9	—	2
1936	45	32	13	29	38	6	1	6
1937	76	49	27	35	90	13	2	11
Total . .	184	132	52	28	176	39		24

Usually, the first discharge in a series of successive discharges is the most intense; however, there have been cases when one of the subsequent discharges was the most intense ^23. Of 33 lightning flashes recorded by Schonland, 88% had the first discharge as the most intense. The luminous intensity of the subsequent discharges depends on the interval between discharges: discharges that follow the preceding ones quickly are intense; the larger the interval, the less intense the discharge proves to be.

b) Interval between discharges and total duration of the lightning. The interval between two successive discharges varies rather greatly and may reach 0.53 sec.; the minimum interval recorded by Schonland is 0.001 sec., and according to McEachron’s data even 0.0005 sec.

In Table 9 are given Norinder’s data \(^{49}\) for the time interval between discharges.

Table 9

Interval between discharges, in sec	Number of recorded cases	Interval between discharges, in sec	Number of recorded cases
0.001–0.002	1	0.07–0.09	15
0.002–0.005	6	0.09–0.11	4
0.005–0.01	9	0.11–0.15	6
0.01–0.03	28	0.15–0.23	1
0.03–0.05	22	0.23–0.32	3
0.05–0.07	11	0.32–0.42	1
		0.42–0.53	2

The most frequently encountered interval is \(\simeq 0.03\) sec. The same result was obtained by McEachron and Stekolnikov \(^{29}\). In contrast to these data, Norinder \(^{45}\) obtained a maximum interval of only 0.005 sec. In Stekolnikov’s opinion \(^{4}\), Norinder measured not the complete multiple discharge, but only part of it, and ordinary pulsations were taken by him for separate discharges.

The maximum duration of multiple lightning, according to the latest data, is 1.53 sec (McEachron \(^{44}\)) and 1.55 sec (Stekolnikov).

§ 5. Diameter of the Lightning Channel

There is no doubt that the diameter of the lightning channel is an extremely important parameter in the theory of the thunderstorm discharge; however, the data on this question are very unreliable and contradictory.

Toepler \(^{46}\) gives 40 cm as the upper limit of the diameter of the channel. However, investigation of the point where lightning strikes the ground indicates that the diameter amounts to only a few centimeters. Belassi \(^{47}\), under laboratory conditions, obtained a discharge (14,000 A) between electrodes and determined the diameter of the channel of this discharge by photography. He obtained a value of 10–25 cm; in Belassi’s opinion, this value exceeds by several times the actual diameter of the discharge stem. In order to clarify this question, Belassi carried out additional investigations and established that the point of incidence of the discharge on the electrode gives a discharge diameter of only 1.5 cm. Along with this, an experiment he performed in passing the discharge through a fib-

… tube shows that, if the diameter of the tube is \(\sim 2\ \mathrm{cm}\), then, when a discharge passes through it, a pressure of up to \(15000\) atm develops in it. Since it is difficult to assume the possibility of the occurrence of such high pressures under normal discharge conditions, it is more natural to suppose that such a pressure arises because the diameter of the discharge channel considerably exceeds the diameter of the tube.

Fig. 23. Photograph of lightning taken with an ordinary camera. By the wind the lightning was split, and separate discharges were obtained.

To determine the diameter of the lightning channel, Schonland\(^{48}\) photographed lightning with a stationary camera. This photograph is shown in Fig. 23. In the photograph it is seen that the discharge consisted of 11 separate successive discharges, which proved to be separated owing to a strong wind (20–30 miles per hour). Three branches \(x\), \(y\), and \(z\) are also visible. From this photograph the channel diameter was determined for each of the discharges and branches. The results are given in Table 10.

Table 10

Discharge number	1	2, 3, 4 (average)	5	6	7	8–9 (average)	10	11	Branches: \(x\) upward	Branches: \(x\) downward	Branches: \(y\)	Branches: \(z\)
Diameter in cm	23	20	16	16	16	15	19	19	16	11	13	17

The maximum value for the diameter is \(23\ \mathrm{cm}\). The most probable value is \(16\ \mathrm{cm}\).

At present there are still too few data to definitively establish the magnitude of the lightning diameter. It is possible that the diameter of the channel is not a constant quantity, but depends on the cloud and on the conditions of development of the discharge. Thus, for example, Belashi^49, studying a discharge under laboratory conditions, showed that the cross-sectional area of the spark channel is directly proportional to the current.

§ 6. Other Types of Thunderstorm Discharge

Up to this point the discussion has concerned discharges that had a negative leader preceding the main discharge. Along with this it was noted that McEachron and Stekolnikov observed the appearance of positive leaders in thunderstorm discharges.

McEachron^33 observed a positive stepped leader for the first discharge, but did not detect the appearance of a return stroke for such a leader. In this type of discharge, although the first discharge was a positive stepped leader, i.e., propagated from the Earth to the cloud, all subsequent discharges have the usual negative arrow-shaped leader, i.e., one going from the cloud to the ground, and a return stroke. The observed velocities of propagation of such positive leaders ranged from \(5.1 \cdot 10^6\) to \(6.3 \cdot 10^7\) cm/sec, whereas the leaders of the subsequent discharges had velocities from \(5.7 \cdot 10^7\) to \(3.9 \cdot 10^9\) cm/sec. The most frequently occurring step length of such a leader proved to be \(\sim 7.5\) m, with a minimum length of \(\sim 5.7\) m and a maximum of \(\sim 20\) m. The interval between steps is from 20 to 100 μsec, with the most probable value being 30 μsec. These characteristics turn out to be considerably smaller in comparison with the analogous data for negative stepped leaders obtained by Schonland^40.

In the majority of such positive leaders no branches could be detected, and only a few discharges had branches also directed upward. Branches directed downward were never observed in an upward-moving leader, and conversely; that is, the branches are always directed in the direction of propagation of the leader.

McEachron^33 found that most discharges at the Empire State Building are characterized by continuous luminosity throughout the entire discharge. This continuous glow was nonuniform in intensity and was accompanied by a continuously flowing current (the data were obtained by comparing photographic and oscillographic sweeps). Against the background of such a continuously flowing current, individual peaks are observed, corresponding to a sharp increase of current in the lightning channel. These current peaks correspond to a sharp increase in the intensity of the glow in the photographs. Such discharges were called by McEachron “continuous discharges.” The duration of the glow of continuous discharges reaches 0.625 sec, with the most frequent values being up to 0.4 sec. It is quite possible that the duration of the glow is still greater, since part of the discharge may not have been recorded because of the weak intensity of the glow.

Of the 47 discharges recorded by McEachron, 34 were continuous, 4 consisted of two successive continuous discharges following one path with some time interval, and 7 others began as continuous discharges accompanied by sharply distinguished discharges. Discharges that could be called “multiple” in the usual sense could not be found in these investigations. Most of the continuous discharges had stepped leaders moving upward. McEachron indicates that the same kind of continuous discharges were observed in Switzerland (Lake Maggiore) and by the Pittsfield Observatory.

The quantity of electricity carried by such discharges reaches 164 coulombs, with an average value of 35 coulombs. Earlier data give a maximum quantity of electricity of 2 coulombs^45 (and a calculated value of 20 coulombs^15).

The character of the development of the lightning discharge discovered by McEachron is extremely interesting. Of equal great interest is the upward-moving (positive) stepped leader discovered by him, not accompanied by a return stroke. This character of discharge development has some analogy with the results obtained by Matthias^50 and Allibone^51 in studying the length of a spark in the laboratory. It was found that a leader discharge between two points sometimes begins simultaneously from both electrodes, producing two leaders moving toward one another. It is possible that the lightning observed by McEachron has the same character of development, and that the leader moving from the cloud to the building and the point of meeting of the leaders were not noticed.

The appearance of discharges without a leader has been noted by a number of authors; however, there has always been the well-known doubt that the leader was simply not noticed because of its low intensity. Workman^52 observed three types of lightning discharge: 1) an ordinary discharge with a leader, 2) a discharge without a leader, and 3) a discharge without a leader, advancing in steps.

The first type of discharge is the usual one and has been considered in sufficient detail above.

A discharge without a leader (the 2nd type), a photograph of which is given in Fig. 24, belongs to the type of “main discharge.” This discharge propagated from the cloud to the Earth, was very intense, and had no leader, although under the conditions of photography the leader could have been recorded. Such a discharge was repeated three more times (this is not shown in the photograph) with intervals of \(1.2 \cdot 10^{-4}\), \(1.3 \cdot 10^{-4}\), and \(2.4 \cdot 10^{-4}\) sec. Workman indicates that such discharges are quite often observed in the locality where the photography was carried out (New

Fig. 24. Discharge without a leader

Mexico), and are usually accompanied by very strong thunder.

The next type of discharge, described by Workman, is a discharge developing in steps; it had not previously been observed anywhere. The discharge consists of four steps and has no leader. The discharge developed as follows: having begun in the cloud, the discharge traveled 0.98 km and suddenly stopped; after 0.008 sec. a second discharge appeared and along the same path traveled 1.2 km and also ceased. After 0.01 sec. a third appeared, which traveled 1.70 km, and finally a fourth—after 0.0098 sec.—which traveled the entire path from the Earth to the cloud. Workman points out that these discharges cannot be leaders, since the interval between them is too large and, moreover, their intensity indicates that they belong to the type of “main discharge.” It is possible that the appearance of such three unfinished discharges can be explained by the fact that the resistance inside the cloud is very great and therefore charges flow slowly from neighboring regions and the discharge that has begun ceases. After some time, when the voltage again rises, the discharge appears again.

Finally, discharges are also observed that end in the air, without reaching the ground (Schonland^40). These discharges (“air discharges”) are divided into two groups: 1) discharges propagate in steps from the cloud into the air, and 2) discharges propagate continuously (similar to an arrow-like leader). All these discharges are essentially leaders and are not accompanied by return discharges.

§ 7. Mechanism of the Thunderstorm Discharge

At the present time there is still no satisfactory theory of the thunderstorm discharge; there are only separate hypotheses and assumptions.

As a result of his numerous investigations, Schonland^53 arrives at the following mechanism of the thunderstorm discharge. The leader of the first discharge and the leader of the subsequent discharge differ in their behavior, which is due to the difference in the mechanism of their development. The leaders of subsequent discharges (arrow-like leaders) move along the path made by the preceding discharge, and this path is already sufficiently ionized. The leader of the first discharge usually has a stepped character and advances in non-ionized air.

Schonland considers that the stepped leader in fact consists of two leaders. The first leader advances continuously in non-ionized air and lays down the path for the second leader. This first hypothetical leader Schonland calls the pilot leader (pilot-leader). The speed of advance of the pilot leader is small—about \(1 \cdot 10^7\) cm/sec. The second leader, which advances in steps, follows the path of this pilot leader. Since the speed of advance of the stepped leader is considerably greater than the speed of the pilot leader, namely of the order of \(10^9\) cm/sec, the stepped leader

periodically catches up with the head of the pilot leader. As soon as the stepped leader reaches the pilot leader, its further advance ceases; there is a pause, during which the pilot leader traverses some additional distance; then the stepped leader appears again, which again follows the path extended by the pilot leader, catches up again, etc. Thus the end of a step is, as it were, the beginning of a pilot leader. In Fig. 25 a diagram is given of the development of such a leader; the dotted line is the path of the pilot leader; the vertical arrows are the steps of the stepped leader (the time is indicated by the arrow). The pilot leader, if it actually exists, must have a weaker luminosity and therefore it is impossible to photograph it.

Fig. 25. Diagram of the advance of a stepped leader (after Schonland)

If \(t\) is the time of the pause between steps, and \(l\) is the length of the step after the pause \(t\), then \(\dfrac{l}{t}\) is the velocity of the pilot streamer, or the “effective” velocity of the stepped leader. Between \(l\) and \(t\) there must exist a definite relation, and indeed, if \(t\) is large, then the following step must be long, and conversely. Analysis of photographs confirms this proposition.

Thus Schonland comes to the conclusion that the stepped leader, like the subsequent leaders, advances along a previously ionized path prepared for it by the pilot leader; but the pilot leader advances in non-ionized air.

Schonland assumes that the pilot leader propagates owing to ionization produced by electrons at the head of the leader. In that case there must exist a certain critical field strength \(E_{\mathrm{кр}}\) at the head of the leader, at which the electron has the critical velocity \(v_{\mathrm{кр}}\), below which ionization by collision cannot occur. This electron velocity—\(v_{\mathrm{кр}}\)—is at the same time the minimum velocity of the pilot leader, since the leader as a whole cannot move more slowly than the ionizing agents. One may use the usual relation between \(E_{\mathrm{кр}}\) and \(v_{\mathrm{кр}}\) in the form

\[ v_{\mathrm{кр}}=\sqrt{\frac{2E_{\mathrm{кр}}e\lambda}{\pi m}}, \tag{1} \]

where \(e\) is the charge of the electron, \(\lambda\) is the mean free path of the electron, and \(m\) is the mass of the electron.

In this expression, according to Townsend, there is contained the assumption that every collision between an electron and a gas molecule is inelastic. Substituting into formula (1) the known values for \(E_{\mathrm{кр}}\) (\(30\,000\ \mathrm{kV/cm}\)) and \(\lambda = 3.8\cdot 10^{-5}\ \mathrm{cm}\) (the value of \(\lambda\) is taken for the mean free path of an electron at \(20^\circ\mathrm{C}\) and \(76\ \mathrm{cm}\ \mathrm{Hg}\)), Schonland obtains for the velocity \(v_{\mathrm{кр}}\) the value \(\sim 3.6\cdot 10^{7}\ \mathrm{cm/sec}\). This is somewhat greater than that obtained from photo-

tographs, the minimum effective velocity of a stepped leader (\(\sim 1.0 \cdot 10^7\) cm/sec); however, as Schonland points out, in the calculation certain assumptions were made (all collisions are inelastic, the value for \(\lambda\) is somewhat overestimated), and if this is taken into account, the value for \(v_{\mathrm{cr}}\) comes out somewhat smaller and close to the observed one—\(\sim 1.0 \cdot 10^7\) cm/sec.

These calculations cannot, of course, lay claim to accuracy, since some quantities were chosen arbitrarily; moreover, the experimental value of the minimum velocity of a stepped leader, obtained from photographs, is also not entirely reliable. In any case, what is important is only that the order of magnitude for the leader velocity comes out correctly, with a field strength at the leader head that does not exceed the permissible value.

Matters are considerably worse in the case of stepped leaders whose effective velocity is of the order of \(2 \cdot 10^8\) cm/sec. In this case the value of the field at the leader head, according to formula (1), comes out extremely large—\(8 \cdot 10^6\) V/cm. Such high gradients can hardly occur in the leader channel. Therefore Schonland divides stepped leaders into two groups: in the first group the effective velocity of the leader is from \(1 \cdot 10^7\) to \(5 \cdot 10^7\) cm/sec; this group constitutes 65% of the observed leaders; the second group consists of leaders with velocities from \(5 \cdot 10^7\) to \(2 \cdot 10^8\) cm/sec and constitutes only 35%.

Schonland calls the first group, as already indicated above, the \(\alpha\)-type, and the second group the \(\beta\)-type (see Fig. 12). Schonland points out that the higher velocities of \(\beta\)-type leaders may arise as the result of some preliminary ionization ahead of the head of the pilot streamer. Thus, Loeb and Cravath\(^{54}\) suggested that the preliminary ionization ahead of the leader head is caused by the presence in the air of free electrons arising from natural causes (cosmic rays, radioactivity, etc.). However, the “productivity” of such natural agents will evidently be small.

More correct is Loeb’s second supposition\(^{55}\), concerning the existence of photoelectric ionization of the air ahead of the streamer head, which facilitates its advance. The existence of preliminary ionization ahead of the pilot leader can explain the observed high velocities of the stepped leader, without assuming abnormally large fields at the leader head. Despite the fact that Loeb’s supposition deserves attention, Schonland believes that for the time being there is no point in invoking photoionization to explain the small group (35%) of leaders, and he allows that for such leaders there exist abnormally large fields at the head. Leaders of this type have extensive branchings and often do not reach the earth, but end in such branchings in the air. Leaders that do reach the Earth have a velocity that decreases as they approach the Earth. Schonland connects such behavior of leaders with the existence in the air of a concentrated positive space charge, formed—

... by processes analogous to processes of expiration from a point (proposed by Wilson, 1925). Such space charges lead to the formation of abnormally large electric fields and, according to Schonland, explain the high velocities of the pilot streamer.

To determine the currents of the pilot leader, Schonland uses Rudenberg’s expression\(^{56}\), which was derived under the assumptions that: 1) the head of the streamer has a hemispherical shape, 2) the charges are distributed uniformly over this hemisphere, and 3) the charge density along the leader channel is very small in comparison with the charge density at the head. Under these assumptions the expression for the current has the following form

\[ i=\frac{E\cdot r\cdot v}{18\cdot 10^{11}}, \tag{2} \]

where \(E\) is the electric field at the head (in volts per centimeter), \(r\) is the radius of the head (in centimeters), and \(v\) is the velocity of the leader (in centimeters per second).

To determine \(r\), one may use Ohlendorf’s calculations\(^{57}\) for the motion of an electron swarm. According to Ohlendorf’s calculations, for an electron swarm that has traversed \(10\ \text{m}\) in a field of \(30\,000\ \text{V/cm}\), \(r\) will be equal to \(1\ \text{cm}\). Substituting these values into formula (2), we find that the currents of slow pilot leaders (\(v\sim 10^{7}\ \text{cm/sec}\)) amount to only \(\sim 1\ \text{A}\). For faster pilot leaders \(r\) will be considerably smaller

\[ \left(r\simeq \sqrt{\frac{l}{v^{2}}},\ \text{where } l=v\cdot t\right), \]

so that at \(v=2\cdot 10^{8}\ \text{cm/sec}\), \(r\) is equal to \(2\ \text{mm}\). Such leaders will have currents, according to formula (2), of the order of \(180\ \text{A}\) (\(E=8\cdot 10^{6}\ \text{V/cm}\)). Thus the currents of pilot leaders are extremely small in comparison with the currents of other leaders; for example, an arrow-shaped leader changes the charge of a cloud by \(\sim 1\) coulomb in a time of \(10^{-3}\)–\(10^{-4}\ \text{sec}\), which corresponds to currents of \(10^{3}\)–\(10^{4}\ \text{A}\). The return stroke has currents of the order of \(10^{4}\)–\(10^{5}\ \text{A}\).

Schonland believes that the cause of the pauses in the stepped leader is a mechanism associated with the gas discharge, and not processes in the cloud. Schonland sees proof of this in the narrow range of pauses (50–90 \(\mu\)sec). The pause is the time required for the field at the leader head to reach the critical value \(E_{\text{cr}}\). This increase of the field may be due either to a decrease in the electron density in the pilot-leader channel (the field thereby increasing in order to maintain the leader current), or to the formation of a positive space charge along the path of the leader. The latter explanation was proposed by Gippel in connection with Lichtenberg figures. However, in Schonland’s opinion, the second supposition is hardly acceptable, since the gaseous end of the leader differs greatly in its nature from the metallic cathode of a spark, and it is difficult to imagine the formation of a positive space charge near the gaseous end of the leader.

The mechanism of development of a leader that moves along a previously ionized path (as, for example, a dart leader toward a subsequent discharge, or a return stroke) differs somewhat from the mechanism of development of a pilot leader. The mechanism of development of a dart leader was proposed by Loeb and Cravath.^54 In Fig. 26 the channel of such a leader is shown schematically, according to the ideas of Loeb and Cravath. In Fig. 26, \(AB\) is the stem of the streamer, \(BC\) is the region ionized by the preceding discharge, in which the electric field has the critical value \(E_{\mathrm{cr}}\), necessary for ionization by collision.

Fig. 26. Diagram of the advance of a discharge according to Loeb and Cravath

In the case of a negative leader (dart-like), the electrons of the region \(BC\) create an electron avalanche as they move forward (from the head); in the case of a positive streamer (return stroke), these electrons form an avalanche by moving toward the streamer head. As soon as \(BC\), owing to this, becomes sufficiently conducting, the streamer immediately reaches point \(C\), and the process continues further. Schonland somewhat extends this hypothesis of Loeb and Cravath, namely, he introduces the time—\(t\)—of effective ionization of the region \(BC\), which is essentially the time required for each initial electron to traverse the mean distance from one electron to another. If \(n\) is the initial density of electrons and \(\bar v\) is the mean velocity of an electron in the region \(BC\), then

\[ t=\frac{1}{n^{1/3}\cdot \bar v}\quad \text{and}\quad V=\frac{d}{t}=n^{1/3}\cdot \bar v\cdot \alpha, \tag{3} \]

where \(\alpha=BC\) and \(V\) is the velocity of advance of the streamer. Thus the velocity of advance of the streamer—\(V\)—depends on the initial density of electrons and on the magnitude of the electric field at the streamer head, since \(\bar v\) and \(\alpha\) depend on the magnitude of the field. For comparison, Schonland gives the following calculations: if the radius of the streamer head is \(1\ \mathrm{cm}\) and the voltage at the head is \(1.5\cdot 10^{6}\ \mathrm{V/cm}\), then the velocity of the streamer in nonionized air will be, according to formula (1), equal to \(7\cdot 10^{7}\ \mathrm{cm/sec}\). If, however, the streamer advances in a previously ionized space where the electron density is \(n=10^{3}\ \mathrm{el/cm^{3}}\), then, according to expression (3), the velocity of the streamer will already be \(1.03\cdot 10^{9}\ \mathrm{cm/sec}\) (with \(\alpha\) equal to \(6\ \mathrm{cm}\)). Consequently, the existence of preliminary ionization explains the high velocities of dart leaders and return strokes. Thus

since with time the electron density $\bar n$ decreases as a result of recombination, the longer the interval of time between two successive discharges, the smaller will be the velocity of the subsequent discharge. If the time is very long, then instead of a continuous dart leader a rapid stepped leader is obtained.

The glow of the leader is usually concentrated near the head, and this indicates that the glow is caused by excitation processes in the strong fields at the head of the leader. If the glow extends to a distance $D$ behind the head of the streamer, then it is obvious that $D \ge v \cdot \tau$, where $v$ is the velocity of the streamer, and $\tau$ is the mean lifetime of the excited state of the molecules. For a dart leader $v = 10^9 \text{ cm/sec}$ and $d$ is about $50 \text{ m}$; hence $\tau = 5 \cdot 10^{-6} \text{ sec}$. This is a rather large value for $\tau$, since it is known that $\tau$ in the spectrum of an arc in nitrogen is obtained as equal to $\sim 10^{-7} \text{ sec}$. This question requires further consideration.

On the question of the multiple character of lightning there are several points of view.

Simpson$^{8}$ explains the multiple character of lightning by his theory of a positive discharge. According to this theory, a discharge proceeding from a positively charged cloud is stopped by the accumulation of negative charges at the “cloud” end of the discharge. However, in the case of a negatively charged cloud this hypothesis is not applicable.

Böhl$^{58}$ proposes his own point of view, according to which the cloud is considered as consisting of separate volumes not connected with one another. The discharge begins from one particular volume, whose potential is lowered in the course of the discharge. This leads to an increase in the potential difference between this volume and a neighboring one, as a result of which a breakdown occurs between the volumes. The cessation of the current to Earth, i.e. the cessation of the discharge, leads to a redistribution of potentials along the cloud, and at the place where the discharge was, the potential will increase and a second discharge may arise, and so on. Calculations show that, for the values of $R$ and $C$ adopted by Böhl ($R = 1000\ \Omega$ and $C = 0.01\ \mu\text{F}$), the process should proceed extremely rapidly, which is in complete disagreement with the experimental data.

Schonland$^{53}$ believes that the multiple character of lightning is caused by the existence of several generating centers in the cloud. The discharge is produced by one of the centers; as a result, the field inside the cloud changes in such a way that a stepped streamer appears from the neighboring generating center, which uses the channel from the cloud to Earth formed by the first discharge and gives the next discharge to Earth.

Schonland sees confirmation of his point of view in the fact that U-shaped discharge channels are observed, which represent two separate discharges from two generating centers, the second discharge partially using the channel of the first discharge. In addition, multiple discharges are observed in clouds of large volume (frontal thunderstorms), in which one may expect

existence of several such centers. According to this point of view, the interval \(T\) between two successive discharges is the time required for the stepped leader to pass from a new cloud center to the one that produced the first discharge, plus the time required for the dart leader to pass from the cloud to the Earth along the channel of the first discharge (this time is not taken into account, since it is small). Consequently, \(T=\frac{D}{v}\), where \(D\) is the distance between the generating centers, and \(v\) is the velocity of the stepped leader. Substituting the values \(T=0.03\) sec. (the mean value) and \(v=2\cdot10^{7}\) cm/sec, we obtain \(D\simeq 6\) km. Schonland considers this value to be a maximum, since the velocity of the leader in the cloud is probably less than the adopted value and, moreover, there may be a delay, which reduces \(T\).

Figure 27 gives the scheme of discharge development proposed by Schonland, where \(a\), \(b\), and \(c\) represent the development of the first discharge, and \(d\), \(e\), and \(f\) the development of the subsequent discharge. In Fig. 27 one can see positive

Fig. 27. Development of the discharge (after Schonland)

streamers going to meet the negative leader. Such positive streamers, going from the Earth to meet the negative lightning leader, were first discovered by McEachron \(^{11,13}\).

There also exists a whole series of hypotheses on the mechanism of the thunderstorm discharge \(^{23,52,58,59}\), some of which are at times speculative in character. As an example, let us consider Albright’s point of view \(^{23}\), which attempts to explain the development of a leader from a positively charged cloud. Albright believes that the discharges he photographed proceed from a positive cloud, since the branches are directed from the cloud toward the Earth. This assertion is incorrect, since it is now already known that the direction of the branches

existence of several such centers. According to this point of view, the interval \(T\) between two successive discharges is the time required for the stepped leader to pass from a new cloud center to the one that produced the first discharge, plus the time required for the dart leader to pass from the cloud to the Earth along the channel of the first discharge (this time is not taken into account, since it is small). Consequently, \(T=\dfrac{D}{v}\), where \(D\) is the distance between the generating centers, \(v\) is the velocity of the stepped leader. Substituting the values \(T=0.03\) sec. (the average value) and \(v=2\cdot10^7\) cm/sec, we obtain \(D\simeq 6\) km. Schonland believes that this value is a maximum, since the velocity of the leader in the cloud is probably less than the adopted value and, moreover, there may be a delay, which reduces \(T\).

In Fig. 27 is given a diagram of the development of a discharge proposed by Schonland, where \(a\), \(b\), and \(c\) are the development of the first discharge and \(d\), \(e\), and \(f\) are the development of the subsequent discharge. In Fig. 27 one can see positive

Fig. 27. Development of the discharge (according to Schonland)

streamers going toward the negative leader. Such positive streamers, going from the Earth toward the negative lightning leader, were first discovered by McEachron\(^{11,13}\).

There is still a whole series of hypotheses concerning the mechanism of the thunderstorm discharge\(^{23,52,58,59}\); some of them are at times speculative in character. By way of example let us consider the point of view of Albright\(^{23}\), who attempts to explain the development of a leader from a positively charged cloud. Albright believes that the discharges photographed by him originate from a positive cloud, since the branches are directed from the cloud toward the Earth. This assertion is incorrect, since at the present time it is already known that the direction of the branches

does not characterize the sign of the charge of the cloud. Albright believes that the positive leader represents the motion of positive particles, and since the velocity of ordinary positive ions is too small, he concludes that such particles may be positrons. This supposition is absurd, since it cannot be assumed that conditions exist in the leader channel for the appearance of such an enormous number of positrons.

From all that has been set forth above it follows that there is as yet no theory that satisfactorily explains the physical nature of the thunderstorm discharge. There is no doubt that further study of lightning and a parallel study (under laboratory conditions) of the mechanism of the long spark will make it possible to solve this question. The work of Stekolnikov and Allibone on the investigation of the spark between electrodes shows that there is an almost complete analogy in the behavior of the long spark and lightning. It has been established that the spark has: 1) a leader (more often from the positive electrode, but sometimes also from the negative) and a return stroke, 2) multiplicity, 3) branches, the direction of which always coincides with the direction of the leader, and even 4) in some cases the spark leader has a stepped character. The velocity of the return stroke in the spark is very great, whereas the velocity of the leader is of the order of \(10^6 — 10^7\) cm/sec, the positive leader advancing faster than the negative one. The first discharge of a multiple spark is weaker and slower and more branched; the subsequent discharges are faster.

All these facts show that the study of the spark will help to solve the question of the mechanism of lightning.

§ 8. Ball Lightning

Ball lightning is a very interesting phenomenon. Up to the present time the nature of this phenomenon remains unclear, since attempts to reproduce ball lightning under laboratory conditions have not been successful.

The existence of ball lightning cannot be subject to any doubt. In 1920 a work by Brand\(^ {60}\) was published, in which he collected all the available material of observations of ball lightning and systematized it. Brand found that, of 600 recorded cases, 215 are quite reliable and deserve consideration. As a result of a critical examination of this material, Brand comes to the conclusion that ball lightning has two forms: the first—when it flies freely through the air, and the second—when it sits motionless on some object or rolls along this object, the so-called “settled” ball lightning. In each of the cases ball lightning has different characteristics.

Brand indicates 14 features of ball lightning.

1. Ball lightning is a spherical, more rarely pear-shaped, electrical discharge that appears during a thunderstorm. Most often ball lightning appears in winter thunderstorms and usually at the end of the thunderstorm.

1. Ball lightning has the appearance of a red luminous sphere with a blue halo, 10–12 cm in diameter. Its outlines are usually misty. Sometimes the balls are dazzlingly white and have a sharp contour.

2. Ball lightning is accompanied by hissing, whistling, or buzzing.

3. After disappearing, ball lightning leaves behind smoke or something like fog, with a sharp odor.

4. The duration of existence of such lightning varies in the interval from small fractions of a second to several minutes, most often 3–5 sec.

5. Ball lightning may appear from the lower part of a cloud or may unexpectedly be found sitting on some object. Sometimes it precedes linear lightning, and then it may be near, or at, the place where the stroke of the linear lightning subsequently occurs.

6. Ball lightning disappears either silently or with an explosion. Sometimes linear lightning strikes ball lightning, and the latter disappears.

7. The speed of ball lightning is very variable. A ball that flies out of a cloud and moves in the direction of the Earth has a considerable speed, of the order of the speed of linear lightning. Near the Earth or in an enclosed room, ball lightning has a speed of about 2 m/sec. Sometimes the ball is carried by an air current, but usually its motion does not depend on the wind. Quite often, in flight, the ball makes strong oscillatory motions and advances in large leaps (up to several meters).

8. Sometimes the ball breaks apart and several small balls are formed. Sometimes two balls appear, surrounded by a necklace of small balls.

9. Flying and settled balls behave differently, although they can pass from one state into the other. A flying ball gives the impression of a strongly stressed electrical discharge with a small current (for example, like Tesla currents), whereas a settled ball has a small voltage but a large current density.

10. A flying ball avoids good conductors and prefers a path through the air. Ball lightning, when it flies through the air, is not dangerous to a person, even when it appears in immediate proximity, since it avoids a person, as it does all conductors.

11. Settled balls are dazzlingly brilliant, white or blue in color. Such balls settle and become fixed on good conductors and prefer high points. Sometimes the balls roll along a horizontally placed conductor, for example along a gutter. Objects on which the balls sit, or along which the balls roll, become strongly heated (a person receives severe burns).

12. When a flying ball passes into the “settled” state, it does this suddenly, throwing itself onto the nearest conductor (for example, water). Upon touching the conductor, the ball remains on it or disappears (quietly or with an explosion). Balls flying out of clouds explode upon striking the Earth.

1. When the reverse phenomenon occurs, i.e., when a sphere passes from the “illuminated” state into the “flying” state, the sphere simply rises and flies away. But such spheres exist only briefly and quickly disappear.

§ 9. Bead Lightning

Bead lightning represents, as it were, an intermediate type between linear and ball lightning. Usually this lightning appears in the form of 20–30 luminous spheres about 8 cm in diameter, arranged one after another at a distance of 0.5–1 m.

Despite the existence of material on the behavior of ball and bead lightning, the physical nature of these phenomena remains completely unclear.

IV. BASIC PARAMETERS OF LIGHTNING

In the present chapter, summaries of data are given for the various most essential parameters of lightning.

These parameters are: 1. The polarity of a thunderstorm discharge. 2. Lightning currents. 3. The quantity of electricity carried by a thunderstorm discharge. 4. Values of the maximum gradients and potentials in a thunderstorm discharge. 5. Parameters of the wave of a thunderstorm discharge, i.e., a) front steepness, b) front length, c) wave length. 6. Multiple discharges.

Most of the data presented make it possible to establish the most frequently occurring values of one or another parameter, i.e., to establish the factor of “repeatability.”

However, the data presented cannot always claim sufficient reliability, because the experimental conditions for determining one or another parameter sometimes give substantial errors; on the other hand, the interpretations of certain measurements sometimes do not correspond to reality.

As a consequence, each such set of data will usually be accompanied by brief descriptions of the experimental conditions under which the measurements were made, and at times the possible sources of error either in the experiment or in the interpretation of individual data will be indicated.

§ 1. Polarity of the Thunderstorm Discharge

The question of the polarity of thunderstorm discharges is of substantial importance not only for the theory of the formation of thunderclouds, but also for the theory of the thunderstorm discharge itself. Initially there existed the opinion that most discharges to the Earth have positive polarity (see Ch. 1), i.e., the cloud was considered to be charged positively with respect to the Earth. However, investigations of recent years, carried out by a number of investigators in different countries and under different conditions, show that this assertion is incorrect. In fact, numerous data attest to the predominance of thunderstorm discharges of negative polarity, i.e., in the majority of cas—

Table 11

Place of registration	Registration conditions	Number of measurements	% of discharges of negative polarity	Registration method	Author (or ref. No.)
USSR	High-voltage transmission line and lightning rod	84	68	Magnetic recording	4
USSR	Lightning receiver 900 m high	6	83	”	24, 25
USSR	Mountainous locality	24	79	Magnetic recording, oscillographic, and klydonographic	29, 36
USA	High-voltage transmission line	358	95	Magnetic recording	61
USA	Distribution lines	1 608	63	”	62
USA	Building 380 m high (Empire State Building)	55	100	Magnetic recording and oscillographic	33
USA	High-voltage transmission line	124	100	Magnetic recording	63
Germany	The same	654	86	”	64
Sweden	Open country	130	56	Cathode-ray oscillograph on frames	45
Switzerland	High-mountain transmission line	12	83	Magnetic recording	65
Africa	Open country	71	100	Cathode-ray oscillograph on antennas	32
Japan	High-voltage transmission line	60	96	Magnetic recording	66
	Total number of registrations	3 186

cases the discharge occurs from a cloud charged negatively. Table 11 is a complete summary of all available data on the question of the polarity of lightning, obtained in 7 different countries.

Table 11 gives the place of registration, the registration conditions, and the registration method. The total number of measurements is given in column 3, and the percentage of discharges of negative polarity is placed in column 4. As can be seen from the table, the majority of the measurements were carried out.

by magnetic recording, i.e., with the aid of ferromagnetics, and chiefly on high-voltage transmission lines. Only in two cases was the recording of discharges carried out exclusively by a cathode oscillograph (Norinder and Schonland). Norinder used a special measurement technique, employing horizontally arranged frame antennas connected to an oscillograph. Schonland used ordinary antennas connected to an oscillograph. Stekolnikov determined the polarity of a lightning discharge sometimes by all three methods, using, along with magnetic recording, an oscillograph and a klydonograph.

Table 11 gives, for all cases, a considerable predominance of discharges of negative polarity. Some exception may be made for Norinder’s data, where there is a slight predominance in the number of negative discharges as compared with positive ones. The data cited make it possible to determine the average percentage of negative discharges, taking into account, of course, the relative weight of each series of measurements. It turns out that the average percentage of occurrence of negative discharges is 75%.

It should be noted that, in addition to “unipolar” discharges, “bipolar” discharges were also observed; namely, in multiple lightning, along with negative impulses, positive discharges are sometimes observed. These “bipolar” discharges were observed comparatively rarely, but by almost all investigators.

§ 2. Lightning Currents

The most widespread method for determining currents in the lightning channel is the method of recording currents with the aid of ferromagnetics[^67]. Ferromagnetic recorders are placed in the most diverse parts of transmission lines: on towers, on individual legs of towers, in ground wires, and in lightning rods. The calculation of the total lightning current that has passed through all current-carrying paths is performed differently by different authors and, in most cases, not sufficiently correctly. Thus, for example, Sporn and Gross[^68] determine lightning currents in three different ways depending on where the lightning strikes the transmission line: (a) when lightning strikes a tower, they add all the currents in adjacent towers; (b) when lightning strikes a ground wire, they add the currents spreading along the ground wires to the nearest towers; and, finally, (c) when it strikes a lightning rod, they take the lightning current to be equal to the readings of recorders located on the lightning rod. With such calculations, quite naturally, completely different results are obtained, which for some reason are averaged by the authors. It may be assumed that the currents calculated by the first two methods, other things being equal, will be deliberately larger than the true current in the lightning stem, owing to the presence of the reflected wave. At the same time, the data of the last method are closer to the actual values of lightning currents.

Lewis and Foust[^61] sum the currents in all towers on which readings of the recorders appear, taking into account possible branching of currents, while completely neglecting the presence of the reflected

waves. From the example of their work one can see the role of the reflected wave, which approximately doubles the readings of all recorders with respect to the current in the lightning conductor standing on the support. Tsaduk^69 similarly sums the readings of recorders located in all possible branches on transmission lines.

Thus, the question of the method for measuring the actual currents of lightning by means of ferromagnetic recorders remains not entirely clear. Along with errors arising from the appearance of the reflected wave, which depends on the magnitude of the wave resistance of the grounding of the supports, there are all sorts of losses caused by the nature of the ferromagnetic recorders themselves. Usually, in most works, the accuracy of determining currents from the readings of ferromagnetic recorders is estimated at 10–15%, but it may be considered beyond doubt that this accuracy is overstated, since the readings of ferromagnetic recorders depend on the shape of the current wave and on other time parameters of the wave. The presence of multiple discharges, and cases of bipolar lightning strokes, also reduce the accuracy of the method of ferromagnetic recording of the amplitude value of the current.

The next most widespread method of measuring lightning currents is the oscillographic method. An oscillographic recording of the current wave likewise gives an insufficiently complete characterization of lightning currents, because the current wave, traveling along the conductor to the branch leading to the oscillograph and partly in the lead-in to the oscillograph itself, usually undergoes changes. Reproduction of the wave that has approached the lightning receiver is sometimes almost impossible. In addition to the direct measurement of lightning currents by an oscillograph, recording of lightning is used according to the inducing action it exerts on the corresponding antennas. Schonland, Stekolnikov, and especially Norinder used this method. Norinder’s use of special loop antennas does not appreciably improve the situation; on the contrary, it introduces a number of difficulties whose elimination is almost impossible.

There is yet another method for determining lightning currents, developed by Bellaschi^47, which consists in calculating the current from the size of the hole produced when a sheet of paper is punctured by the spark. By this method Collins^70 measured a rather large number of cases of overvoltages on a transmission line due to thunderstorm discharges. It is risky to rely on the accuracy of this method, although a number of Bellaschi’s investigations in recent years, under laboratory conditions, have brought the accuracy of the method up to that obtained with ferromagnetic recorders.

It is of interest, from purely formal considerations, to construct a general summary table of the probability of occurrence of particular values of currents on the basis of data taken from original works. Such a table, of course, gives only a certain approximate idea of this important parameter of the thunderstorm discharge. The construction of a summary table may be justified by the fact that the measurement technique is in the main one and the same, the accuracy of measurement probably likewise does not differ greatly, and the remaining conditions

are likewise of the same type; moreover, the general distribution of currents among all the authors is relatively similar.

For the construction of summary Table 12, the following data are used: Stekolnikov\(^4\) (USSR), McEachron and McMorris\({}^{33, 62}\) (USA), Sporn and Gross\({}^{68}\) (USA), Lewis and Faust\({}^{71}\) (USA), Collins\({}^{70}\) (USA), Dauka\({}^{69}\) (Germany), Norinder\({}^{45}\) (Sweden), Rukaku and Kato\({}^{66}\) (Japan). From the data of the table, Fig. 28 was constructed.

Table 12

Currents, kA	Number of measurements	% of “repeatability”
0—5	2 002	60,7
5—10	359	10,8
10—20	369	11,1
20—30	220	6,6
30—40	183	5,5
40—50	63	1,9
50—60	36	1,1
60—70	23	0,7
70—80	15	0,4
80—90	11	0,3
90—100	11	0,3
100—120	10	0,3
120—140	6	0,15
140—160	2	0,05
160—180	1	0,025
220—230	1	0,025
	3 312	100%

It follows from Table 12 that

82% of all data do not exceed . . . . . . . . 20 000 A
96% » » » . . . . . . . . 50 000 »
99,4% » » » . . . . . . . . 100 000 »

In addition, the average probable value of the current in supports may be taken as up to 10 000 A.

In conclusion, it should be noted that all investigations, in essence, still do not give an answer concerning the actual value of lightning currents, but characterize only the order of magnitude of the current in the lightning channel.

§ 3. The Quantity of Electricity Carried by a Thunderstorm Discharge

Direct measurement of the quantity of electricity carried during a thunderstorm discharge has not been performed, owing to the experimental difficulties accompanying the application of ordinary recording methods to such processes.

The usually quoted value of the quantity of electricity in a lightning stroke—20 coulombs—represents, to a considerable

Fig. 28. Distribution of data by current values

to a considerable extent a calculated and very approximate number, obtained in his time by Wilson ^12, ^15 in constructing the theory of thunderstorm formation. The most widespread method of determining the quantity of electricity under pulsed conditions consists in the graphical integration of an oscillographic record of the change of the lightning current with time. It is clear that the total error in this case is rather large; moreover, the current wave itself, as shown on the oscillogram, does not always give a correct idea of the true lightning current (see § 2).

In determining the quantity of electricity carried by a thunderstorm discharge, one must distinguish between the total quantity of electricity and the quantity contained in one pulse in multiple discharges. The rather large percentage of multiple discharges, the nonuniform distribution of currents in the separate pulses of a discharge, the bipolarity encountered in a multiple discharge, and the different duration of the pulses in a discharge—all this entails great complications in the simultaneous determination both of the total quantity of electricity and of the quantity of electricity in each separate pulse. Therefore investigators usually give either the quantity of electricity contained in the given pulse or the total quantity; admittedly, they do not always indicate sufficiently clearly which particular quantity they measured.

Determinations of the quantity of electricity in a thunderstorm discharge occur in a very small number of works. Stekolnikov ^24 gives, for the quantity of electricity of one pulse of a thunderstorm discharge, a maximum value not exceeding 0.5 coulomb. The value cited, as is evident, differs sharply from the value of 20 coulombs. Of course, the figure of 20 coulombs may be considered to comprise the total quantity of electricity of a multiple discharge, but even then, taking the mean probable multiplicity as 4 (see § 6), we obtain a tenfold discrepancy. Norinder’s measurement results are in agreement with Stekolnikov’s data. Norinder indicates that to obtain a quantity of electricity of ~20 coulombs the currents must be ~10^6 A or of very great duration, ~1000 μsec.

An entirely different picture is given by the latest results of McEachron, who studied lightning strokes to the Empire State Building (New York) ^33.

Table 13 characterizes, according to McEachron’s data, the “repeatability” of one or another quantity of electricity falling on the entire multiple discharge.

Table 13

Quantity of electricity in coulombs	Number of measurements	Quantity of electricity in coulombs	Number of measurements
0—10	2	60—70	1
10—20	4	70—80	2
20—30	5	80—90	0
30—40	5	90—100	1
40—50	3	100—160	0
50—60	3	160—170	1
			27

The main point that follows directly from Table 13 is the extraordinarily large quantities of electricity, actually reaching as much as 164 coulombs. The mean value of the quantity of electricity is determined as 30–40 coulombs for the entire discharge. These values are almost twice as large as the commonly accepted figure of 20 coulombs, if this figure is referred to the whole discharge, and many times larger than previous data. If 20 coulombs are considered as belonging to a separate impulse, then the discrepancy is somewhat reduced.

As a result of examining the experimental data on the measurement of the quantity of electricity obtained in a thunderstorm discharge, it is clear that there are large discrepancies, which can perhaps be determined by the lightning itself. In connection with the fact that lightning currents are not actually measured, the cited quantities of electricity are, of course, very approximate. The difference in the data, of course, goes beyond the limits of experimental error and may possibly be explained, as has already been indicated, by the different arrangement of the experimental stations, the relief of the locality, the structure of the cloud, etc.

§ 4. Values of the Maximum Potentials and Gradients in a Thunderstorm Discharge

The principal measurements of potentials and gradients arising during a thunderstorm and a thunderstorm discharge, in essence, refer to the period 1929–1932. As is known, beginning in 1934, a whole series of investigators shifted to the use of ferromagnetics for measuring the currents arising when lightning strikes transmission lines, and almost entirely ceased making measurements of voltages and gradients. In connection with this, even those experimenters who still work with oscillographs and klydonographs deal only with questions of currents, polarities, multiplicity, charac-

characteristics of the wave, etc., leaving aside potentials and gradients. Therefore there are very few data from measurements of gradients, and especially of potentials.

The total potential of the cloud relative to the Earth is estimated by Wilson\(^{12,15}\), as a result of extrapolation and a whole series of assumptions, at 100–1,000 million V.

Peek\(^{72}\) also arrives at these figures on the basis of comparisons of a laboratory spark with lightning.

Direct measurement of lightning potentials can hardly be imagined, but knowledge of the gradients at several points of the space through which the discharge passes may prove sufficient for a more or less reliable determination of the potential. Measurements of gradients were made by Wilson at the surface of the earth. Schonland and Lewis and Foust likewise measured, by means of oscillographs, the field gradients arising near antennas.

In 1937 Simpson and Scrase\(^{7}\) (see Ch. I) measured field gradients at various heights with the aid of balloons, probes, and an “alti-electrograph.” But these measurements did not give a sufficiently complete picture of the values of the gradients in the region of the thunderstorm center, for the reason that all the measurements were carried out chiefly in other parts of the cloud, with the aim of refuting Wilson’s theory of thunderstorm formation.

The field gradients near the surface of the Earth were measured, as indicated, by Wilson, Schonland and Lewis and Foust, and proved to be within the limits of 5–280 kV/m. These gradients are small in comparison with the breakdown gradients obtained in the laboratory (it is known that the breakdown gradient in a plane air capacitor is 30 kV/cm).

If one assumes a relatively uniform distribution of the field from the Earth to the cloud, then the total voltage obtained is close to that which is given, as an estimate, by Wilson and Peek (see above).

§ 5. Parameters of the Thunderstorm-Discharge Wave

An oscillographic record of a thunderstorm-discharge wave, with a sensitivity of approximately \(100\,\mu\text{sec}\) over the whole scale, makes it possible to register an individual discharge pulse. The characteristic parameters of the wave—such as: wave amplitude, wavelength, front length, steepness—all these, it would seem, should be comparatively easy to determine. Leaving aside the question of what the oscillograph records (see § 2), it is necessary to note the following: very often, when deciphering an oscillogram, it is difficult for the experimenter to determine the beginning of the process, because of the presence of oscillations near the region of the initial rise of the wave. This inevitable error sometimes reaches a large magnitude, which becomes comparable, for example, with the length of the wave front. Different authors define the beginning of the wave differently; as a result, when comparing a number of data one can judge only approximately the “repeatability” of particular parameter values. This is made all the more complicated by the fact that

far from all authors give a description of the method for calculating the parameters of the wave. In addition to everything said, it should be noted that all distorting effects of the lead-in conductors, and especially of the antennas themselves and lightning rods, are chiefly reflected in the wave parameters of the impulse.

A fairly large number of experimenters have measured the parameters of the wave of an impulse caused by a lightning discharge, but nevertheless relatively few data have been obtained on this question.

For characterizing the wave, data are given on: wave length, front length, and front steepness.

Wave length. As a result of considering a number of works, one may conclude that all the data on wave length obtained by individual authors prove to be fairly uniform (this is possibly explained by the comparatively small number of measurements). We give a summary table on the wave length of a lightning discharge.

Table 14 is compiled from the data of: Stekolnikovs[^24], Bell and Price[^74], Georg and Itona[^75], Gross and Cox[^76], Pick[^72], Sporn and Lloyd[^77], Norinder[^15]. Table 14 presents a summary of all data on the wave length of a lightning discharge.

Table 14

Wave length in μsec	Number of discharges	%
0—10	29	15.6
10—20	51	27.4
20—30	47	25.3
30—40	18	9.7
40—50	18	9.7
50—60	16	8.6
60—70	4	2.1
70—80	2	1
80—90	0	—
90—100	1	0.5
	186

As is seen from Table 14 and Fig. 29, the average wave length proves to be of the order of 10—30 μsec. Ninety-eight percent of all measurements give a wave length of less than 70 μsec.

It is known that lightning discharges give on the oscillograph either an aperiodic record or an oscillatory one. Many authors note this, but it is most fully illustrated by Stekolnikov’s data[^4]. Thus, out of a total of 95 measurements, 43 proved to be aperiodic, 30 oscillatory, and 22 unknown. The determination of the wave shape was made by comparing the readings of ferromagnetic instruments[^67].

In conclusion, we note that the wave length in a lightning discharge lies within the limits of 10—100 μsec (this, of course, is—

series of oscillations) or the wavelength lies in the interval \(10^5\)—\(10^6\) cm.

Length of the wave front in a thunderstorm discharge. As was indicated above, the presence of errors in calculating the wave parameters has the most serious effect on the determination of the front length.

Fig. 29. Distribution of data by wave lengths

Table 15 gives a summary of data on front length, collected from the works of Stekolnikov\(^{24}\), Sporn and Lloyd\(^{77}\), Norinder\(^{45}\) and Lewis\(^{78}\).

Table 15

Front length in \(\mu\)sec	Number of discharges	%
0—2	22	10.7
2—5	85	41.8
5—10	77	37.5
10—20	11	5.4
20—30	4	2
30—40	3	1.3
40—60	1	0.4
60—80	1	0.4
80—100	1	0.4
	205	100%

Despite the existing scatter of readings for the front length, the main part of the measurements refers to times up to 20 \(\mu\)sec. 95% of all measurements have a wave-front length of less than 20 \(\mu\)sec. 90% of all measurements lie below 10 \(\mu\)sec.

Steepness of the front of the wave of a thunderstorm discharge. This wave parameter has been measured most rarely, owing to the difficulties that accompany the determination of the rate of rise of the front from oscillographic records. Graduation here, apparently, is very difficult.

Measurements made by Stekolnikov\(^{4,24}\) and Norinder\(^{45,79,80}\) give values for the steepness of the front of the order of several thousand amperes per microsecond.

§6. Multiple discharges

Photographs of lightning taken with the Boys camera and other cameras make it possible to separate in time the successively occurring

pulses in a thunderstorm discharge. Oscillographic recording of thunderstorm discharges with a relatively small time sweep also gives an idea of multiplicity.

On the basis of the data of Stekolnikov^25, McEachron^44, and Schonland^40, Table 16 has been compiled.

Table 16

Number of impulses in a multiple discharge	Number of observations	%
1	215	61,6
2	45	12,9
3	26	7,5
4	21	6,0
5	13	3,7
6	8	2,3
7	6	1,7
8	4	1,1
9	2	0,6
10	3	0,8
11	1	0,3
12	2	0,6
13	1	0,3
14	—	—
15	1	0,3
. . .	. . .	. . .
27	1	0,3
	349	100%

It follows from Table 16 that the most probable value of the multiplicity may be expected to be equal to 4.3, not counting the number of single discharges, which occur most frequently (215 out of 349). If single discharges are taken into account, then the mean degree of multiplicity falls to ~2.3.

The total duration of a multiple discharge is given most fully by Stekolnikov, McEachron, and Schonland. The maximum duration of a multiple discharge was observed in Stekolnikov’s measurements—1.55 sec, McEachron’s—1.53 sec, and Schonland’s—0.93 sec. As can be seen, the duration of multiple lightning is far from “lightning-fast.” The most frequently occurring duration of a discharge does not exceed 0.25 sec.

The time intervals between the individual impulses of a multiple discharge. The sequence of impulses in a multiple discharge occurs at a rate far from uniform. The time intervals between impulses are very different, and therefore in general the total duration of one or another thunderstorm discharge is not a direct function of the degree of multiplicity; thus, for example, the greatest total duration of a discharge is not always found among discharges with maximum multiplicity.

It may be considered that 80% of all measurements give time intervals between impulses of less than 0.1 sec. The maximum interval was observed in the measurements of Stekolnikov (1937) and proved equal to 0.93 sec.

In conclusion of this chapter we shall present a summary table of the most probable values of the principal parameters of a thunderstorm discharge.

Table 17

Parameter	Most frequently occurring value	Maximum registered value	Minimum registered value
Polarity	Negative (out of 4 disch. 3)	—	—
Lightning currents registered in supports	up to 20,000 A	220–230 kA	0.5 kA
Quantity of electricity	up to 2 coulombs	164 coulombs for the entire discharge	0.5 coulomb
Wavelength, μsec	10–30	100	<10
Front length, μsec	5–10	80–90	<1
Steepness of the front	5,000 A/μsec	—	—
Multiple-stroke character	1	40 disch.	—
Duration of a multiple discharge	0.2–0.6 sec.	1.55 sec.	—
Time intervals between impulses in a multiple thunderstorm discharge	0.03–0.05	0.93 sec.	0.001 sec.

Table 17, compiled on the basis of the preceding data taken from the works of a number of authors, gives an approximate picture of the parameters of lightning.

V. CONCLUSION

The study of the phenomenon of the thunderstorm discharge is of enormous interest both from the technical and from the physical points of view. The physical nature of lightning, as is evident from all that has been set forth, remains not yet clarified. The existing theories of spark propagation (Townsend’s theory, Loeb’s theory and Cravath’s54) give a fairly graphic representation of the mechanism of the phenomenon, but do not always describe the physics of the phenomenon sufficiently completely and, of course, do not unite the complex of phenomena—spark, lightning, and thunderstorm formation. The general problem of the electrical state of the Earth does not have a sufficiently deep theoretical basis. From the experimental side, as has been shown, there is a comparatively large amount of material on questions of linear lightning, and also on the question of thunderstorm formation. Materials on the study of the laboratory spark are likewise available in the corresponding literature. All this material, obtained in various schools,

with the results of various investigators, for the most part proves to be consistent. In some cases the available experimental material may be a good criterion for the correctness of one or another proposition of the theory. This last applies, for example, to the character of the development of the thunderstorm discharge, the velocity of propagation of the individual stages of the discharge, multiplicity, etc. In other cases, for example, in questions of the amount of electricity carried by a thunderstorm discharge and of the wave parameters, a still rather large number of observations is required in order to obtain sufficient statistics. In some questions the general method of determining one or another parameter is not entirely reliable. However, the general statistical data concerning the magnitudes of the principal parameters of lightning are apparently close to the real values (see Ch. IV, Table 17).

The work being conducted with the laboratory spark (Stekolnikov, Allibone, and others), in parallel with investigations of thunderstorm discharges in the field and on transmission lines (Stekolnikov, Schonland, McEachron, Lewis and Foust, Norinder, and others), is undoubtedly a reliable means of solving the general problem.

Work with “long” sparks, i.e. with discharges at voltages of several million volts, deserves great attention as a transitional stage toward the study of real lightning. It is all the more necessary because almost all the characteristics of lightning can be reproduced in a laboratory spark, including multiplicity and a stepped leader. In addition, work on obtaining large currents in the spark, analogous to currents in the lightning channel, by means of special current generators, and the study of the behavior of a high-voltage spark at large currents, are also essentially necessary.

Only a comprehensive study of this complex question will help to reveal the nature and to represent the real mechanism of the origin and development of the thunderstorm discharge.

This entire complex of questions is becoming extremely urgent for the Soviet Union in connection with the general problem of the Great Volga and the construction of the Kuibyshev hydroelectric complex.

LITERATURE

1. Keller, Atmospheric Electricity, 1920, Publ. NKP.
2. I. Stekolnikov, A. Akopyan, A. Belyakov, Lightning and Protection against Its Effects, Publishing House of the Academy of Sciences of the USSR, 1938.
3. Brooks, Meteorological Office Geophysical Memoir, 23 (1925).
4. Stekolnikov and Lampl, Electricity, No. 5, 1938.
5. Simpson, J. I. E. E., 67, 1269, 1929.
6. P. Lenard, Meteor. Z., 39, 249, 1904.
7. Simpson and Scrase, Proc. Roy. Soc., A 161, 309, 1937.
8. Simpson, Proc. Roy. Soc., A 111, 56, 1926.
9. Allibone and Schonland, Nature, 128, 794, 1931.
10. Lewis and Foust, A. J. E. E., 54, 934, 1935.
11. McEachron and McMorries, G. E. Rev., 39, No. 10, 1936.

1. C. T. R. Wilson, J. F. I., 208, 1, 1929.
2. McEavans and McEachron, G. E. Rev., 39, No. 9, 1936.
3. E. W. Schumann, Physik. Z., 26, 81, 1925.
4. C. T. R. Wilson, Phil. Trans. Roy. Soc., A 221, 73, 1920.
5. J. C. Gott, Proc. Roy. Soc., A 151, 665, 1935.
6. Goodlet, J. I. E. E., 81, 1, 1937.
7. Ross Gunn, Terr. Magn. & Atm. El., 40, 79, 1935.
8. Dauzeré, C. I. G. R. E. N. T., No. 311, 1935.
9. Dauzeré, C. I. G. R. E. N. T., No. 322, 1937.
10. C. V. Boys, Nature, 118, 749, 1926.
11. C. V. Boys, Nature, 127, 25, 1931.
12. G. Allbright, J. Appl. Phys., 8, No. 5, 1937.
13. I. Stekolnikov, Electricity, No. 2, 1937.
14. Stekolnikov and Valeev, Electricity, No. 1, 1938.
15. N. Myakishev, Novosti tekhniki, No. 25, 1937.
16. Stekolnikov and Myakishev, Electricity, No. 11, 1938.
17. Stekolnikov, Electricity, No. 8, 1937.
18. Stekolnikov, Electricity, No. 1, 1939.
19. Schonland, Malan and Collens, Nature, 134, 177, 1934.
20. Schonland and Collens, Proc. Roy. Soc., A 143, 654, 1934.
21. Schonland, Hodges and Collens, Proc. Roy. Soc., A 166, 56, 1938.
22. McEachron, Elec. Eng. 57, 493, 1938, J. F. I., 227, 149, 1939.
23. J. F. Peters, El. World, 183, 1924.
24. F. Peek, Dielectric Phenomena in High-Voltage Engineering, 1934, ONTI, Energoizdat.
25. C. V. Boys, Nature, 122, 310, 1928.
26. H. H. Haffert, Proc. Phys. Soc., 10, 176, 1890.
27. B. Walter, Ann. Phys., 18, 863, 1905.
28. A. Larson, An. Rep. Smithsonian Inst., p. 119, 1905.
29. Schonland, Malan and Collens, Proc. Roy. Soc., A 152, 595, 1935.
30. McEachron, Elec. Eng., 53, 1633, 1934.
31. Walter, Phil. Mag., Series 7, 20, 1144, 1935.
32. Malan and Collens, Proc. Roy. Soc., A 162, 175, 1937.
33. McEachron, Elec. Eng., 57, 510, 1938.
34. H. Norinder, J. F. I., 220, 69, 1935.
35. Teopler, Hermsdorf-Schomburg, Mitt., 25, 734, 1926.
36. Bellashi, Elec. Eng., 54, 837, 1935.
37. Schonland, Phil. Mag., 23, 503, 1937.
38. Bellashi, Elec. Eng., 56, No. 10, 1937.
39. Matthias, E. T. Z., 58, No. 32, 1937.
40. Allibone, J. I. E. E., 82, 513, 1938.
41. Workmann, Snoddy and Beems, Physics, 7, 375, 1936.
42. Schonland, Proc. Roy. Soc., 164, 132, 1938.
43. Loeb and Cravath, Physics, 6, 125, 1935.
44. Loeb, Rev. Mod. Phys., 8, 267, 1936.
45. Rudenberg, Wiss. Veröff. Siemens-Konz., 29, Part 1, 1930.
46. Ollendorf, Archiv Elek., 26, 1932, 1932.
47. Bewley, Gen. Elec. Rev., 36, 516, 1933.
48. Ollendorf, Archiv Elek., 27, 169, 1933.
49. G. C. Simson, Nature, 113, 677, 1924.
50. Lewis and Foust, Elec. Eng., 56, 101, 1937.
51. McEachron and McMorries, Elec. Eng., 57, 307, 1938.
52. E. Bell, Elec. Eng., 55, 1306, 1936.
53. Grunewald, J. C. L., H. T. S., Report, No. 316, 1937.
54. K. Berger, Bull. S. E. V., No. 6, 1936.
55. Rukkaky and Katoh, E. T. J., 2, 175, 1938.
56. Foust and Henderson, Elec. Eng., 54, 373, 1935.
57. Sporn and Gross, Elec. Eng., 56, 245, 1937.
58. Zaduck, E. T. Z., No. 17, 475, 1935.
59. Collins, Elec. World, 103, 688, 1934.
60. Lewis and Foust, Elec. Eng., 56, 452, 1937.

1. F. Peek, A. I. E. E., Tr., 50, 1077, 1931.
2. Lewis and Foust, A. I. E. E., Tr., 49, 317, 1930.
3. Bell and Price, A. I. E. E., Tr., 50, 1101, 1931.
4. George and Eaton, A. I. E. E., Tr., 50, 877, 1931.
5. Gross and Cox, A. I. E. E., Tr., 50, 1118, 1931.
6. Sporn and Lloyd, A. I. E. E., Tr., 49, 905, 1930.
7. Lewis, Gen. Elec. Rev., 39, 543, 1936.
8. H. Norinder, J. F. I., 218, 717, 1934.
9. H. Norinder, E. T. Z., No. 5, 105, 1938.