W. Elenbaas, The high pressure mercury vapour discharge, Selected Topics in Modern Physics, II, North-Holland Publishing Company, 1951, Amsterdam, 173 pp., 80 figs., 15 tables. Bibliography: 138 titles.

V. Elenbaas, High-Pressure Mercury Discharge.

In 1951 the Dutch series “Selected Topics in Modern Physics” began to appear. In addition to the work under review, it included: J. Rosenfeld, Theory of the Electron, and S. de Groot, Thermodynamics of Irreversible Processes.

The book under review is a monograph, chiefly summing up the author’s 20-year work on creating a theory of the high-pressure mercury discharge.

As is known, the theory of gas discharge at low and medium pressures (approximately up to 1–10 mm of mercury) is distinguished by complexity and cumbersomeness. Under these conditions there is not yet thermodynamic equilibrium of the separate processes that determine the discharge mechanism. It is therefore necessary to take exact account of the role of each of the processes separately, which requires knowledge of such atomic characteristics as excitation functions, ionization functions, etc. In a high-pressure discharge the conditions under which they may be regarded as thermodynamic equilibrium are, to one degree or another, approached, which makes it possible greatly to simplify the methods of theoretical analysis of the properties of such a discharge.

In thermodynamic equilibrium it is sufficient to know the temperature and pressure of the gas in order to characterize exactly the conditions of excitation and ionization of the atoms in the discharge. Of the atomic constants only the critical excitation and ionization potentials are needed. The thermal point of view on the mechanism of the high-pressure discharge has long appeared in the literature, but mainly in connection with Petrov’s theory of the carbon arc. There were also long-standing naïve and erroneous attempts to apply this same point of view to the mercury discharge. However, the development of the modern thermal theory of the mercury discharge began approximately 20 years ago. The necessity of creating such a theory was dictated by the rapid development of the manufacture of mercury lamps. In particular, the thermal theory played a decisive role in the creation of super-high-pressure mercury lamps possessing enormous brightness.

The value of Elenbaas’s book lies in the systematic exposition of the thermal theory of the high-pressure mercury discharge. The principal shortcoming of the book is the absence of elements of a critical attitude toward the thermal theory. This theory, alongside its achievements, has weak points, which are glossed over in the exposition. As we shall see below, the thermal theory is presented in a somewhat embellished form.

Let us proceed to a review of the concrete content of the book.

The first chapter is introductory in character and contains rather heterogeneous material. The chapter begins with a brief historical sketch of the development of the construction of high-pressure mercury lamps. Next comes a definition of the concept of a high-pressure mercury discharge (above 10 mm of mercury). The definition is connected with the onset of a sharp increase in radiation output with increasing pressure. At the end of the chapter the question of the mechanism of the high-pressure discharge is touched upon. However, this question is treated superficially. The author briefly sets out the thermal theory of the discharge, but avoids the question of the arguments that make the applicability of this theory legitimate. The question of the establishment of thermodynamic equilibrium, with which the question of the applicability of the thermal theory is connected, is discussed in the book, or rather touched upon, here and there, as we shall see, without the necessary persuasiveness.

Therefore the author’s assertion concerning the applicability of the Boltzmann and Saha formulas for determining the concentrations of excited atoms and ions in the discharge remains unproved in this chapter. The introduction of the full statistical sum of states (formula 1.33, p. 9) is superfluous, for in the book this sum is nowhere used. At the end of the chapter an approximate estimate is given of the discharge temperature, which turns out to be approximately 5000° K.

The subsequent chapters are based on the application of the Boltzmann and Saha formulas to the theory of the mercury discharge.

The second chapter is devoted to applications of the theory in an elementary form. First of all, the effect of contraction of the discharge is examined, which is explained by the fall of temperature from the axis of the discharge toward the walls.

The author does not indicate that the solution of an integral equation of Abelian type, to which the recalculation of experimental data for intensities is reduced, is associated with large errors arising in the differentiation of experimental curves (p. 14).

In Table 1 the second and even the first digits after the decimal point are clearly unrealistic. In general, throughout the book one senses an excessive fascination with “accuracy” in writing down numbers.

Of interest is the analysis of the dependence of the total radiation intensity on the power supplied to the discharge. Of particular practical importance is the fact that the total radiation intensity does not depend on the amount of mercury per unit length of the discharge column. Also important are the data on the potential gradient and the semi-empirical theory leading to a formula connecting the gradient with the power, the amount of mercury, and the lamp diameter.

The third chapter is devoted to the main discharge parameter—the temperature. Various methods for determining the discharge temperature are described here.

All the principal methods are indirect in character, but they lead to results that agree fairly well with one another. The most interesting methods are: by absorption of X-rays (density); by broadening of spectral lines. The calculation of the temperature from the absolute intensity of the yellow lines does not make a convincing impression, owing to the diversity found in the literature in the values of transition probabilities (see p. 37). In this respect, the calculation made with the aid of Wien’s formula and data on the intensities of the lines of the visible triplet is more justified (see Izv. AN SSSR, 1938, p. 305). The verification of the correctness of the temperature data on the basis of formulas for the electron mobility is, of course, very approximate (p. 49), which is not noted in the book.

In the fourth chapter the basic differential equation for the distribution of temperatures in the discharge is derived, and solutions of this equation are analyzed.

The equation takes into account only two kinds of energy losses: a) by radiation and b) by thermal conductivity. The neglect of other types of losses is argued quite convincingly. However, the formula (4. 2. 3, p. 55) for radiation losses raises objections. In this formula the phenomenon of reabsorption of radiation in the discharge is in no way taken into account, although it is known that a large part of the radiation arising in the volume of a mercury discharge is reabsorbed (see, for example, Izv. AN SSSR, 1936, p. 441).

The basic equation makes it possible to find important similarity conditions for discharges (p. 55). These conditions suggested the design of ultra-high-pressure capillary lamps. As noted on p. 56, the similarity conditions are violated at the experimental point, which is connected with the inaccuracy of the basic equation.

The introduction of an effective discharge temperature is useful.

The chapter ends with an exposition of the results of numerical integration of the basic equation by various authors. It should be pointed out that this laborious work did not yield any substantially new results, and on the whole was of little value in view of the approximate character of the basic equation.

The fifth chapter is specially devoted to convection in the discharge; the small magnitude of convective energy losses is emphasized. For cylindrical lamps this is probably correct. Of interest is the analysis of the question of the transition of the laminar motion of vapors into turbulent motion, which is accompanied by “spiraling” of the discharge column.

In the sixth chapter questions connected with the influence of the most varied factors on the mercury discharge are collected. These include the magnetic field, rotation about the axis, and, finally, the addition of inert gases and cadmium.

The latter question is indeed important in connection with the problem of correcting the chromaticity of mercury lamps. A somewhat comical impression is produced by the “luminous” calculations on pp. 103—104, where the theoretical figure 1.002 appears, and after graphical integration the same figure 1.002 is obtained from indirect experimental data!

The small seventh chapter (only 4 pages) somehow oddly disrupts the sequence of exposition, for it is devoted mainly to a superficial description of ultra-high-pressure lamps.

The author practically does not concern himself with the theory of spherical lamps developed by German researchers. Such a limitation of the book’s content seems excessive to us. After all, the whole problem of the high-pressure mercury discharge is not so broad that a selection of material dictated narrowly by the author’s personal scientific interests should be permissible within it.

Exclusion of questions of the theory of spherical lamps is all the more incorrect because these lamps are of great practical interest. At the same time, in spherical lamps the electrodes play a substantial role, which introduces significant changes into the foundations of the thermal theory of these lamps.

The eighth chapter is devoted to the spectral properties of the high-pressure mercury discharge. First of all, it contains fairly detailed spectral characteristics of the line spectrum of the discharge. Then the question of the influence of discharge parameters on line intensity is discussed theoretically. This discussion is notable for its brevity and reduces everything to changes in the discharge temperature. Considerable attention is devoted to the important question of continuous spectral bands both near the line 2537 Å and of recombination and molecular bands. The chapter ends with a section that is particularly interesting concerning the lowering of the effective ionization potential of mercury atoms. The point is that at a sufficiently high density of atoms and ions the ionization potential ceases to be an atomic constant and begins to decrease noticeably, which is accompanied by the disappearance of lines beginning with high energy levels.

The ninth chapter is a mixture of quite heterogeneous questions. Here, first of all, there are important data on the influence of pressure on the potential gradient and a formula for calculating the pressure. Then, with the aid of Gvozdover’s formula, small effects under the given conditions associated with the influence of positive ions on electron mobility are analyzed. The very short discussion of phenomena at the electrodes sets forth critically the views of Weizel, Rompe, and Schen. The author rightly points out the limited nature of the “minimum principle” (minimum potential drop).

The question of the absorption of radiation in the discharge is set out very briefly and insufficiently. Here the results of corresponding Soviet works are almost not used. For example, the important question of the angular distribution of the radiation intensity of the discharge is not touched upon at all. The chapter ends with a very useful section devoted to determining lamp dimensions for given lighting-engineering and electrical-engineering parameters.

Finally, the last, tenth, chapter bears the laconic title—equilibrium. This chapter is of a purely physical character and analyzes the elementary processes that determine thermodynamic equilibrium in the discharge. The author says that all the preceding material testifies to the correctness of the thermal point of view and that only questions concerning details of the processes occurring in the discharge remain.

It seems to us that all the preceding material still requires critical reconsideration from the standpoint of the unambiguous necessity of the thermal point of view for its explanation. Unfortunately, there are still few decisive experimental facts that unambiguously and quantitatively confirm the correctness of the thermal point of view. All calculations,

based on the thermal point of view, are of a crude, semiempirical character. Therefore, an independent consideration of elementary processes appears necessary and interesting.

First of all, the author shows that, in thermal equilibrium, the principal excitation is produced by electrons, and not by atoms. There has hitherto been some confusion on this question. Further, on the basis of data from Soviet works, it is shown that in the excitation of atoms to high levels the main role is played by stepwise processes. Unfortunately, the question of establishing equilibrium is considered less convincingly. A necessary condition for equilibrium is the overwhelming predominance of electron collisions over spontaneous optical transitions. Radiation leaves the discharge outward and disrupts the closed character of the system.

The author compares these processes for a discharge at a pressure of 0.88 atmosphere, which he adopts as a standard, and obtains the ratio \(2^{1/2}\). As the author himself notes, this figure is too small for establishing true equilibrium. To this it must be added that the figure itself is not very reliable.

In discharges at higher pressures the situation is better. In general, however, the question of the validity of the thermal point of view remains topical.

On the whole, despite the shortcomings indicated, the book is undoubtedly of interest to specialists in the physics of gas discharges and light sources, and may be useful if, in using it, one takes into account the one-sidedness noted above and its insufficient criticality. The latter is especially characteristic of workers in company laboratories, among whom is the author of this book as well (Elenbaas heads the discharge-lamp department of the Philips firm’s laboratory).

The book is well illustrated and provided with a subject index.

V. A. Fabrikant