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V. N. Kessenikh. Radio Wave Propagation, Gostekhizdat, Moscow, 1952, 488 pp., price 13 rubles 10 kopecks.
Gostekhizdat has issued, in a print run of 10,000 copies, V. N. Kessenikh’s book Radio Wave Propagation, intended to serve as a textbook for students of radiophysics specialties taking the corresponding courses at universities.
Radio-wave propagation is one of the important and interesting disciplines, encompassing a broad range of questions in the physics of electromagnetic fields. In view of the advances achieved in this field in recent years, there is undoubtedly a pressing need for a new textbook in which, alongside an exposition of the old classical work, the results of the latest investigations would be surveyed and systematized.
Unfortunately, the book written by V. N. Kessenikh not only fails to meet this purpose, but also does not satisfy a number of elementary requirements imposed on any scientific publication in general.
Let us dwell on some of the characteristic errors made by V. N. Kessenikh in scientific, historical, and methodological questions.
- A considerable part of the questions connected with radio-wave propagation is treated by the author from fundamentally incorrect positions and is in a number of cases accompanied by gross errors. Thus, in chapter 13, V. N. Kessenikh, considering the problem of the reflection of radio waves from a linear ionospheric layer, uses at the beginning of the layer only one boundary condition—the equality of the electric fields—“forgetting” that the problem concerns the solution of a second-order differential equation requiring the imposition of two boundary conditions. Naturally, the result obtained by the author turns out to be completely wrong. In particular, from the solution given in the book it does not follow (contrary to the author’s assertion) that in the absence of absorption the modulus of the coefficient of reflection of radio waves from the layer must be identically equal to unity.
Further, in chapter 2, V. N. Kessenikh, criticizing the works of a number of scientists devoted to the question of the magnitude of the electric field acting in an ionized gas, asserts that “the average scalar potential in an ionized medium has no... dipole component. The magnetic moment of the currents caused by the displacement of electrons under the action of an external field is preserved and completely determines the dielectric permittivity of the plasma” (p. 102).
It follows from this statement that the author denies the applicability of the concept of polarization to a plasma and believes that the dielectric constant is due to the magnetic moment of the currents flowing in the medium. Yet it is well known that the magnetic moment of currents determines not the dielectric but the magnetic permeability, whose distinction from unity, incidentally, practically need not be taken into account in analyzing the propagation of radio waves in the ionosphere. We shall not dwell in detail
on these errors, since they are analyzed in detail in the article by V. L. Ginzburg in ZhETF, 25, No. 4, 488 (1953).
The author errs likewise in presenting the foundations of the theory of the electromagnetic field, asserting, for example (p. 30), that “as a property of real things, lines of force exist in the same way as annual rings in the trunk of a tree or slip planes in a plate of mica,” and criticizing the point of view set forth on this matter in the well-known textbook by I. E. Tamm, Fundamentals of the Theory of Electricity, where, in particular, with regard to the concept of lines of force, it is said that “the concept has a conditionally auxiliary significance and that lines of force serve only for the graphical representation of the direction of the electric vector.” On p. 39 V. N. Kessenikh denies the applicability of the concept of the flux of electromagnetic-field energy to the case of static fields, and on this occasion he once again considers the directly opposite assertion of I. E. Tamm in the textbook already mentioned to be incorrect. In connection with this we note that the unambiguous localization of the Umov–Poynting vector and, in particular, the applicability of this concept to a static field follow from general considerations of relativistic invariance (see V. A. Fok, Uspekhi fiz. nauk, 45, 160 (1951)).
Chapter 8 is set forth at a level far from contemporary (at the level of Kessenikh’s old works—1932 and 1940). The author does not consider it necessary to give a precise and clear formulation of the electrodynamic problem to be solved in this chapter (as, incidentally, in some others as well), and therefore only after reading the whole chapter in its entirety can one guess his intentions. The author’s aim, apparently, was a “construction of a scheme” (following his own terminology) for the excitation of a cylindrical vibrator of finite length by the example of the rigorous solution of the problem of the excitation of an infinite cylindrical wire by a concentrated source of energy. In doing so, three different problems are mixed into one:
1) excitation of an infinitely long ideally conducting cylindrical wire by a concentrated source of e.m.f.;
2) excitation of an infinite wire possessing finite conductivity;
3) excitation of a finite segment of a thin cylindrical wire by a concentrated e.m.f.
The author writes: “For a circular wire of radius \(\rho\), the intensity of the electric and magnetic fields propagating along the \(z\)-axis is expressed as
\[ E_\rho=\frac{A}{\rho}e^{ikz},\qquad H_\varphi=\frac{A}{\rho}e^{ikz}. \tag{40.1} \]
This solution... was only slightly modified by A. Sommerfeld by introducing a boundary condition on the surface of a wire of finite conductivity while preserving the exponential dependence on \(z\). Sommerfeld’s solution, constructed with the aid of Hankel functions in the external medium and Bessel functions in the internal medium, is not a solution satisfying possible physical conditions for the excitation of oscillations along the wire, but is a particular solution of the equation, constructed with the aid of chosen functions” (p. 271).
This statement contains two gross errors. First, the solution (40.1), although it satisfies Maxwell’s formal equations, in reality does not describe any real field, since an infinitely large flux of energy carried by this wave in the \(z\)-direction is associated with it. The “slight modification” introduced by Sommerfeld consisted in transforming the formal solution (40.1) into a physically realizable solution. Secondly, any electromagnetic wave satisfying Maxwell’s equations and carrying, for finite field amplitude,
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a finite flow of energy, is physically existent in the sense that it can be excited by sources of e.m.f. distributed in finite regions or by current sources of finite power. The opposite assertion of V. N. Kessenikh, clear from the cited quotation, is an error incompatible with the well-known theorem of uniqueness of the solution of electrodynamic problems. Besides everything else, the author misleads readers (chiefly students) by passing over in silence the fact that a surface wave of the “Sommerfeld wave” type not only “satisfies the physical conditions for the excitation of oscillations along the wire,” but at the present time also finds application in the form of various systems of single-conductor transmission lines.
In §§ 41, 42, and 43 of Chapter Eight V. N. Kessenikh solves the problem of the excitation of an infinite perfectly conducting cylinder by a concentrated source of e.m.f. distributed over the surface of a toroidal belt, referring his work to the time of the 1930s and clearly ignoring all the results obtained by other authors in subsequent years (in particular, the well-known works on the theory of thin antennas), which, incidentally, is wholly inconsistent with the purpose of a textbook as such. On p. 282, in summing up the results of the solution obtained for the excitation of an ideally conducting cylinder, the author incorrectly comments on the work of V. V. Vladimirsky, supposing that the latter, five years later, simply repeated Kessenikh’s conclusion, only slightly generalizing it. In the meantime V. V. Vladimirsky solved the problem of the excitation of a “Sommerfeld wave” and, naturally, could not have repeated the conclusions of V. N. Kessenikh, who to this day does not recognize this wave as a physical reality.
V. N. Kessenikh’s “explanation” of the well-known paradoxes connected with spectral expansion is utterly untenable. In an unclear formulation on p. 320 of one of these paradoxes, V. N. Kessenikh answers it as follows: “It is evidently just as easy to answer this question as, for example, to answer the question: where are and what are the people present in a room doing if their number is equal to the difference between the number of those who entered and those who left, and if this difference is equal to zero” (sic!). No further “explanations” on this score followed. Then, in discussing the second paradox, the author, proposing for the readers’ attention the question: “If the spectral components exist after the beginning of the process, must they exist for an infinitely long time?”, answers it himself in the following manner: “The answer to this question lies in the fact that the really existing spectral components are extinguished and distorted by thermal fluctuations. This is also the cause of the phenomenon that an oscillatory circuit tuned to the carrier frequency of high-frequency-pulse oscillations repeated at a low frequency selects oscillations at the carrier frequency, and not harmonics of the pulse-repetition frequency. Fluctuations acting in the intervals between pulses smear out and suppress the action of the higher harmonics of the pulse-repetition frequency” (!). Since thermal fluctuations have no relation whatever to the question posed, any comments would be superfluous.
In Chapter 15 the theory of nonlinear effects is set forth. The cornerstone of this theory in V. N. Kessenikh’s exposition turns out to be the proposition that every medium, since it possesses absorption, also possesses nonlinear properties. However, this proposition is no more meaningful than, for example, the assertion that linear media do not exist at all and that the concept of a linear medium is an abstraction, of whose real realization one can speak only with one or another degree of accuracy. Indeed, if this proposition of V. N. Kessenikh is taken as a starting point, then from it there would immediately follow the existence of nonlinear effects in the propagation of radio waves in strongly absorbing seawater, in the propagation
of radio waves along the earth’s surface, etc. Such effects are, of course, possible, but, despite the fact that, for example, absorption in seawater is many times greater than in the ionosphere, they are so small that up to the present time they have not been detected. Therefore V. N. Kessenikh’s exposition is, in essence, devoid of content, for it does not reveal the specific character of radio-wave propagation in the ionosphere with respect to the occurrence in it of nonlinear effects, nor does it reveal the difference between the ionosphere and other media in this respect.
In analyzing the effect of “multiplication” of signals, V. N. Kessenikh comes to the conclusion that this effect is connected with the fact that the “extraordinary” wave is reflected not only from that region of the ionosphere where the refractive index for it first becomes zero, but partially enters the higher-lying, denser layers of the ionosphere, being reflected once more from the layer where the refractive index for it becomes zero a second time (see, for example, pp. 239, 347). The circumstance that, in this case, the “extraordinary” wave must traverse a considerable path in a medium where the refractive index for it is negative, and even becomes infinite, does not trouble the author of the book. The erroneousness of the point of view expressed by the author is shown in the already cited article by V. L. Ginzburg.
The number of examples of this kind could, if necessary, be increased.
- V. N. Kessenikh devotes much attention to the history of domestic science in the field of radio-wave propagation. In a number of cases he correctly emphasizes the priority and great significance of these works. However, even in historical questions the book is not free from serious shortcomings.
On p. 206 V. N. Kessenikh, for example, writes that formula (29, 20), obtained from a rigorous solution of the problem of the attenuation of the field of a dipole located on the plane surface of the Earth (“Zommerfeld attenuation function”), is “one of the special cases of Vvedenskii’s quadratic law.” The great practical importance is well known of the quadratic formulas obtained by B. A. Vvedenskii in 1928 for calculating the field of ultrashort waves. These formulas were the first practical formulas in world practice for calculating the field of ultrashort waves at not very large heights of the transmitter and receiver above the Earth. However, Vvedenskii’s quadratic formulas were obtained by him as a special case of the “reflection formulas.” Therefore the above-cited assertion by V. N. Kessenikh completely distorts reality.
Equally unfounded is V. N. Kessenikh’s presentation on p. 305 of V. A. Fok’s fundamental works in the form of a “variant” of Vvedenskii’s well-known theory of diffraction propagation of radio waves.
Further, the well-known problem of the reflection of radio waves from a linear layer, investigated by Gans as early as 1915 and then by Hartree in 1931, is set forth on p. 340 and later as though it had first been solved by L. A. Zhekulin in 1934.
The number of examples analogous to those given above could also be considerably increased.
- The pedagogical and methodological side of V. N. Kessenikh’s book also cannot be regarded as satisfactory.
The author does not set himself the aim of revealing the physical content of the problem and acquainting the reader with the ways and methods of its solution. In accordance with this, as a rule, he avoids carrying out “intermediate” conclusions even in those cases where they play a fundamental role. The author’s poor methodological orientation is manifested in the construction of the book, where first the practical features of propagation of all ranges of radio waves are set forth (Chapter IV), and, without derivation, various practical formulas and graphs are given. Only in
in the subsequent chapters (V, VI, VII, IX, X) attempts are made to consider “the simplest types of wave processes and some methods of mathematical physics.” Therefore, even leaving aside the numerous errors, one may assert that the book cannot teach anything about the essence of the material presented by the author. On p. 19 V. N. Kessenikh writes: “A radiophysicist, collaborating with an engineer in solving practical problems, must remember that his chief purpose is to assist the engineer and the practitioner ... by making use of little-noticed phenomena...,” and not primarily to study the fundamental problems of radiophysics.
On p. 23 V. N. Kessenikh declares: “...we want... to give a detailed exposition of important theorems which are either incompletely or incorrectly presented in widely used textbooks.” It follows that important theorems in the existing textbooks have hitherto been presented either incompletely or incorrectly.
Not being able to cite all the examples of V. N. Kessenikh’s implementation of his methodological principles (this would take too much space), let us examine only one section of Chapter VII, bearing the title “Formulas for Calculating the Field Strength” (pp. 265–268). After obtaining the usual Sommerfeld integral (formulas (39,16), (39,17); there are misprints in both formulas!) the limiting cases of vacuum \((k_1 = k_2)\) and an ideal conductor \((k_2 = \infty)\) are first considered, as in all books. Usually, given a dipole moment, the field of dipole radiation is then obtained. Kessenikh, however, does the opposite: assuming that the fields should be equal to
\[ P_0 \frac{e^{ikR}}{R} \quad \text{and} \quad 2P_0 \frac{e^{ikR}}{R}, \]
he determines from this the dipole moment and the radiation reaction for \(k_1 = k_2\) and \(k_2 = \infty\). At the end of page 265 it is said: “In intermediate cases the amplitude \(\mathcal E_0 l /(1 + b_1 + b_2)\) will take values depending on the details of the device,” “the arrangement of the antenna.” But in intermediate cases neither the amplitude nor the structure of the field is known, and therefore it is unclear what the author is striving for. Undoubtedly, such confusion can mislead the reader.
On p. 266 it is indicated that expression (39,22) \(E \approx k^2\Pi\) is obtained under the condition
\[ \left|\frac{k}{k_0}\right| \gg 1. \]
However, the latter condition has no relation to expression (39,22), since this expression is obtained under an entirely different condition, namely, for \(k_0 R \gg 1\).
The transition from \(E\) first to \(A(x)\), then to \(W(\rho)\) and \(W(\rho, z)\), is methodologically unjustified. Further, it is completely incomprehensible why, in considering the general case, the factor \(\mathcal E_0 l /(1 + b_1 + b_2)\) has dropped out of relation (39,27).
On p. 267 equation (39,28) suddenly appears, which has not been derived anywhere. The boundary condition (39,30) is also not derived.
The boundary condition (39,33), taken from Fock, is written in such a way that it contradicts the solution given below: indeed, substituting the solution (39,34) into condition (39,33), one can verify that for \(z = 0\) relation (39,33) proves incompatible. In reality (39,33) is valid only for \(\zeta \ne 0\). The solution (39,34), writes Kessenikh, “was given by Leontovich in the form \(W = \ldots\).” This statement is not supported by anything. In such cases it is customary at least to check the correctness of the solution by substitution. Moreover, from this one may understand that the solution (39,34) was first given by Leontovich, whereas in fact it was given by Weyl. In formula (39,35) it is written, as in Leontovich, \(\sqrt{\rho}\), whereas in Leontovich the quantity \(\rho\) corresponds, in Kessenikh’s notation, to the quantity \(y\). Thus, in Kessenikh, \(\rho\) denotes something entirely different, which creates confusion.
Concerning expression (39.38) it is said: “For the modulus \(|W(x)| = A(x)\) one obtains Van der Pol’s asymptotic formula, which gives results coinciding with Shuleikin’s calculation \(A(x) = \ldots\)” (39.38). However, this is not an asymptotic formula; no formula at all can be obtained from \(W(x)\), and it is an empirical interpolation formula, chosen so as to describe the exact curve. It is perfectly clear that the reader can derive very little from acquaintance with such a text.
Further, such paragraphs as 75, 81, 83, 87, 88, 89, 91, 92 are highly characteristic. These paragraphs contain practically nothing except the heading, and are included in the book, probably, for “completeness,” whereas the questions touched upon in them are very important. As an example we quote here in full § 91, “Solar radio noise”: “The radiation produced by the outer layers of the chromosphere and the solar corona, as already indicated in § 77, contains radio-frequency components lying mainly in the meter-centimeter and meter wavelength range. These fluxes consist of a more stable thermal (fluctuation) part and an unstable turbulent and ‘thunderstorm’ part. For more detail on this see the literature indicated in § 77.” And this is all that the author considered it possible to report about solar radio noise.
Above we have dwelt on a whole series of V. N. Kessenikh’s errors, far from exhausting all the shortcomings of the book noted both by us and by other members of Gorky State University who took part in its discussion. It seems to us, however, that there is no need to enumerate here all the errors and deficiencies of V. N. Kessenikh’s book, thereby increasing the volume of the review.
In conclusion we shall give only one example illustrating the style of exposition adopted by the author when commenting on works “objectionable” to him. Thus, of the well-known German scientist A. Sommerfeld, the results of whose works at one time played a substantial role in the development of the theory of radio-wave propagation, V. N. Kessenikh writes literally the following: “It is interesting to note that the choice of particular solutions made by Sommerfeld changed depending on the manual on the theory of cylindrical functions that he had to use,” and so on in the same spirit (p. 271). Such a manner of “discussing a question” is out of place in any serious book, and all the more so in a book intended to serve as a textbook for future specialists.
Thus, acquaintance with V. N. Kessenikh’s book Radio Wave Propagation shows that:
1) the book is written at a low scientific level, not corresponding to the contemporary achievements of science, and contains numerous gross errors;
2) the book is defective also methodologically (the arrangement of the material, the lack of clarity of the exposition, the unproved nature of the conclusions, an unacceptable manner of exposition that at times goes so far as frivolity, and so on), and cannot be used as a textbook;
3) despite the large amount of factual material collected in the book, its use for reference is hindered by the methodologically incorrect systematization of this material, to say nothing of the presence of errors.
The publication of V. N. Kessenikh’s book in a mass print run and its approval as a textbook by the Ministry of Higher Education is a misunderstanding, all the more regrettable because the scientific and theoretical level of the book in no way corresponds to the leading position held by Soviet radiophysicists working in the field of radio-wave propagation.
G. G. Getmantsev, S. A. Zhevakin,
M. M. Kobrin, M. A. Miller