SOME PROBLEMS OF GAS DISCHARGE OPTICS

V. A. Fabrikant

“Luminous electric discharges are impressive and magnificent. There is something alluring in them that is not present in simpler and more commonplace phenomena; they arrest the attention by their beauty, variety, and mysteriousness, as well as by the possibilities of their applications.”

—K. K. Darrow

The optics of an electric discharge in vapors and gases still cannot be regarded as a fully established branch of physics, possessing unity and coherence. This is all the more strange because the role of gas-discharge optics in the emergence of the modern theory of the structure of matter is well known. Indeed, in essence, the study of line spectra emitted in an electric discharge by vapors and gases led to the discovery of the fundamental features of the structure of atoms and molecules.

However, in all these investigations, which set themselves the aim of elucidating the structure of normal and excited atoms, it was natural to try to exclude the influence of the discharge conditions. In questions connected with the structure of the spectrum this was quite possible, but when one turns to the analysis of the intensities of spectral lines, great difficulties immediately arise. The intensities proved to depend equally both on the structure of the radiating atoms and on the conditions of excitation and the “conditions of existence” of the excited atoms, i.e., on the conditions of the discharge. The probability of a transition between the corresponding atomic energy levels, often called the intensity of a spectral line, sometimes does not affect the real intensity of the spectral line at all, and sometimes affects it in a rather complicated and indirect way.

At the same time, knowledge of the optical properties of a gas discharge is acquiring ever greater significance. Optical processes in the discharge plasma undoubtedly play a large role in the general mechanism of the discharge. Optical methods make it possible to penetrate more deeply into the mechanism of the discharge without introducing any disturbances.

V. A. FABRIKANT

Finally, a characteristic feature of the development of new light sources is that they make use of radiation from an electric discharge in vapors and gases. Sometimes this radiation is used directly (sodium and mercury lamps), sometimes the radiation is first transformed (luminescent lamps), but in any case, in every new light source the process of converting electrical energy into radiant energy begins in a gas discharge.

The classical object for work on the study of gas discharge is the mercury discharge. This is explained both by the physical properties of such a discharge and by its great practical importance. In powerful mercury rectifiers for currents of the order of tens of thousands of amperes, and in miniature luminescent lamps with powers of the order of a few watts, a discharge in mercury vapor operates.

The present article is a brief review of some results obtained at the All-Union Order of Lenin Electrotechnical Institute named after V. I. Lenin (VEI) in the field of the optics of the stationary gas discharge. The review was prepared for the twenty-fifth anniversary of VEI. The following took part in carrying out the work: F. A. Butaeva, L. M. Biberman, A. S. Kanel, K. I. Panevkin, V. L. Pul'ver, G. N. Rokhlin, V. A. Fabrikant, B. M. Yavorskii, I. P. Tsirg, and others.

We shall not adhere to chronological order, but will try to present a logically connected picture.

The work of VEI may be divided into three groups:
1) investigation of the mechanism of optical processes in a gas discharge;
2) application of optical methods to the study of the general mechanism of a gas discharge;
3) determination of elementary atomic constants from the characteristics of the discharge.

From the point of view of the mechanism of radiation, discharges at low and high pressure differ sharply. Most of the results presented below will refer to the low-pressure discharge. In such a discharge the connection between elementary atomic constants and the macroscopic characteristics of the discharge is manifested most clearly.

1. FEATURES OF THE PLASMA OF A LOW-PRESSURE DISCHARGE

The plasma of a low-pressure discharge contains two gases with sharply different temperatures: the gas in the usual sense of the word, consisting of atoms, and an “electron gas,” consisting of free electrons.

The temperature of the atomic gas is of the order of hundreds of degrees (on the absolute scale), while the temperature of the electron gas, called the electron temperature, reaches tens and even hundreds of thousands of degrees.

Such an astonishing coexistence in one volume of two gases with sharply different temperatures is qualitatively explained quite simply. Electrons, as charged particles, are accelerated

electric field acting parallel to the axis of the discharge. The electron gas is, as it were, heated by the field. This field, naturally, does not act on neutral atoms. Owing to collisions of electrons with atoms and with one another, their motion has a very complex zigzag character. The presence of a directed current in the discharge manifests itself only as a wind (drift) blowing in this electron atmosphere. As in the ordinary atmosphere, the velocity of the wind is considerably less than the mean velocity of the chaotic motion of the gas particles.

The chaotic nature of the motion of the electrons is accompanied by the establishment of a Maxwellian distribution in energy. Strictly speaking, only because of this circumstance does it make sense to speak of an electron temperature characterizing the distribution of electrons in energy. The mean energy of an electron is, as usual for monatomic gases,

\[ \frac{3}{2} k T_e, \]

where \(T_e\) is the electron temperature, and \(k\) is Boltzmann’s constant.

Figure 1 shows the Maxwellian distribution in energy. We emphasize that along the abscissa axis the energy of the electrons is plotted, and not the velocity, as is usually done. The energy of electrons is expressed in electron-volts. It is also customary to express the electron temperature in electron-volts: 1 volt corresponds to \(7800^\circ\) K. The maximum of the Maxwellian curve corresponds to an electron energy equal to one third of the electron temperature.

Fig. 1. Maxwellian distribution of electrons by energy. Typical relation between the excitation potential and the maximum of the Maxwellian curve.

If the electric field “heats” the electron gas, then collisions with atoms “cool” the electron gas. As is known, collisions of electrons with atoms may be elastic and inelastic. Inelastic collisions, in turn, are divided into impacts of the first and second kind.

In an elastic collision an electron transfers to an atom a very small fraction of its energy, on the average equal to

\[ 2\frac{m}{M}, \]

where \(m\) is the mass of the electron, and \(M\) is the mass of the atom. The smallness of this quantity explains the possibility of the existence of a large temperature difference between the atomic and electron gases.

In a low-pressure discharge the main role is played by inelastic impacts of the first kind. However, only comparatively fast electrons can make these collisions. The excitation potentials usually lie considerably to the right of the maximum of the Maxwellian distribution curve—

V. A. FABRIKANT

... of electrons over energies. The electron temperature will be the lower, the smaller are the excitation and ionization potentials of the gas atoms. In Fig. 1, \(V_a\) is the excitation potential. The shaded area represents the number of electrons capable of participating in inelastic collisions of the first kind.

At small current densities and low pressures, when secondary processes do not play an appreciable role, the energy imparted by electrons to atoms in collisions of the first kind must be entirely transformed into radiation. In discharges of this type a collision of the first kind is, in general, the principal process in the mechanism of atomic excitation. The number of collisions of the first kind is determined by the excitation function of the given atom, and by the concentration and temperature of the electrons.

For such discharge conditions it is possible to solve one of the fundamental problems of gas-discharge optics—establishing the relation between the absolute intensity of the radiation of a discharge, on the one hand, and its electrokinetic characteristics, on the other. Since the excitation functions cannot be expressed in analytic form, one has to use a reasonable approximation.

The choice of a suitable approximation made it possible to obtain an analytic relation for the intensity of a spectral line as a function of atomic constants and electronic characteristics¹

\[ I_\nu = C n N_e Q(V_m)\sqrt{T_e}\, f(T_e,V_a,V_m), \tag{1} \]

where \(C\) is a known constant, \(Q(V_m)\) is the effective cross section of the atom at the maximum of the excitation function, \(T_e\) is two thirds of the electron temperature, \(V_a\) is the excitation potential, \(N_e\) is the electron concentration, \(n\) is the concentration of normal atoms, and \(f(T_e,V_a,V_m)\) is a factor taking into account the distribution of electrons over velocities and the form of the excitation function.

Using (1), one can solve problems of three different types: 1) \(n\), \(N_e\), \(T_e\), and the excitation function are known—it is required to determine the intensity of the spectral line \(I_\nu\); 2) \(I_\nu\) and the excitation function are known—it is required to determine \(N_e\) and \(T_e\); 3) \(I_\nu\), \(n\), \(N_e\), and the form of the excitation function are known—it is required to determine the atomic constant \(Q(V_m)\). We shall consider in succession the results obtained in all three directions.

2. ABSOLUTE INTENSITY OF THE RESONANCE RADIATION OF A DISCHARGE

The most suitable object for solving problems of the first type is the sodium discharge used in sodium lamps. For the sodium atom there are highly reliable data of Christoph² and Haft³ on the excitation function. On the other hand, Drayvesteyn and Warmoltz⁴ carried out careful measurements of \(N_e\), \(T_e\), and \(I_\nu\) in a sodium discharge under various conditions, varying over very wide ...

within the limits (current strength, vapor pressure, addition of helium, neon, and argon).

In Fig. 2 the electron temperature \(T_e\) is plotted along the abscissa, and along the ordinate—the reduced intensity of the sodium \(D\)-lines, equal to the ratio \(I_\nu\) to the product \(nN_e\). It is clear that, according to (1), the reduced intensity should be a function only of the electron temperature. The solid curve was calculated theoretically on the basis of formula (1); the triangles, circles, and crosses depict the experimental results. We see that good agreement is observed between calculation and experiment, despite the fact that absolute quantities are involved. It is interesting that, in those cases where Druyvesteyn and Warmoltz themselves express doubt about the values obtained by them, our calculation gave sharply discrepant points (for example, near \(T_e = 2\)).

Fig. 2. Reduced intensity of the resonance radiation of a sodium discharge.

After the sodium discharge it was natural to turn to a more complicated object—the low-pressure mercury discharge. The low-pressure mercury discharge is of interest not only from the point of view of its application in new light sources and ionic current converters, but also as a classical object for all possible investigations in the field of gas-discharge physics. B. N. Klyarfeld\(^5\), with the aid of Langmuir probes, very thoroughly investigated the electrokinetic characteristics of a low-pressure mercury discharge—\(N_e\) and \(T_e\).

In the sodium discharge it was practically possible to confine oneself to consideration of the doublet level \(3^2P_{\frac{1}{2}, \frac{2}{3}}\) and the doublet resonance line 5889.963—5895.930 Å. In the mercury discharge the situation is much more complicated—it is necessary to take into account excitation of at least four levels \(6^1P_1\) and \(6^3P_{0,1,2}\). From the levels \(6^1P_1\) and \(6^3P_1\) the mercury resonance lines 1849.57 and 2536.52 Å begin, while the levels \(6^3P_0\) and \(6^3P_2\) are metastable. The excitation potentials \(V_a\) for the level \(6^1P_1\) are 6.67 volts, and for \(6^3P_1\), 4.86 volts, i.e. they differ by 1.81 volts, which is a very appreciable amount. The form of the excitation functions of these levels is also very different. Analysis of the literature data showed that \(Q(V_m)\) for \(6^1P_1\) should exceed approximately threefold \(Q(V_m)\) for \(6^3P_1\), and that \(Q(V_m)\) for the levels \(6^3P_{0,1,2}\) are related

V. A. FABRIKANT

with one another approximately as the statistical weights of these levels\(^{6,7,8}\), i.e. as \(1:3:5\).

The course of the intensities of the lines 1849.57 and 2536.52 Å with changing pressure was calculated on the basis of the data of B. N. Klyarfeld. The results of the calculation led to the very important conclusion that at the very lowest pressures the intensity of the line 1849.57 Å should considerably exceed the intensity of the line 2536.52 Å\(^{3}\). As the pressure increases, the ratio of the intensities changes to the opposite one, owing to the lowering of the electron temperature, in view of the above-mentioned difference between the excitation potentials. Measurements by Rossler and Schönher published later\(^{10}\) qualitatively confirmed the correctness of the calculated course of the curve for the line 2536.52 Å. Later, measurements were carried out at the All-Union Electrotechnical Institute, which also gave qualitative agreement with the theory. The maximum of the intensity curve for the line 2536.52 Å proved to lie in the region of pressures close to that predicted theoretically (\(10^{-2}\) mm Hg)\(^{11}\).

Fig. 3. Effect of pressure on the ratio of the intensities of the mercury lines 1849.57 and 2536.52 Å.

Since the line 1849.57 Å is extremely strongly absorbed by air, a special procedure had to be used for its investigation. The circumstance was used that the luminescence of willemite is excited by both resonance lines of mercury.

A layer of willemite was placed on the inner wall of the tube, part of which was covered with uviol glass transmitting only the line 2536.52 Å; the transmission of the glass for the line 2536.52 Å was measured separately. Measurements of the brightnesses of the free surface of the willemite and of the surface covered with uviol glass made it possible to estimate the role of both lines in the excitation of the phosphor and to determine a quantity proportional to the ratio of the intensities of these two lines.

In Fig. 3 the solid curves show the experimental course of the quantity proportional to the ratio of the intensities of the lines 1849.57 and 2536.52 Å\(^{11}\). The dashed line gives the theoretical curve calculated from formula (1). We see that at a small current strength (0.3 A) there is qualitative agreement in the course of the experimental and theoretical curves. The appreciable influence of the current strength on the ratio of the intensities indicates the role of secondary processes not taken into account by formula (1).

Finally, formula (1) was applied to the calculation of the inelastic losses for the excitation of all four levels \(6''P\), both radiating and metastable.

As indicated above, the probabilities of excitation to metastable levels are very high. Therefore, a considerable fraction of the discharge power must be expended on the excitation of metastables. The total power expended on inelastic losses is obtained by the corresponding summation. Here again agreement is observed between theory and experiment, despite the absence of any arbitrary constants.

3. STUDY OF THE ELECTROKINETIC CHARACTERISTICS OF THE DISCHARGE

We proceed to the use of relation (1) for determining \(N_e\) and \(T_e\), i.e., for studying the general mechanism of the discharge.

A mercury discharge in a magnetic field was chosen as the object, for in the presence of a magnetic field the use of a Langmuir probe is very complicated and can lead to large errors \(^{12}\).

The lines 3704, 3906, and 5791 Å, emitted in transitions between comparatively high levels and therefore having little reabsorption, were investigated.

The variation of the intensities over the cross section in a longitudinal magnetic field, in the light of two spectral lines \(X — 3906\) and \(O — 5791\) Å, proved to be identical. Since these lines have different excitation potentials, the coincidence of the curves testifies to the constancy of the electron energy over the cross section of the discharge. Measurements of the intensity distribution made it possible to determine directly the distribution of electron concentrations over the cross section of the discharge \(^{13}\).

Fig. 4. Effect of a magnetic field on electron energy.

Measurements of the ratios of the intensities of the lines 3704, 3906, and 5791 Å made it possible to determine the course of the electron temperature as a function of the strength of the longitudinal magnetic field, shown in Fig. 4. The observed decrease of the electron temperature was later interpreted theoretically by Tonks \(^{14}\). On the other hand, it was shown that, in the diffusion regime, a longitudinal magnetic field can cause contraction of the discharge only through a change in the boundary conditions at the wall of the discharge tube \(^{15}\).

Relation (1) was also used to determine the decrease of the electron temperature with increasing current in neon, helium, and argon discharges \(^{16}\). The results obtained in this way agree quite well with the data of probe measurements.

4. DETERMINATION OF THE EFFECTIVE CROSS SECTIONS OF ATOMS

The discharge in potassium vapor, as also the sodium discharge, is characterized by the fact that a considerable part of the supplied power is converted into radiation of the resonance line.

Processing, by means of formula (1), the results of probe measurements by B. N. Klyarfel’d \(^{17}\) made it possible to determine the effective cross section \(Q(V_m)\) of the potassium atom for the process of excitation of the levels \(5\,P_{\frac{1}{2},\,\frac{3}{2}}\), from which the resonance lines 7645.99 Å \(^{18}\) originate.

This quantity proved, for different discharge conditions, to be practically one and the same and equal to \(720\ \mathrm{cm}^2/\mathrm{cm}^3\), which indicates a very high probability of excitation. The latter is a consequence of the very low excitation potential. It should be noted that the direct determination of the effective cross section \(Q(V_m)\) for potassium is made difficult by the necessity of experimenting with very slow electrons.

With the aid of relation (1), \(Q(V_m)\) was also determined for the excitation functions of metastable atoms of inert gases (helium, neon, and argon) \(^{16}\).

Relation (1) was generalized to the case when excitation occurs not only from the normal state, but also from already excited intermediate states.

In the presence of such processes of cumulative excitation, the intensity of the spectral line will already be expressed in the following form:

\[ I_\nu = C_\lambda N_e \sqrt{T_e}\left[nQ(V_m)f(T_e,V_a,V_m) + n_a Q(V_{ma})f_a(T_e,V_{aa},V_{ma})\right], \tag{2} \]

where \(n_a\) is the concentration of excited atoms, \(Q(V_{ma})\) is the effective cross section of excited atoms.

At sufficiently low pressure it can be shown that \(n_a\) is proportional to the electron concentration \(N_e\), and, consequently,

\[ I_\nu = aN_e + bN_e^2, \tag{3} \]

where \(a\) and \(b\) depend on the electron temperature, atomic constants, and the gas density \(^{19}\).

Relations (2) and (3) make it possible to determine \(Q(V_{ma})\)—the effective cross section of excited atoms, if \(Q(V_m)\)—the effective cross section of normal atoms—and the concentration of excited atoms \(n_a\) are known. Experiments were carried out, in a certain sense analogous to Wood’s experiments on the cumulative optical excitation of mercury vapor.

A low-pressure mercury discharge was chosen as the object (\(10^{-3}\ \mathrm{mm}\ \mathrm{Hg}\)), since, as indicated above, for this purpose

For the discharge there are exhaustive data for \(N_e\) and \(T_e\) by B. N. Klyarfeld. In this discharge, by means of absorption measurements, \(n_a\) was determined—the concentration of atoms at the levels \(6^3P_{0,1,2}\) (see below), and the intensity of the lines of the visible mercury triplet \(7^3S_1 — 6^3P_{0,1,2}\)—5461, 4358, and 4047—was measured\({}^{19}\). The course of the intensity, beginning with two amperes, differs sharply from a straight line passing through the origin and corresponds no longer to formula (1), but to formula (2).

Especially convincing is Fig. 5, where the squares of the electron concentrations, \(N_e^2\), are plotted on the abscissa axis, and on the ordinate axis—the differences between the ordinates of the experimental curve and the straight line passing through the origin. According to (3), these differences must be proportional to \(N_e^2\), which is indeed observed with great accuracy.

According to Ganley and Shaffernicht\({}^{20}\), \(Q(V_m)\) for normal mercury atoms is equal to \(1.2\ \mathrm{cm}^2/\mathrm{cm}^3\). Using the results of the intensity measurements and the results of the absorption measurements, it was possible, with the aid of formula (2), to determine the effective cross section \(Q(V_{ma})\) of the excited atoms (at the levels \(6^3P_{0,1,2}\)), which turned out to be approximately \(12\ \mathrm{cm}^2/\mathrm{cm}^3\).

Thus the effective cross section of excited atoms exceeds by an order of magnitude the effective cross section of normal atoms. Later this result was confirmed by a direct calculation of the effective cross section of excited atoms. The value obtained for the effective cross section shows that cumulative processes must play a very large role in the excitation of the upper levels.

Fig. 5. Proportionality between the number of acts of stepwise excitation and the square of the electron concentration.

A series of works devoted to quantum-mechanical calculations of the effective cross sections of excited atoms adjoins these studies\({}^{21}\). In them were calculated the functions of stepwise excitation for hydrogen, helium, and mercury, as well as the function of stepwise ionization of hydrogen. In all cases the effective cross sections of excited atoms exceed many times the effective cross sections of normal atoms.

It is important to emphasize that it is the large transverse cross section of excited atoms, and not a low excitation potential, that determines the enormous role of cumulative processes in the discharge at high current strengths. This is explained by the fact that the concentrations of excited atoms in the best case reach the Boltzmann values, and usually are considerably lower than them.

V. A. FABRIKANT

5. GENERAL PICTURE OF THE EXCITATION OF ATOMS IN A LOW-PRESSURE DISCHARGE

Excited atoms constitute a very substantial component of the plasma of a gas discharge. In these atoms an appreciable fraction of the energy is accumulated and, most importantly, excited atoms actively participate in the most varied processes occurring in the gas discharge. They facilitate ionization, acting as an admixture with a low ionization potential; they also “heat” the electron gas in collisions of the second kind; and, finally, excited atoms determine all the optical characteristics of the discharge.

The question of the concentrations of metastable atoms is solved more simply than for radiating atoms.

The basic differential equation for the concentration of excited atoms may be written in the following form\(^9\):

\[ \frac{d^2 y_a}{d x^2}+\frac{1}{x}\frac{d y_a}{d x}-B_a q_e y_a = B_a q_e, \tag{4} \]

where \(y_a\) is the reduced concentration of excited atoms, equal to the ratio of the concentration \(n_a\) to the concentration \(n_a^0\) established under conditions of temperature equilibrium; \(x=r/a\), where \(a\) is the radius of the discharge tube, \(q_e\) is the distribution of electrons over the cross section of the discharge, and \(B_a\) is a parameter characterizing the conditions of existence of excited atoms and proportional to the ratio of the probability of destruction of an excited atom in the volume, due to collisions of the second kind with electrons, to the probability of such an atom reaching the wall of the discharge tube.

Fig. 6. Distribution of excited atoms over the cross section of the discharge.

Figure 6 shows solutions of equation (4) for different values of the parameter \(B_a\); here the concentration of excited atoms at the wall was assumed equal to zero.

Subsequently, the question of the role of the boundary conditions was investigated, and the corresponding expressions were obtained, into which, naturally, the relation between the mean free path and the radius of the tube entered\(^ {22}\).

For small values of \(B_a\), i.e., when excited atoms are destroyed at the walls, their distribution is described by a Bessel function of zero order. As \(B_a\) increases, the distribution deviates more and more strongly from the Bessel form (see, for example, \(B_a=50\); the Bessel function is shown by the dashed line), and as \(B_a\) tends to infinity, the reduced concentration tends to a constant value equal to unity.

The question of the distribution of excited atoms over the cross section of the discharge is also of independent interest, but this question is especially important ...

question for determining the effective lifetime of excited atoms in the discharge. Only in the case of a Bessel distribution of atoms over the cross-section of the discharge is the diffusion lifetime of excited atoms constant over the cross-section of the discharge. Thus, collisions of the second kind affect the lifetime of excited atoms in two ways: directly (in the volume) and through a change in the probability of diffusion to the walls. It can be shown that the parameter \(B_e\) is approximately proportional to the product of the current and the pressure.

The applicability of the consequences following from equation (4) to radiating atoms required special discussion. Equation (4) was based on the assumption that the laws of ordinary diffusion are applicable, which is strictly valid only for metastable atoms.

For radiating atoms the fundamental process is, of course, not the diffusion of the atoms themselves, but the diffusion of the radiation emitted and absorbed by the atoms.

However, the laws of diffusion of radiation in a gas are extremely complicated by the non-exponential law of attenuation of a beam of photons propagating in the gas. The non-exponential character is connected with the non-monochromaticity of the emission and absorption lines. The use of the analogy between the diffusion of photons and of atoms makes it possible to generalize equation (4) also to radiating atoms, but this analogy has its limits \(^{23}\).

Even at low mercury-vapor pressures of the order of \(10^{-2}\) mm Hg, the absorption coefficient for the center of the 2537 Å line is about 10, and for the 1850 Å line about 100. Thus photons corresponding to these lines will be able to travel approximately 1 mm and 0.1 mm, after which they will be absorbed.

As a result of the acts of absorption, new excited atoms will arise, indistinguishable from those which emitted the corresponding photons. These newly excited atoms will again emit photons, and so on, until the photons escape from the discharge tube to the outside. At first sight such a photon “relay” from atom to atom is completely harmless from the point of view of the final result. This, however, is far from the case.

While the photon is flying from atom to atom, it is, of course, in complete safety; but during the photon’s “stops” in atoms it is threatened by serious danger from quenching collisions. Each of the excited atoms formed along the photon’s path has a chance of perishing as a result of a quenching collision.

The total time during which a quenching collision can occur is equal to the number of “stops,” i.e., the number of absorption events, multiplied by the duration of each stop, i.e., by the lifetime of the excited atom. It is clear that it makes sense to introduce an effective lifetime of the excited atom equal to this total time. The effective lifetime is thus equal to the mean interval of time from the moment of exc—

of the photon’s occurrence at some point in the gas volume until the moment when the photon exits outside. The times required for the photon to traverse interatomic distances are not taken into account, in view of the great magnitude of the speed of light.

As the pressure increases, the number of “stops” of the photon will increase, and consequently the effective lifetime will also increase. With the increase of the effective lifetime, the role of quenching collisions will grow. Therefore high pressures are disadvantageous for the generation of resonance lines strongly absorbed by the gas. It should be emphasized that, in the absence of quenching collisions, an increase in the effective lifetime of excited atoms would not be dangerous.

Approximately, for emitting atoms the effective lifetime \(\tau_r\), determined by photon diffusion, is equal to:

\[ \tau_r = \frac{3(ka)^2}{\mu_1^2}\tau, \tag{5} \]

where \(ka\) is the effective optical density of a gas layer whose thickness is equal to the radius of the tube \(a\), \(\mu_1\) is the first zero of the Bessel function of zero order \((2.4)\), and \(\tau\) is the lifetime of an isolated atom.

The square of the effective optical density increases approximately in proportion to the product of \(k_0\) (the absorption coefficient for the center of the line) and the radius \(a\). On the other hand, as is known, \(k_0\) is inversely proportional to \(\tau\). As a result, paradoxical as it may be, \(\tau_r\) depends only weakly on \(\tau\), but, of course, depends strongly on the gas density. If quenching processes are present, then \(\tau_r\) strongly affects the intensity of the radiation. The role of quenching processes is determined by the product of the probability of quenching and \(\tau_r\), i.e. by the number of quenching collisions experienced by an atom during the time \(\tau_r\). Conversely, the atomic constant \(\tau\) does not play an essential role.

Therefore diffusion of radiation must have a strong effect on the intensity of the radiation emitted by the discharge, and a detailed study of the laws of this diffusion is of great interest.

6. EXPERIMENTAL DETERMINATION OF THE CONCENTRATION OF EXCITED ATOMS IN A LOW-PRESSURE DISCHARGE

For the experimental determination of the absolute concentrations of excited atoms in a discharge, two methods were developed, based on measurements of the absorption of lines absorbed by excited atoms.

The first, the method of identical sources, consists in measuring the absorption of a line emitted by one discharge tube in another discharge tube identical to it. In the case of identical tubes, the absorption is a function of a single unknown—the concentration of absorbing atoms in both tubes. For the transition from absorption to concentrations,

it is necessary to know the atomic constant \(k_0\), the absorption coefficient for the center of the line, the line shape, and the hyperfine structure of the line. The absorption method has a considerably higher sensitivity than the anomalous-dispersion method.

The second, perhaps more elegant, method consists in measuring the angular distribution curve of the intensity of a line absorbed by excited atoms. It is most convenient to measure the ratio of the intensities in the direction of the axis of the discharge tube and in the perpendicular direction. It is clear that this ratio of intensities is a single-valued function of the absorption and, consequently, of the concentration of the absorbing atoms.

The identical-sources method was applied to the study of the mercury discharge\(^{19,24}\), and the angular-distribution method to the study of the neon discharge\(^{16}\).

In the mercury discharge, the greatest interest was presented by the metastable atoms \(6^3P_0\) and \(6^3P_2\), and by the atoms \(6^3P_1\), which emit the resonance line \(2536.52\) Å. To determine the concentrations of atoms at the levels \(6^3P_{0,1,2}\), the lines of the visible triplet of mercury, 5461, 4358, and 4047 Å, were used. As is known, the 5461 Å line is absorbed by atoms at the \(6^3P_2\) level, the 4358 Å line by \(6^3P_1\), and the 4047 Å line by \(6^3P_0\).

The measurements were carried out on tubes of diameter 32 mm, used by B. N. Klarfeld in probe measurements.

Fig. 7 shows the results of measurements at a pressure of \(10^{-3}\) mm Hg and at different current strengths.

Table 1 gives the results for various lines at constant current strength and at different pressures.

Table 1

Concentrations of atoms at the levels \(6^3P_{0,1,2}\)

Fig. 7 shows that at a pressure of \(10^{-3}\) mm Hg the concentrations of excited atoms are proportional to the electron concentrations. In other words, at such a low pressure, collisions of the second kind, which destroy excited atoms, do not play a noticeable role. Extremely characteristic of the discharge was the fact that the concentration of metastables at the \(6^3P_2\) level proved to be much higher than at the \(6^3P_0\) level. This is explained by the greater probability of excitation

of the level \(6^3P_2\) in electron impacts of the first kind. The level \(6^3P_2\) seems, as it were, to overhang the level \(6^3P_1\).

The concentration at the level \(6^3P_1\) at the very lowest pressures is considerably less than at the metastable levels, but with increasing pressure it begins to become comparable with them.

This is explained by the growth of \(\tau_r\) for the level \(6^3P_1\), on the one hand, and, on the other hand, by the increase in the number of collisions that destroy metastables in the volume of the discharge.

Fig. 7. Proportionality between the concentration of excited atoms and the concentration of electrons.

The course of the concentration of metastable atoms as a function of the discharge-current strength was obtained by a second, absorption method, by measuring the ratio of intensities in two directions.

The measurements were carried out in a very wide tube (50 mm), and a very sharp maximum of the concentration in the region of small currents was obtained. Comparison of this result with the data of the well-known works of Kopfermann and Ladenburg \(^{25}\) shows that the course of the concentration is strongly affected by the decrease of the electron temperature with increasing current, and that the authors mentioned did not attain the conditions of temperature equilibrium. The latter also follows directly from the considerations set forth in the preceding section.

7. STUDY OF RADIATION DIFFUSION BY MEANS OF LUMINESCENT PROBES

To study the optical processes occurring in the volume of a discharge, a new experimental method was developed, based on the use of luminescent probes \(^{26}\).

A luminescent probe is a probe coated with a luminophore sensitive to the radiation under investigation. Such a probe is introduced into the discharge volume, and the brightness of its glow is measured. It is clear that a gas which strongly absorbs resonance radiation is completely transparent to the glow of the probe. Thus, the probe transforms strongly absorbed resonance radiation into radiation that freely emerges from the volume of the gas. The brightness of the surface

...of the probe is proportional to the energetic illuminance produced on its surface by the exciting radiation.

Just as is done in the theory of the light field\({}^{27}\), it is not difficult to show that the mean luminance of a spherical probe is proportional to the volume density of the radiation exciting the phosphor, and that the difference of the luminances of the two sides of a flat probe is proportional to the projection, onto the normal to the plane of the probe, of the Poynting vector of the same radiation. For a cylindrical discharge column of sufficiently great length it can be shown\({}^{28}\) that:

\[ \operatorname{div}\mathbf{S}=\frac{1}{\eta}\frac{1}{r}\frac{d\left[r(B_1-B_2)\right]}{dr}, \tag{6} \]

where \(\mathbf{S}\) is the Poynting vector, \(\eta\) is the luminescence yield, and \(B_1\) and \(B_2\) are the luminances of the two sides of a flat probe perpendicular to the radius of the discharge tube. Relation (6) makes it possible to determine the divergence of the radiation or, what is the same thing, the power of the radiation sources \(R\) at any point of the discharge volume.

Using the analogy between the diffusion of photons and atoms, one can obtain a simple formula for determining the effective length of the photon mean free path:

\[ \bar{\lambda}=\frac{3}{2}\, \frac{B_1-B_2}{\dfrac{d(B_1+B_2)}{dr}} . \tag{7} \]

Formula (7), unlike (6), is approximate in character because of the fundamental differences, indicated in the fifth section, between the diffusion of photons and that of atoms.

It is possible to obtain a formula more exact than (7) for determining \(\bar{\lambda}\), but, in essence, the discussion would then no longer concern \(\bar{\lambda}\), but another, more complicated quantity\({}^{28}\).

As the first object for the application of luminescent probes (lumiprobes), a low-pressure mercury discharge was chosen. In a low-pressure mercury discharge almost all the radiation consists of two ultraviolet resonance lines, 1849.57 and 2536.52 Å, which effectively excite the corresponding phosphors.

Special experiments were carried out to select the shape and dimensions of the probe and the types of phosphors\({}^{11}\). Also, with the aid of a series of control experiments, possible sources of error in measurements with lumiprobes were clarified.

Up to now, the main part of the measurements has been made with flat probes, perpendicular to the radius of the discharge tube and moved across the discharge by means of a magnet.

The probes were coated either with willemite, sensitive to both resonance lines of mercury, or with zinc beryllium silicate with a high manganese content and sensitive only to the 2536.52 Å line. A glass filter opaque to the 1849.57 Å line was sometimes slipped over the willemite probes.

In general, a large amount of data concerning the volumetric characteristics of the radiation has been obtained with the aid of lumisondes.

We shall confine ourselves to only a few examples.

In Fig. 8 are shown the sums of the brightnesses of the two sides of a visible flat probe, i.e., quantities proportional to the volume density of radiation. In Fig. 9 are shown the differences of the brightnesses of the two sides of a flat probe, i.e., quantities proportional to the Poynting vector at each point of the discharge.

A change in pressure has little effect on the distribution of the volume density of radiation, but has a pronounced effect on the distribution of the radiation fluxes.

Fig. 8. Distribution of the volume density of radiation over the cross section of the discharge.

Fig. 9. Distribution of radiation fluxes over the cross section of the discharge.

Fig. 10. Distribution of radiation sources over the cross section of the discharge.

Using appropriate luminophores and filters, it proved possible to obtain the course of the volume density of radiation for both resonance lines of mercury separately. It turned out that the volume density of radiation of the line 1849.57 Å decreases toward the edge of the discharge several times more steeply than that of the line 2536.52 Å.

In Fig. 10 is shown the course of the divergence of the radiation over the cross section of the discharge, calculated with the aid of formula (6). Since the radiation arises mainly as a result of electronic impacts, it was to be expected that the distribution curves of \(R\) should be similar to the curves of the electron distribution over the cross section of the discharge.

Measurements of the electron distribution with Langmuir probes showed that, indeed, the indicated similarity takes place, but that certain deviations are observed, the nature of which still requires further investigation.

With the aid of formula (7), the effective free-path lengths of photons were determined. In Fig. 11 are shown the free-path lengths—

mean free paths of photons \(\bar{\lambda}\) for both resonance lines. The curve with crosses corresponds to \(\bar{\lambda}\), determined with a Willemite probe and representing the weighted mean \(\bar{\lambda}\) for the individual lines. A noticeable increase of \(\bar{\lambda}\) toward the edge of the discharge is characteristic, caused by self-reversal of the spectral lines. At the edge the principal role is played by photons arriving from the distant central layers of the discharge.

The nonconstancy of \(\bar{\lambda}\) is one of the most striking manifestations of the fundamental difference between the diffusion of photons and atoms (as is also the weak influence of pressure on the distribution of volume density).

From the nonconstancy of \(\bar{\lambda}\) it follows that the distribution of the volume density of radiation (Fig. 8) does not coincide with the distribution of the concentration of emitting atoms.

The distribution curve of the emitting atoms must always fall off toward the walls of the discharge tube considerably more steeply than the photon distribution curve, since the volume density of radiation is proportional to the product of the concentration of the emitting atoms and \(\bar{\lambda}\).

The ratio between \(\bar{\lambda}\) for the individual resonance lines is consistent with the value of the atomic constants for these lines. The absolute values of \(\bar{\lambda}\) themselves, determined by means of luminescent probes, should also be regarded as reasonable.

It is interesting to note that the effective value of \(\bar{\lambda}\) for photons is considerably lower than the corresponding mean free path of a mercury atom. This is explained by the fact that the optical diameter of a mercury atom is many times greater than the gas-kinetic diameter.

Fig. 11. Effective lengths of the free paths of photons.

8. INVESTIGATIONS OF PHYSICAL PROCESSES IN LUMINESCENT LAMPS

In luminescent lamps of the modern type, a discharge is used in a mixture of mercury vapor with argon. The mercury vapor pressure is of the order of \(10^{-2}\) mm Hg and the argon pressure is about \(4\) mm Hg.

The discharge in luminescent lamps serves as a source of short-wavelength ultraviolet radiation, exciting the phosphors deposited on the inner wall of the discharge tube. Therefore the study of the mechanism of excitation of the resonance lines in a mixture of mercury vapor and argon is of particular interest.

First of all, measurements were carried out with the addition of various inert gases: helium, neon, argon, and krypton at various

pressures[^23]. It was established that the most economical gas, in the sense of exciting phosphors, is krypton. However, the difference between argon and krypton is small, and therefore it is rational to use argon. It is interesting to note that helium and neon gave much greater brightnesses, but the power consumed increased so much, in comparison with argon and krypton, that the economy fell sharply.

The output of radiation from luminescent lamps has a maximum at a mercury-vapor pressure close to the region of the maximum intensities calculated theoretically. But since the calculation was made for a discharge in pure mercury vapor, it was important to clarify the role of argon.

In a sodium discharge the role of inert gases clearly reduces only to a change in the concentration and temperature of the electrons. In a mercury discharge, owing to the presence of metastable states, a more complex picture is to be expected. The presence of an inert gas hinders the diffusion of metastables to the walls of the discharge tube.

First of all, with the aid of Langmuir probes, measurements were made of the concentrations and temperatures of electrons in a pure mercury discharge and under the conditions of a luminescent lamp[^30]. It turned out that the presence of argon raises the electron concentration from \(2 \cdot 10^{10}\) to \(2.6 \cdot 10^{11}\), i.e., by an order of magnitude, and lowers the electron temperature from \(18\,100^\circ\) to \(12\,600^\circ\), i.e., by approximately one and a half times. According to formula (1), such a lowering of the electron temperature leads to a ratio of the intensities of the lines \(1849.57\) and \(2536.52\ \text{\AA}\) of \(0.44\) instead of \(1.14\) for a pure mercury discharge.

Thus, the ratio of the intensities should change by a factor of \(2.6\).

The role of argon, however, is not limited only to changing the electronic characteristics of the discharge. The presence of argon lowers by approximately two orders of magnitude the probability that metastable mercury atoms will reach the walls. However, measurements of the absorption of visible triplet lines did not show a corresponding increase in the concentration of metastable atoms. Measurements were made of the decay of absorption of the visible triplet after the luminescent lamp was switched off. These measurements were carried out with the aid of a multistage photocell of P. V. Timofeev and a cathode oscillograph. As a result it turned out that the lifetimes of the levels \(6^3P_0\) are \(6 \cdot 10^{-5}\ \text{sec}\), \(6^3P_1\) are \(10^{-5}\ \text{sec}\), and \(6^3P_2\) are \(4 \cdot 10^{-5}\ \text{sec}\)[^31]. The lifetimes of the metastables are orders of magnitude smaller than the corresponding diffusion lifetime. Thus, there exist processes that very effectively destroy metastables in the volume of the discharge. Such processes may be collisions of the first and second kind with atoms and electrons.

The most interesting point here is that the metastables can pass to the \(6^3P_1\) level, thereby taking part in the generation of the \(2536.52\ \text{\AA}\) line.

In particular, metastable atoms \(6^3P_0\), as a result of collisions of the first kind, are raised to the level \(6^3P_1\), while the metastable \(6^3P_2\) atoms, in collisions of the second kind, descend to the same level \(6^3P_1\).

Thus, the level \(6^3P_1\) is excited not only directly from the normal state, but also through metastable levels. This latter circumstance greatly increases the overall probability of excitation of the level \(6^3P_1\), and, consequently, also the intensity of the 2536.52 Å line originating from this level.

Without taking such transitions into account it is impossible to explain the experimentally observed values of the yield of the 2536.52 Å line, which reach 60% of the power supplied to the discharge column\(^ {32}\).

In a special lamp the influence of argon on the luminous efficiency of a fluorescent lamp was investigated. An increase in luminous efficiency by a factor of 2.4 was established when argon was introduced into a pure mercury discharge.

With the aid of luminescent probes, the influence of argon on the volume optical characteristics of the discharge was clarified. Argon, of course, does not change the conditions for the diffusion of the resonance radiation of mercury, but it strongly changes the distribution of electrons over the cross section of the discharge. Therefore, when argon is added, the fall-off of the distribution curve for the divergence of the radiation becomes much sharper, while the distribution curve of the volume densities of radiation changes rather weakly\(^ {11}\).

The data obtained also testify to the large role of argon in the mechanism of excitation of the resonance radiation of mercury.

The role of the 1849.57 Å line in exciting the phosphor layer in fluorescent lamps was investigated especially thoroughly. In selecting mixtures of phosphors for fluorescent lamps it had been established that the spectral radiation curves of mixtures of certain phosphors depend on the excitation conditions.

By means of a series of control experiments with selective filters it was shown that variations of the spectral curves are caused by changes in the ratio of the intensities of the 1849.57 and 2536.52 Å lines in the exciting radiation\(^ {33}\).

After this, the experiments were transferred inside fluorescent lamps. Here, with the aid of a filter opaque to the 1849.57 Å line, it was possible to prove that approximately half of the intensity of the glow of the luminescent layer is due in origin to the 1849.57 Å line\(^ {30}\).

This result was in sharp contradiction with the viewpoint established in the literature, according to which the luminescent layer is excited only by the 2536.52 Å line\(^ {32}\).

In 1946, works appeared\(^ {34}\) that established the essential role of the 1849.57 Å line in a number of photochemical processes occurring under the action of radiation from a discharge in a mixture of argon and mercury vapor. These works confirm to a certain extent the results of measurements with phosphors.

A complete answer will be provided by the measurements now begun with the aid of a vacuum monochromator.

9. THE INFLUENCE OF PRESSURE ON THE INTENSITY OF RADIATION FROM A DISCHARGE IN METAL VAPORS

The transition from a low-pressure discharge to a high-pressure discharge is accompanied by a peculiar behavior of the intensity of lines corresponding to the upper energy levels.

As the pressure is increased, the mechanism of the discharge at first becomes very complicated, owing to the growing role of secondary processes; but at sufficiently high pressures there again occurs the familiar simplification of the picture of the discharge, in connection with the establishment of conditions close to thermodynamic equilibrium. For a discharge at “intermediate” pressures, for the time being only statements, mainly of a qualitative character, are possible.

Fig. 12. Influence of pressure on the intensity of cadmium lines.

Kreffft discovered a nonmonotonic course of the light output of a mercury discharge with increasing pressure. Systematic investigations of the influence of pressure on the intensity of the visible lines of mercury, cadmium, and zinc showed that, for all metals, a characteristic course of the intensity is observed, with a sharp minimum in the pressure region of the order of several mm Hg. Figure 12 shows the results of measurements for cadmium[^35].

The existence of a maximum follows from relation (1), but the position of this maximum for lines emitted in transitions between upper levels is shifted toward higher pressures. The reason for the shift lies in the processes of stepwise excitation, in which the intensity is already determined by relation (2).

The drop in intensity after the maximum is caused by the fall of the electron temperature with increasing pressure. This drop should be the stronger, the higher the excitation potential of the line; as is seen from Fig. 12, this is in fact observed for cadmium. In mercury the course of the intensity is strongly distorted by reabsorption of the radiation. This was shown by measurements of the course of the intensity of lines with a common upper level and, finally, by special experiments in which the influence of pressure on the shape of the curve of the angular distribution of intensity was investigated. It turned out that, as the pressure increases, the curves of the angular distribution of the intensity of the lines of the visible triplet are sharply deformed. For the green line, a departure from the Lambertian curve is observed, while for the blue line, on the contrary, there is an approach to this curve. All these results indicate a significant course of reabsorption of lines absorbed by atoms at the levels \(6^3P_{0,1,2}\).

The growth of intensity in the region of high pressures is associated with contraction of the discharge column. In the contracted column a sharp increase in the gas temperature is observed. Comparison of the intensities of spectral lines at high pressure and at the pressure corresponding to the minimum of the intensity curve led to the establishment of a definite regularity^36: the higher the excitation potential of the line, the more strongly the intensity increases with increasing pressure.

10. OPTICAL PROPERTIES OF THE MERCURY DISCHARGE AT HIGH AND SUPERHIGH PRESSURES

As was indicated, the establishment of conditions close to thermodynamic equilibrium is characteristic of a high-pressure discharge. Owing to the large number of collisions, the sharp distinction between the gas temperature and the electron temperature disappears. The principal characteristic of the discharge becomes a single temperature, determining both the excitation and the ionization of atoms. The distribution of atoms over excitation levels corresponds to Boltzmann’s formula; the degree of ionization agrees fairly well with Saha’s formula^37. In both of these formulas the temperature enters into the exponent of the exponential function. Thus, the determination of the temperature of the discharge plasma acquires special importance. At the same time it is clear that any direct methods for determining the temperature of an ionized gas are practically infeasible, and the use of indirect optical methods is necessary.

By means of the method of identical sources, the absorption of visible lines in the column of a high-pressure mercury discharge (one atmosphere)^38 was measured. For the lines of the visible triplet, large absorption values were obtained, practically independent of the current strength. For the lines 5790.66—5769.60 Å the absorption is small and increases noticeably with the current.

The results of the absorption measurements made it possible to determine the ratios of the concentrations of absorbing atoms on the levels \(6^3P_{0,1,2}\). Using these ratios and Boltzmann’s formula, the temperature of the discharge channel was determined, proving to be approximately \(6400^\circ\mathrm{K}\). If, in addition to equilibrium between collisions of the first and second kind, equilibrium also sets in between optical processes, the discharge already acquires the properties of a black radiator. In this case, of course, what is involved is not strict equilibrium, but a sufficiently large reabsorption of radiation in the discharge.

The intensity of a spectral line in this case is determined by Wien’s formula:

\[ I_\lambda=\frac{3.7\cdot 10^{-5}S}{\lambda^5}e^{-\frac{1.43}{\lambda T}}\Delta\lambda, \tag{8} \]

where \(S\) is the emitting surface, and \(\Delta\lambda\) is the effective width of the line.

The principal difficulty arising in the application of formula (8) for calculating the absolute intensity of a line consists in determining \(\Delta \lambda\).

As objects for the application of (8), the lines of the visible triplet emitted by a high-pressure mercury discharge were chosen. With the aid of a three-prism spectrograph of large dispersion, the shape of the lines of the visible triplet under these conditions was investigated\({}^{39}\). The results of the measurements are shown in Fig. 13. For the line \(4046.56\) Å the effective \(\Delta \lambda\) is approximately \(0.40\) Å; for the line \(4358.34\) Å, \(\Delta \lambda\) is \(0.55\) Å. Since there were only indirect data on the temperature of the discharge, it was meaningful to apply formula (8) not to the calculation of intensities, but, conversely, to the determination of the effective temperature of the discharge from known line intensities. After substituting the known \(I_\lambda\), \(S\), and \(\Delta \lambda\), values close to \(6000^\circ\) K were obtained for \(T\), which agrees well with other estimates. Thus, a high-pressure mercury discharge, in the light of the lines of the visible triplet, is close in its properties to a blackbody radiator.

Fig. 13. Shape of the lines emitted by a high-pressure discharge.

Strong reabsorption leads to a Lambertian form of the curves of the angular distribution of the intensities of these lines. The angular-distribution curve for the yellow line is much broader, which corresponds to smaller reabsorption\({}^{38}\).

It is not difficult, owing to this, to observe a noticeable “yellowing” of the color of a mercury lamp when observing at small angles to the axis of the discharge.

The reabsorption of the visible mercury lines is due to excited atoms. Therefore one should expect pulsations in the shape of the angular-distribution curves when lamps are supplied with alternating current; these pulsations were detected by special stroboscopic experiments\({}^{40}\).

In addition, periodic oscillations of the color of mercury lamps are observed, caused by differences in the time behavior of the yellow line and of the lines of the visible triplet\({}^{41}\).

Reabsorption causes a strong redistribution of intensities within multiplets. Here it is possible to reveal certain general qualitative relations, especially in the ultraviolet part of the spectrum\({}^{42}\).

The occurrence of high temperatures in a discharge is closely connected with the presence of a sharp temperature drop toward the edge of the discharge column. The latter circumstance complicates the question of the effective temperature of the discharge^39 and leads to the appearance of a peculiar fluorescence of the edges of the discharge. Powerful streams of radiation emerging from the central parts of the discharge column excite fluorescence at the edges of the discharge column and thereby disturb the local thermodynamic equilibrium in these zones.

A discharge at the so-called ultra-high pressures, of the order of tens and even hundreds of atmospheres, is in its properties close to a high-pressure discharge. However, ultra-high pressures lead to extraordinary broadenings of spectral lines. In Fig. 14 are shown the results of measurements for the line \(4358.54\ \text{Å}\)^43. The individual curves correspond to different pressures; the higher the voltage on the lamp, the correspondingly higher the pressure. We see that a gas discharge at such pressures already begins to lose its properties as a selective radiator. The sharp asymmetry in the broadening of the spectral lines is noteworthy, which is directly connected with the nature of the factors causing the broadening.

Fig. 14. Shape of lines emitted by an ultra-high-pressure discharge.

The path of development of ultra-high-pressure lamps was somewhat peculiar. Elenbaas established a similarity principle for high- and ultra-high-pressure discharges^44. According to this principle, one should expect a strong increase in the brightness of the discharge with a simultaneous increase in pressure and decrease in the diameter of the discharge tube. Indeed, capillary ultra-high-pressure lamps were constructed, possessing brightnesses comparable with the brightness of the Sun. But spherical ultra-high-pressure lamps soon appeared, possessing the same optical characteristics, but contradicting the Elenbaas similarity principle^46.

In these lamps there must arise significant convection, substantial in cylindrical lamps and not taken into account in the Elenbaas theory.

To clarify the role of convection in spherical ultra-high-pressure lamps, experiments were carried out with lamps falling freely from a height of 16 meters^46. During the free fall, the luminous cord of the discharge was photographed by a specially designed camera falling together with the lamp. In addition, blackening marks were recorded on each plate. Simultaneously on...

cathode oscilloscope, the change in voltage across the lamp and the current during the process of free fall was observed. Fig. 15 shows the results of measurements of the brightness distribution in the discharge cord.

Weakening of the convective flows causes a noticeable widening of the discharge cord. Thus, convection plays an essential role in the formation of the contracted discharge column in spherical ultra-high-pressure lamps. The convective flows, as it were, wash around the contracted column.

At the same time, an increase in the voltage across the lamp in the free-fall regime was found. This increase in voltage is explained by an increase in the resistance of the lamp, caused by a decrease in the effective temperature in the discharge column. The decrease in temperature, in turn, is connected with the widening of the discharge column.

Fig. 15. Brightness distribution in a freely falling ultra-high-pressure lamp.

Unfortunately, the falling time was insufficient, and the inertia of the convective flows in the bulb was clearly making itself felt. Increasing the falling time by increasing the height of fall is, of course, extremely difficult. Here it will be necessary to seek methods of disrupting the convective flows at the beginning of the fall.

Summing up all that has been set forth, one is involuntarily reminded of Goethe’s words: “In the sciences there is much that is reliable, provided one is not embarrassed by exceptions and knows how to respect problems.”

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