Bibliography

K. I. Krylov, Physical Foundations of Electrovacuum Technology, GEI, Leningrad—Moscow, 1949, 336 pp., price 14 rubles.

The book under review is a revision of a course of lectures delivered at the Leningrad Electrotechnical Institute named after V. I. Lenin, and is intended as a textbook for students of electrotechnical institutions of higher education. It is the first attempt to create a special physics course for an electrovacuum engineer. This is the author’s great merit.

The book contains two large sections:
1) the kinetic theory of gases; 2) electronic phenomena. The physics of gas discharge is not included in the book, although, as the author himself indicates (p. 5), the course on the physical foundations of electrovacuum technology contains a corresponding section. Evidently, together with gas discharge the theory of the structure of the atom also dropped out, which, as will be seen below, led to serious methodological difficulties.

The exposition of the kinetic theory is preceded by a brief introduction containing material from probability theory. This is reasonable, since probability theory is absent from the higher-school mathematics course. It seems to us only that it would have been far simpler and more straightforward to give a direct derivation of Stirling’s formula. The author correctly begins the kinetic theory with an exposition of Lomonosov’s ideas, but he should have given not only Lomonosov’s conclusions, but also his arguments. Lomonosov very sharply juxtaposed the outwardly contradictory properties of gases and believed that the only way to resolve this contradiction was to introduce kinetic concepts. Lomonosov’s argument has retained its freshness and clarity even in our day.

In introducing distribution functions, the author did not emphasize the general features of the statistical method of consideration, but the derivation of the distribution functions itself is constructed methodologically correctly. It hardly made sense to introduce the virial theorem only for the derivation of the equation of ideal gases (p. 35), especially since subsequently the question of the relation between the time average and the ensemble average is not touched upon anywhere. In discussing the Maxwell distribution only the three-dimensional case is considered, although in electrovacuum technology the one-dimensional problem is very important as well. There is an excessive enthusiasm for elementary but cumbersome calculations (for example, the calculation of the number of collisions, pp. 56–62). Here the modest physical results do not justify the lengthy and not very meaningful calculations. All these “strict” calculations are far from strict in their foundations and therefore make little sense. The question of the distribution of free-path lengths can be presented more simply by making use of the multiplication theorem...

probabilities (given in the book). On the other hand, in considering transport phenomena, the exponential character of this distribution function should have been emphasized (as well as the possibility of integration to infinity in formula 178, p. 74). In general, sufficient space is devoted to transport phenomena, but the shortcomings of the theory of diffusion are noted too mildly (for example, the roughness of formula 269). In table 9 on p. 99, for some reason, the data for the hydrogen–oxygen mixture are given twice and differ sharply. Questions of rarefaction, important for vacuum engineers, are discussed in considerable detail: flow through tubes and effusion from an orifice. Classical statistics concludes with a discussion of the adsorption of gases on the surface of a solid body, after which Fermi statistics is given. Fermi statistics is introduced very formally and abstractly (for example, the question of the magnitude of the phase cell, and the question of the indistinguishability of particles), which will undoubtedly make it difficult for students to master it. Here again there should have been fewer derivations (which in any case are not carried through to the end) and more physics.

Finally, let us make several general comments on the exposition of kinetic theory as a whole. A major shortcoming must be considered the absence of any mention of the distribution in a field of force, which is very important for electrovacuum technology. This is all the more strange since the Maxwell distribution is essentially obtained as a special case of the general distribution (formula 65, p. 40). Another defect is the almost complete absence of any connection with thermodynamics. (The connection of entropy with probability is given in passing, in the form of a footnote on p. 137, already in the statistics of Fermi!) In Soviet textbooks a narrowly utilitarian approach is out of place. By reducing the derivations, more attention could have been given to the conceptual side of the matter. One should not think that an engineer does not need this. The cultivation of a worldview is a task no less important than the communication of a certain sum of formal knowledge.

The second part of the book is, perhaps, less formal and more physical in character, although here too there are unnecessary derivations. The second part begins with electron optics. Here, for some reason, the well-known works of Boguslavsky are not mentioned. The exposition of the foundations of electron optics is conventional, but somewhat cumbersome. It was hardly necessary to introduce a volume charge when deriving the basic equation (103) (p. 175), after which it ceased to be homogeneous with respect to \(V\) (contrary to the assertion on p. 176). Equation (131) should have been written directly from the law of conservation of energy, indicating that the Lorentz force cannot in general change the energy of the electron (and giving a simple explanation). The text on p. 185 creates the impression that the axially symmetric field has, in this respect, some special properties. In analyzing the focusing action of fields, one should have emphasized the increase of the force returning to the axis as the angle of inclination of the electron trajectory increases. Then the whole exposition would at once have acquired “flesh and blood” and ceased to be formal.

Several pages in the book are devoted to the exposition of elements of accelerator theory. Here one is surprised by the absence of even a brief exposition of Veksler’s important works. This is all the more strange since the author, in the preface, mentions Veksler’s work, while in the text he lists other Soviet works on accelerators (in particular, his own). At the same time, the exposition of the end of § 36, devoted to the cyclotron, proves to be incomplete, with no indication of the way out found by Veksler for extending the capabilities of accelerators.

It is incorrect that the dependence of mass on velocity is presented in the book not as an experimental fact, but only as a consequence of the theory of relativity (see p. 153).

After electron optics there comes a large paragraph devoted to the wave properties of the electron. This paragraph is not entirely successful. One could not, without any explanation, write down the Lorentz transformations and immediately apply them to obtain the basic wave-mechanical relations. Either the meaning of the Lorentz transformations should have been explained (which, of course, is difficult), or they should have been dispensed with. The absence in the book of a discussion of the structure of the atom will, of course, make it more difficult to assimilate the wave-mechanical ideas.

The theory of thermionic emission is presented clearly and thoroughly, and all questions connected with the role of space charge and initial velocities are considered. It seems to us that the reason for the appearance of a double layer at the boundary of a metal is formulated in a not entirely usual and precise way (polarization of atoms, p. 224).

On pp. 239–240 there is inconsistency in the estimates of the transparency of the potential barrier (0.93 and 0.5).

The author rightly gave attention to the operation of the cathode in the pulsed regime, but it was hardly worth reproducing here all the tabular material. Questions of autoelectronic emission are covered sufficiently fully and clearly, but the shot effect is presented too laconically.

The photoelectric effect is also considered briefly, but already in historical sequence, and the important role of Russian scientists in the development of the doctrine of the photoelectric effect is shown.

The exposition of the theoretical work on the photoelectric effect is on the whole successful, but it was scarcely necessary to present the theory of Campbell and Fowler, which has not gained general acceptance. Much space is devoted to secondary emission, which is quite correct. Secondary emission plays a major role in electrovacuum devices (both positive and negative).

At the end of the book a short bibliography is given, not very carefully selected. For example, it includes the certainly far too difficult books by Gibbs and Pauli, and does not include such an important book as Landau and Lifshitz’s Mechanics of Continuous Media.

As is evident from all that has been said, K. I. Krylov’s book is not free of serious shortcomings. It pays insufficient attention to the education of the student’s physical outlook, and the necessary proportions in the presentation of the material are not always found. However, the latter is connected with the novelty of the task. K. I. Krylov undoubtedly has the credit of having made a beginning in a very important matter, and the book, even with the shortcomings indicated, will be useful.

V. Fabrikant