Ionization by Collisions of the Second Kind in a Gas Discharge

A. A. Zaitsev and E. M. Reichrudel, Moscow

1. Introduction

Among the elementary processes occurring in an electric discharge in a gas, alongside excitation by electron impact, reverse effects may also take place. The latter proceed approximately according to the scheme:

excited molecule + electron ⇄ normal molecule + electron with kinetic energy.

In these impacts the excitation energy of the molecule is converted into the kinetic energy of the electron. Such collisions, according to Klein and Rosseland[^1], were called collisions of the second kind, in contrast to collisions of the first kind, in which, conversely, the kinetic energy of the electron in its collisions with a molecule (atom) of the gas is converted into excitation energy of the molecule (atom).

Subsequently the term “collision of the second kind” came to be applied to all phenomena in which excitation energy is transferred from one atom to another or is converted into the kinetic energy of one or both of the colliding particles.

As early as 1912 Wood[^2] experimentally observed the “quenching” of the resonance radiation of a mercury tube when an admixture of air was introduced into it. Wood at that time explained this phenomenon by collisions of air molecules with mercury atoms. Franck and Cario[^3] proposed an elegant method and were the first to establish experimentally the existence of collisions of the second kind. In their experiments a mixture of mercury vapor and thallium (or cadmium) was illuminated by a mercury arc. As a result of absorption of the mercury lines in the mixture, the so-called sensitized fluorescence was observed. Only the mercury was optically excited, but in the fluorescence spectrum lines of thallium (or cadmium) were also found; this probably occurred as a result of collisions of the second kind between thallium atoms and excited mercury atoms.

Holst and Oosterhuis[^4] observed the formation of an arc in neon at a potential difference of 7.5 V, and in argon at 3.5 V, whereas the lowest critical potentials of these gases are 16.7 and 11.5 V, respectively. To explain this low-voltage arc phenomenon Holst and Oosterhuis invoked collisions of the second kind.

This did not concern excited atoms, but ions which, upon recombination with other ions, release their neutralization energy. However, in a low-voltage arc, as follows from the work of Compton and Eckart[^5], the effect of ion recombination apparently plays only a secondary role, and the very existence of an arc in neon and argon, under the conditions observed by Holst and Oosterhuis, can be explained only in part by collisions of the second kind.

In 1926 Franck and Jordan[^6] pointed out that the scattering of electrons in strongly ionized gases, observed in Langmuir’s work[^7], can be explained by collisions of the second kind. But after Penning[^8], and then Langmuir and Tonks[^9], observed oscillations with a very short wavelength (about 50 cm) in discharges of this kind, it became more probable that the cause of the anomalous scattering of electrons is these oscillations.

Strauß[^10] observed, in a volume in which excited molecules were present as a result of the oxidation of phosphorus, electrons with velocities exceeding those that could have been produced by the applied potential difference. The author explained the appearance of these electrons by collisions of the second kind. More refined experiments carried out by Latyshev[^11] confirmed this point of view.

In parallel with these works, studies were also carried out of collisions of the second kind between excited atoms of the main gas and impurity atoms in a discharge tube.

Ordinary excited atoms have a very short lifetime (\(\sim 10^{-8}\) sec), and, generally speaking, at small currents the probability of their meeting an electron or an impurity atom is small. But there exist excited states from which an atom cannot pass to the normal state by spontaneous radiation. These are the so-called metastable states, whose lifetime is many times greater (\(10^{-4}\)—\(10^{-1}\) sec) than that of ordinary excited states. The presence of metastable atoms greatly increases the probability of a collision of the second kind, being especially noticeable at small currents.

The work of a number of investigators[^12] has established that metastable atoms can readily pass into the normal state as a result of their collisions with atoms of certain impurities. This process is considerably more probable than the transition in collisions with atoms of the main gas. In this case the potential energy of the metastable atom is converted into the energy of the impurity atom colliding with it; the latter can thus be ionized or pass into an excited state with a short lifetime, from which the atom, emitting radiation, passes into the normal state. The chemical and optical phenomena that occur in collisions of the second kind have been investigated in a large number of works. A complete and critical discussion of these works has been given in the book by Mitchell and Zemansky[^13]. In a discharge in a pure gas, metastable atoms can

significant intensity, which accelerate ionization and excitation. For example, in order to excite the sharp terms emitted by sodium atoms for the lines of the visible spectrum, it was suggested, according to Dorgelo,^14 to excite the atoms by means of a metastable level, i.e., first the atom is excited to a metastable level, and then the atom makes a transition to a higher unstable level. Direct excitation to the upper unstable level is limited by the lack of electrons of the high energy required for this.

In a discharge in a mixture of gases, metastable atoms can cause excitation of impurity atoms and, consequently, emission of the lines of the impurity spectrum. In this case both arc and spark spectra may be excited. Frericks^15 observed excitation of Mg and Cd atoms in a discharge in neon.

Duffendack and Smith,^16 Duffendack and Wolfe^17 studied the excitation of the spectra of molecular gases introduced as impurities into a discharge in noble gases. Among the more recent spectral investigations one should note the work of Frisch,^18 who observed excitation of luminescence in a mixture of mercury and sodium vapors in a discharge tube with a hollow cathode. A considerable increase was observed in the intensity of the sodium lines whose excitation potential differs by 0.02–0.04 V from the excitation potential of the \(^{3}P_{0}\)- and \(^{3}P_{1}\)-levels of mercury atoms. An asymmetry was established in the probability curve for collisions of the second kind between mercury and sodium atoms: collisions of the second kind are less probable when the excitation potential of the mercury atoms lies above the excitation potential of the sodium atoms. The role of collisions of the second kind in exciting the luminescence of a mixture of sodium vapor with vapors of Mg, Cd, and Zn was also established.

The works of Fabrikant and his collaborators^19 are devoted to elucidating the role of stepwise excitation in the general process of excitation of atoms, and to using observations of the intensity of radiation and absorption for a quantitative estimate of the concentration of excited atoms in a discharge in metal vapors in connection with the study of the role of collisions of the second kind. Some results of measurements of the luminous efficiency in the positive column of a discharge in neon under various conditions, made by Klarfeld and Tarasov,^20 apparently find their explanation in the role of metastable atoms.

In the present article, chiefly the influence of metastable atoms on the electrical parameters of a gas discharge is considered.

2. The influence of collisions of the second kind on the ignition potential of a discharge

The presence of excited, in particular metastable, atoms in a gas-discharge tube can lead to the following processes:

1. Metastable atoms facilitate ionization by electron impact in the gas volume, since less energy is required to ionize an excited atom than to ionize a normal one. Thus the presence of metastable atoms leads to an increase in the degree of ionization of the gas. Metastable atoms are especially effective under conditions in which the discharge contains an admixture of another gas with an ionization potential lower than the excitation potential of the metastable level of the principal gas. Then the excitation energy of the metastable atom of the principal gas is sufficient to ionize the impurity atom. The new ions and electrons obtained in this way, being accelerated by the electric field, participate in the avalanche-like ionization process (volume effect).

2. Metastable atoms can also use their excitation energy to liberate electrons from the surface of electrodes with which they come into contact (surface effect). For such emission it is necessary only that the excitation potential of the metastable atom be sufficient to liberate electrons from the metal surface.

Most often the surface effect is combined with the volume effect. Penning^21 and others established that the ignition potential in argon and neon is lowered if small doses of gases are admixed to them whose ionization potential \(V_i\) is lower than the excitation potential of the metastable level \(V_{\text{met}}\) of the principal gas, i.e., \(V_{\text{met}} > V_i\); the process may be represented as follows:

\[ \text{metastable atom of the principal gas} + \text{impurity atom} \rightleftharpoons \text{normal atom of the principal gas} + \text{impurity ion} + \text{electron}. \]

Some data from Penning’s first work are given in Table 1. The measurements were made in a cylindrical discharge tube with plane electrodes at different pressures of the principal gas and with different doses of impurity.

TABLE 1

Here \(Pd\) is the product of the gas pressure, expressed in millimeters of mercury, and the distance \(d\) between the electrodes (in centimeters), \(V_z\) is the ignition potential of the discharge in pure neon, \(V'_z\) is the ignition potential of the discharge in neon with an impurity, \(V'_i\) is the ionization potential of the impurity,

From Table 1 it is evident what a considerable lowering of the ignition potential can be achieved by means of an impurity. For example, if to neon, the excitation potentials of whose metastable atoms are 16.5 and 16.6 V, one adds 0.05% of mercury vapor (the ionization potential is 10.4 V), then the ignition potential is lowered, other conditions being equal, from 400 to 150 V. An analogous lowering is obtained in argon with an admixture of mercury.

From Fig. 1 it is evident that the lowering of the ignition potential depends on the pressure of the principal gas and on the percentage of impurity.

Fig. 1.

Fig. 2.

Penning explained the observed phenomenon by the action of metastable atoms. So long as the principal gas, in which there are neutral metastable atoms, is pure, breakdown of the discharge gap does not occur; but if there is an impurity in the gas whose atoms can be ionized by the energy of the metastable atoms of the principal gas, then the discharge may occur already in a weaker electric field.

The curves shown in Fig. 2 indicate under what conditions the effect of lowering the ignition potential in neon increases and is greatest. The curves have a maximum when the admixture of argon to the principal gas amounts to several thousandths of a percent. The course of the curve is readily explained precisely by collisions of the second kind.

If the percentage content of the impurity is small, then the decrease of the ignition potential is also insignificant, since the probability of collision of a metastable atom with an impurity atom under these conditions is small. With increasing impurity content the effect grows. With a further increase in the percentage of impurity, energy losses of electrons (elastic and inelastic) in their collisions with impurity atoms become more and more noticeable. This circumstance, in the cases of mixtures under consideration, where the impurity atoms have a lower ionization potential than the principal gas, causes a decrease in the probability of excitation of metastable atoms. The consequence of this is a decrease in the effect of change of the ignition potential at large impurities. The effect of change of the ignition potential upon addition-

of various impurities to the main gas, observed by Klärfeld²², is in many cases connected with collisions of the second kind.

In studying the action of excited atoms it is necessary to be able to vary their concentration arbitrarily. It is very difficult to establish the absolute concentration of metastable atoms. In many cases, knowledge of at least the relative concentration of metastable atoms in the discharge is useful. One of the methods for arbitrarily varying the concentration of metastable atoms is to illuminate the discharge from outside with the appropriate radiation. By absorbing a quantum of radiation, a metastable atom can pass to one of the neighboring ordinary excited levels, from which a spontaneous transition to the normal state by radiation is possible. As a result, the lifetime of the metastable atoms, and consequently their concentration, decreases. The convenience of the method lies in the fact that the filling conditions of the discharge tube are thereby preserved.

This method was first used by Penning²¹ in studying the influence of metastable atoms on the ignition potential of a discharge.

3. Metastable atoms in a stationary discharge

Paschen was the first to indicate a method for detecting the presence of metastable atoms; for this purpose, strong absorption of resonance radiation is used by a gas in which there are atoms in a metastable state.

This method of absorption of light by an excited gas is at present the most widely used for measuring the lifetime of metastable atoms. Zemansky²³ gave a formula for the theoretical calculation of the lifetime. According to this formula,

\[ \frac{1}{t}=\frac{B}{p}+Cp, \]

where \(p\) is the gas pressure, \(B\) and \(C\) are constants characteristic of the given gas and temperature; the coefficient \(B\) also depends on the configuration of the tube. The results of experiments by various authors²⁴˒²⁵ give satisfactory agreement with the formula for \(t\) given by Zemansky. Knowing the lifetime of metastable atoms, one can draw certain conclusions about their concentration; for this it is necessary to know the number of metastable atoms newly arising per unit time in a unit volume. For the concentration \(N\) of metastable atoms the relation \(N=qt\) is valid, where \(q\) is the number of metastable atoms arising in a unit volume in 1 sec., and \(t\) is their mean lifetime.

If the excitation functions were known, then from them it would be possible to obtain the direct excitation of atoms by colli...

rameters of the electrons, and from this determine the value of \(q\). Kopfermann and Ladenburg\(^{26}\), Levy\(^{27}\), and Shen\(^{28}\) studied the dependence of the concentration of excited atoms on the current strength by the method of anomalous dispersion. The authors found thereby that the concentration of metastable atoms in the discharge in the noble gases they used increases at small current densities proportionally to the magnitude of the current. Beginning with a certain value of the current, the increase of concentration slows down, and at 100 mA (in neon) and 50 mA (in argon) saturation of the concentration sets in. The onset of saturation is explained by the authors by the fact that, at larger currents, collisions of metastable atoms with electrons begin to play a substantial role in their destruction. According to Kopfermann and Ladenburg, the saturation state is associated with the establishment of thermodynamic equilibrium between excited atoms and electrons. In this case the Boltzmann formula makes it possible to calculate the electron temperature, which in the present case is considered to coincide with the “specific temperature” of the distribution. In a recently published article, Fabrikant and Panevkin\(^{29}\) point out that the saturation of the concentrations of excited atoms observed by Kopfermann and Ladenburg and others cannot be explained by the establishment of equilibrium between collisions of the first and second kind. According to Fabrikant and Panevkin, the principal cause of the saturation of the concentrations of excited atoms must be regarded as the decrease of the electron temperature with the current. It is quite obvious that a decrease in the temperature of the electrons with current, resulting in a decrease in the number of newly arising metastable atoms per unit time and, consequently, in a decrease—at constant lifetime—of their concentration, must be invoked to explain the saturation phenomenon.

It is hardly possible, however, to disregard the role of the ionization of metastable atoms by electrons. The very decrease in the temperature of the electrons with increasing current at small current densities finds its explanation in stepwise ionization. But it is rather difficult to say more definitely about the relation of the two factors (decrease of temperature and destruction of metastable atoms) in the saturation effect, since the quantitative considerations that can be given here are of a very rough approximate character.

a) Effects in the discharge plasma. The study of the influence of metastable atoms in a stationary discharge in inert gases has been carried out since 1928. A number of investigators found that the currents to a negatively charged probe in the positive column of a discharge in neon are greater than is expected according to probe theory.

The probe theory, created by the works of Langmuir and Mott-Smith\(^{30}\), makes it possible, from the current-voltage characteristics of probes, to determine the principal parameters of the plasma of a gas discharge. By the probe method one can measure the space potential, the concentration and mean energy (temperature) of the electrons in the positive column of the discharge. The theory is especially well justified over a wide interval of probe potentials for a discharge in mercury vapor. It is precisely

in view of the great theoretical and practical fruitfulness of the probe method, it was expedient to investigate experimentally deviations from this theory.

The first measurements by Morse and Uterhoven[^31] showed that the current to a probe in neon at a negative potential of about 150 V relative to the surrounding space is twice as large as that calculated from the probe potential and the thickness of the layer surrounding it. The authors considered one of the probable causes to be ionization by metastable atoms in the layer surrounding the probe, produced by radiation coming from the discharge. The results of the work of Uterhoven and Harrington[^32] show that, at low neon pressures, 15–50% of the current to a negative probe arises owing to secondary emission of electrons, the greater part of which is due to uncharged particles, probably metastable atoms.

Oliphant[^33] also believes that the secondary emission of electrons under the action of neutral particles, which he observed in a helium discharge, involves metastable helium atoms. Investigations by Langmuir and Found[^34] and by Sivak and Reichrudel[^35] in a neon discharge at pressures of 0.5–2 mm Hg showed that an electron current from a negatively charged probe exists not only when the probe is situated in the discharge plasma, but also when the probe is located far outside the plasma. The experiments show that these currents are much larger (by hundreds of times) than would be expected from the relation obtained by Langmuir and Compton on the basis of Schottky’s diffusion theory. They are connected with the concentration of metastable atoms near the probe, but could not be explained by secondary emission of electrons produced by ions or metastable atoms directly diffusing from the plasma, since the mean free path of these particles under the experimental conditions was too small.

The occurrence of metastable atoms near the surface of the probe could be caused by short-wavelength resonance radiation diffusing from the discharge and exciting the atoms of the gas. However, resonance radiation is absorbed and re-emitted by the gas atoms millions of times before it reaches the walls or the probe. The absorption coefficient of the gas \(\alpha_0\) for resonance radiation, according to Ladenburg’s classical theory,[^36] is given by the expression

\[ \alpha_0=\frac{Ne}{\nu_0 m v}, \]

where \(N\) is the number of atoms per unit volume in the normal state, \(\nu_0\) is the frequency of the resonance radiation, \(v\) is the mean velocity of the gas atoms, and \(e\) and \(m\) are the charge and mass of the electron. Substituting the numerical values of these quantities for neon at a pressure \(p=1\) mm Hg, we obtain \(\alpha_0=1.55\cdot 10^5\), or the “mean free path” of the resonance radiation under these conditions is equal to \(6.45\cdot 10^{-6}\) cm.

As a result of the short mean free path of the resonance radiation, a strong scattering of its energy occurs, and it does not

IONIZATION BY IMPACTS IN A GAS DISCHARGE

can be transported over a greater distance; therefore there must be a rapid decrease in the density of electrons, positive ions, and metastable atoms with distance from the source. Therefore, in order to explain the mechanism of the occurrence of metastable states at large distances from the discharge, Langmuir uses the features of resonance lines established by Wood^37—namely, that the emission line is broader than the absorption line. The absorption coefficient for the center of the resonance line is greater than for the edges.

The radiation from the edges of the broadened resonance line can be transported over greater distances. When the broadened resonance radiation, traveling along the tube, is finally absorbed, the greater part of it is re-emitted in the form of narrow lines, which are strongly absorbed. This process consists in the conversion of radiation having a long “mean free path” into radiation with a short mean free path, or a large absorption coefficient.

Taking into account that re-emitted radiation has a large absorption coefficient, one may assume that only radiation re-emitted near the electrode can reach it. Thus, owing to the re-emitted, strongly absorbed resonance radiation, metastable atoms are created near the probe. The latter, encountering walls and electrodes, can cause secondary electron emission from them.

Fig. 3. \(p = 1\) mm, \(V_A = 250\) V, \(I_A\) — 1.5 mA

A calculation made by Langmuir shows that the energy absorbed per unit volume in 1 sec., and consequently also the number of metastable atoms formed, decrease inversely as the third power of the distance from the radiation source (the positive column). The experimental results are in agreement with this conclusion. Fig. 3 shows changes in the probe characteristics due to metastable atoms, obtained in the experiments of Reichrudel and Spivak^35. The observations were carried out with movable probes in neon. To regulate the concentration of metastable atoms the authors used an external neon illuminator. The change in the probe current under illumination, i.e., upon decreasing the concentration of metastable atoms, occurs both in the ionic part of the characteristic and in the electronic part. If the probe is placed not in the positive column, but outside it, the probe currents decrease when the concentration of metastable atoms in the discharge is decreased. At high negative probe potentials the decrease of the current upon

illumination can be explained by a decrease in the secondary emission from the probe, caused by metastable atoms, and by the subsequent Townsend avalanche. The difference in the changes of the current under illumination when the probe is located on the axis and at the wall of the tube is connected with the fall in the concentration of metastable atoms at the wall of the tube.

Electron emission from the probe may also be attributed to the direct photoeffect of the broadened resonance line. In this connection, a discussion arose in the literature as to which plays the greater role: metastable atoms near the probe or the direct photoeffect. Kenty^38, on the basis of his experiments with a flat probe placed outside the positive column and oriented arbitrarily, parallel or perpendicular to the axis of the discharge tube, asserts that the increase in current in the case of perpendicular orientation of the probe is a consequence of the liberation of electrons from the surface of the probe by the directing agent, namely by the direct photoeffect of the radiation coming from the column of the discharge.

Fig. 4a and b. Arrangement of the experiment. Л — illuminating lamp. C — layer. З — probe.
Change in the compensated ion current at different distances of the light beam from the surface of the probe.
Probe in the positive column. Discharge current \(I_A = 4\ \mathrm{mA}\)

To separate the effect of metastable atoms in the liberation of electrons from the surface of the probe from the direct photoeffect, Reichrudel and Spiwak^35 also carried out the following experiments. Toward a negatively charged probe placed outside the column, from the side opposite the radiation, a small glass wall was brought near. The latter, by destroying the metastable atoms near the probe, did not substantially change the directed radiation from the discharge; when the wall was brought up to the probe from behind, the currents to the probe decreased, which must be attributed mainly to the action of metastable atoms (surface and volume). Parallel experiments in mercury vapor showed the absence of analogous changes. In other experiments by the same authors, around the probe

a light barrier was set up, which made access of metastable atoms to the surface of the probe difficult, but did not interfere with the directed radiation. The arrangement of the experiment and the results are shown in Fig. 4 a and b. Bringing the beam of light closer to the surface of the probe caused a change in the compensated current to the probe.

These experiments showed that, in the liberation of electrons from the probe, the chief role is played by metastable atoms, and not by the photoelectric effect. Similar results were obtained by Duffendack and Smith[^39].

A number of phenomena observed in the positive column of a glow discharge are also directly connected with the action of metastable atoms. Hidrik and Duffendack[^40] measured the potential gradient in the column in mixtures of the noble gases He, Ne, Ar with one another and in mixtures of each of these gases with mercury vapor. Simultaneously with measurement of the field, observations were made of changes in the spectral characteristic of the column when the composition of the gases in the mixture was varied. The experiments were carried out at a discharge-current strength from 20 to 40 mA and at a gas pressure from 5 to 30 mm Hg. The authors found that the addition of mercury vapor at room temperature to neon causes a decrease of the field in the column by 45%, whereas the addition of mercury to argon or helium causes a small increase of it. With a mercury-vapor content in the mixture of 0.03% or more, the spectra of neon and argon in the light emission of the column almost disappear, and only the mercury spectrum remains. When less than 0.4% neon or argon is introduced into helium, a noticeable increase of the electric field in the column occurs, and the emitted spectrum is almost completely transformed from the arc spectrum of helium respectively to that of neon or argon. Hidrik and Duffendack explain the results obtained by the action of collisions of the second kind between metastable atoms and ions of one gas and neutral atoms of another gas. A necessary condition for a large effect on the electrical and spectral characteristics of the positive column, observed when a small dose of another gas is added to one gas, is the close resonance existing between the metastable states of the principal gas. Thus, according to Hidrik and Duffendack, the action of metastable atoms can not only decrease the field in the column, but in certain cases also increase it. A decrease of the field occurs in those cases when collisions of metastable atoms of the principal gas with normal atoms of the impurity, leading to ionization of the latter, have a high probability. This occurs, for example, in neon with a small admixture of mercury vapor. Here, to the processes which take place in the column in pure neon, there is added another process, proceeding according to the equation

\[ \mathrm{Ne}_{\mathrm{met}} + \mathrm{Hg} \rightleftarrows \mathrm{Hg}^{+} + \mathrm{Ne} + e + \text{kinetic energy} \]

\[ \begin{array}{cccc} 16.64 & 16.62 & 0.07 & -0.07 \\ 16.54 & 16.71 & -0.08 & 0.17 \end{array} \]

where \(\mathrm{Ne}_{\mathrm{met}}\) is a metastable neon atom, \(\mathrm{Hg}^{+\prime}\) is an excited singly ionized mercury atom, and the numbers below are energies in electron-volts. Since there is no large difference between the excitation energy of metastable neon atoms and the ionization energy of mercury atoms with simultaneous excitation of the ions formed, the probability of the process written above in a mixture of neon with mercury is high. But this process leads to ionization and, consequently, to a decrease of the field in the column as compared with pure neon. As already stated, spectroscopy shows that in this case the mercury lines appear sharply, whereas the neon lines almost go out. This was to be expected according to the equation written. In pure neon, metastable atoms are destroyed predominantly by collisions of the first kind with atoms and electrons. In a mixture of neon with mercury, however, metastable atoms perish predominantly owing to collisions of the second kind with normal mercury atoms, in which ionization of mercury atoms occurs and, simultaneously, excitation of the mercury ion. This circumstance decreases the share of the energy accumulated in metastable atoms and lost through radiation, and increases the share of this energy going into ionization in the column. If the effect of the decrease of the field were caused by direct ionization of the impurity atoms under the experimental conditions, then the same or, possibly, a greater decrease of the field could be expected in a mixture of helium with a small amount of mercury. However, an admixture of mercury to helium does not decrease the field but, on the contrary, increases it somewhat.

An increase of the electric field occurs in those cases when the ionization potential of the impurity atoms is higher than the excitation potential of the metastable atom of the principal gas and, at the same time, there exist excited levels in the impurity atoms that are in close resonance with the metastable level. Under these conditions the metastable atoms of the principal gas can no longer ionize the impurity atoms, but instead a new process appears in the mixture, leading to the destruction of metastable atoms. Such a process is the collision of metastable atoms with impurity atoms, in which the latter are excited at the expense of the energy of the metastable atoms. This phenomenon is observed in a mixture of helium with a small admixture of neon. The excitation potential of metastable helium atoms, as is known, is less than the ionization potential of neon atoms. The process of excitation of neon atoms in collisions with metastable helium atoms will proceed according to the equation

\[ \begin{aligned} \mathrm{He}_{\mathrm{met}}+\mathrm{Ne} &\rightleftarrows \mathrm{Ne}^{\prime}+\mathrm{He}+\text{kinetic energy}\\ 20.51 \qquad &\quad 19.69\\ 19.73 \qquad &\quad 20.62 \end{aligned} \]

Here \(\mathrm{Ne}^{\prime}\) denotes a neon atom excited to an unstable level. This process excludes one of the processes occurring in pure helium according to the equation

\[ \mathrm{He}_{\mathrm{met}}+e=\mathrm{He}^{+}+2e+\text{kinetic energy}, \]

leading to the ionization of metastable atoms. Therefore a large amount of the energy obtained from the field, owing to neon, is lost to radiation, whereas in pure neon this energy went into ionization. A decrease in the ionization coefficient causes the field to increase. A decrease in the field upon addition of an impurity should also occur in the case when the ionization potential of the impurity atoms is less than the excitation potential of the metastable level of the main gas, but the probability of second-kind collisions leading to ionization is so small in comparison with the probability of such collisions between metastable atoms and impurity atoms, in which excitation of the latter occurs, that as a result the ionization coefficient decreases. Such a case occurs in a mixture of helium with a small amount of argon.

As is known, in the column the loss of ions and electrons at the walls of the discharge tube is completely compensated by ionization in the volume. If in a homogeneous gas, when ionization of metastable atoms by second-kind collisions may be neglected, compensation of losses at the walls occurs by ionization in the column at a quite definite mean energy—the temperature of the electrons—then the same compensation in a discharge in a gas mixture, when metastable atoms take an active part in ionization along with electrons, is possible at a lower electron temperature. The decrease in concentration in this case should thus lead to an increase in the electron temperature \(T_e\). Indeed, Spivak and Reichrudel\(^\mathbf{41}\) observed a noticeable increase in \(T_e\) when illuminating a discharge in neon with a small argon impurity by external neon radiation. Figure 5 shows the semilogarithmic probe characteristics obtained by these authors in neon when the discharge was illuminated (dashed line) and without illumination (solid curve).

Fig. 5. \(I_A = 4\) mA, \(V_A = 70\) V

Spivak and Reichrudel discuss the possibilities of those cases in which the action of metastable atoms should cause not a decrease in \(T_e\), but an increase in it.

Dorgelo, Alting, and Boers\(^\mathbf{42}\) measured the electron temperature in the column in pure neon and in neon in one case with an impurity of argon, in another—with mercury vapor of different concentration. The experiments were carried out at a discharge current of 2 A and a gas pressure of 5 mm Hg. It turned out that an argon impurity to neon causes a decrease, and this decrease continues continuously with increasing argon pressure in the mixture. However, the introduction into neon of mercury vapor up to 0.32% causes an increase in \(T_e\), and only with a further increase in the mercury concentration does \(T_e\) begin to decrease, and at 0.38% \(T_e\) of mercury assumes a value smaller than in pure neon. Yuterhoven and Verburg\(^\mathbf{43}\) produc-

A. Zaitsev and E. Reikhgrudel

conducted measurements of the electron temperature in a mixture of neon with sodium at a discharge current of 1 A. The concentration of sodium vapor was determined by the temperature of the walls of the discharge tube. The authors also found that small admixtures of sodium to neon cause an increase in \(T_e\), which reaches its maximum value at a tube-wall temperature of \(240^\circ\), when the concentration of sodium atoms in the mixture is approximately \(0.01\%\). With a further increase in the sodium admixture, \(T_e\) decreases.

Still earlier, Jürchowen and Verburg observed an increase in the potential gradient in the positive column in the mixtures He + Na, Ar + Na, Ne + Ar, Ne + Hg, and He + Cs, as compared with the gradient in the corresponding pure noble gas. In all these cases of gas mixtures, the ionization potential of the admixture is lower than the ionization potential of the principal gas. Therefore it would have been natural to expect here not an increase of the gradient but, on the contrary, its decrease. As was said, in the experiments of Hiedrick and Duffendack, an admixture of mercury vapor to neon at room temperature sharply decreased the potential gradient. In the experiments of Jürchowen and Verburg, however, on the contrary, mercury vapor introduced in small quantity into neon causes an increase of the electric field in the column. Likewise, in the experiments of Dorgelo and his coauthors, an admixture of mercury to neon in small quantity causes not a decrease in the electron temperature, as might have been expected according to the work of Hiedrick and Duffendack, but an increase in it. This contradiction in the results of the experiments of Hiedrick and Duffendack, on the one hand, and of the experiments of Jürchowen, Verburg, and Dorgelo, Alting, and Bores, on the other, may perhaps be explained by differences in the experimental conditions. Hiedrick and Duffendack worked at such small currents (20–40 mA) that the role of metastable atoms in ionization in the discharge is indeed large. In the experiments of Jürchowen, Verburg, Dorgelo, and his coauthors, however, the discharge current was so considerable (1 A and higher) that the special role of metastable atoms in the discharge was already to a significant extent lost.

The influence of ionization by collisions of the second kind at low pressures (from 0.5 to 3 mm Hg) and at discharge currents from 5 to 10 mA on the electron temperature, the potential gradient in the column, and the potential drop in the layer of positive charges at the wall in mixtures of neon with argon and neon with mercury was studied by Zaitsev\(^{44}\). The effect of ionization by collisions of the second kind in the column could be estimated in the following way. In a discharge in pure neon, collisions of the second kind in the volume of the column do not play an essential role. The role of collisions of the second kind becomes appreciable only in a mixture of two gases. If the addition to neon of a small dose of argon or mercury, at which the ionization of admixture atoms by direct collisions with electrons is insignificant, causes a change in the characteristic of the column, then this change at small currents may mainly be ascribed to ionization by collisions of the second kind between metastable neon atoms and admixture atoms. However, the value of the admixture density at which collisions of admixture atoms with electrons may still be neglected is not very large. With an increase in the admixture density, ionization by direct collisions...

collisions with electrons increases. To accurately assess the role of collisions of the second kind, it is necessary to be able to separate the effect of ionization of an impurity in collisions of the second kind from the effect of ionization by electrons. Schottky’s equations, written with allowance for ionization by collisions of the second kind, make it possible to carry out this separation of the two effects. Indeed, from Schottky’s theory there follows the relation

\[ \frac{\alpha_1}{\mu_1}+\frac{\alpha_2}{\mu_2}+\frac{\alpha'_2}{\mu_2} = \frac{k}{e} T_e = \frac{2}{3} V_0 \left(\frac{2.4}{R}\right)^2; \]

where \(\alpha_1\) is the number of ionizations of atoms of the first gas produced by one electron per unit time, \(\alpha_2\) is the same for the second gas, \(\alpha'_2\) is the number of pairs of ions and electrons formed by an electron per unit time in the volume due to collisions of the second kind, and \(\mu_1\) and \(\mu_2\) are, respectively, the mobilities of the ions of the first and second gas.

The ratios \(\frac{\alpha_1}{\mu_1}\) and \(\frac{\alpha_2}{\mu_2}\) can be calculated. And if the electron temperature is measured experimentally, \(\frac{\alpha'_2}{\mu_2}\) will also be known. Thus the quantities \(\frac{\alpha_2}{\mu_2}\) and \(\frac{\alpha'_2}{\mu_2}\) can be compared for various gas mixtures. Experiments have shown that a small admixture of argon to neon lowers the electron temperature and also the electric field in the column. It was found in this case that, approximately up to an argon density in the mixture of \(0.01\%\), ionization by collisions of the second kind plays the predominant role in the effect (Fig. 6). At higher argon densities the effect of decreasing the temperature and the potential gradient must already be ascribed to ionization of the impurity by direct collisions with electrons. In the case of an admixture of mercury vapor to neon, the predominant role in ionization by electrons should begin at an impurity density less than \(0.01\%\).

Fig. 6. \(T_e\) (in pure Ne) \(= 3.2\ \mathrm{V}\), \(i_A = 7.5\ \mathrm{mA}\), \(p = 8\ \mathrm{mm\ Hg}\)

In some cases the opposite effect occurred, i.e. an admixture of argon increased \(T_e\) and the potential gradient. This phenomenon is apparently explained by the fact that, in this case, accidental gases entered the tube together with the argon. The presence of incidental unfavorable gases in the tube, even in insignificant quantities, can produce noticeable effects, chiefly because they may serve as centers for the formation of heavy ions in the column.

As is known, the potential drop in the positive charge layer at the wall is connected with the electron temperature. With a decrease of \(T_e\)

the magnitude of this drop should decrease. Experiments confirm this proposition. Table 2 gives the measured values of the potential drop in the layer for various mixtures. The measurement was carried out with illumination of the discharge by external radiation and without illumination.

TABLE 2

As is seen from Table 2, an admixture of argon to neon in an amount of 0.01%, when ionization by collisions of the second kind predominates over ionization by electrons, decreases the potential drop in the mixture by 0.5 V. Illumination of the discharge up to 0.5% Ar in the mixture causes an increase in the magnitude of the drop, and this directly shows that metastable atoms in the discharge in the mixture decrease the potential drop in the layer. Illumination of the positive column in neon with an argon admixture likewise causes an increase in the potential gradient. Fig. 7 shows the corresponding curve, giving the dependence of the illumination effect on the argon density. Along the abscissa is plotted here the argon density; along the ordinate—the change of the gradient under illumination. It is seen from the figure that the illumination effect, significant at small admixture densities, decreases with an increase of this density. A change of the potential gradient in the column in neon under illumination was also observed by Reichrudel and Spivak. Fig. 8 shows the curve obtained by them for the dependence of the illumination effect on the magnitude of the discharge current. Along the abscissa is plotted the current strength; along the ordinate—the potential gradient under illumination (dashed line) and without illumination. It is seen from Fig. 8 that the change of the gradient under illumination increases with decreasing current strength.

Fig. 7.

b) Effect in the cathode parts of the discharge. De Groot^46 observed a change in current density upon transition from a normal discharge in pure neon to a discharge in neon with an admixture of argon. This and several other phenomena taking place in the self-sustained discharge were explained by Penning by the ionizing role of metastable atoms. The normal discharge is a limiting case of an abnormal discharge, when the influence of the tube walls on the discharge is reduced to nothing. For this reason, for a theoretical study

normal discharge is simpler than anomalous discharge. However, obtaining a stable normal discharge is associated with considerable experimental difficulties. These difficulties increase in connection with the need to control strictly the composition of the gas in experiments carried out to study the role of metastable atoms.

Spivak and Reichrudel\(^{46}\) studied the influence of metastable neon atoms on the processes in the cathode regions of an anomalous discharge in pure neon and in neon with a small admixture of argon at low pressures (from 0.2 to 1 mm Hg). It was found that metastable atoms participate both in volume and in surface ionization. Reducing the concentration of metastable atoms by illuminating the discharge with the corresponding external radiation causes an increase in the cathode potential fall, if the discharge current is kept constant. Fig. 9 shows a pair of curves expressing the change in the burning potential when the distance between the electrodes is varied. Along the ordinate is plotted the difference of the potentials applied to the electrodes; along the abscissa, the distance between the electrodes. The parameter here is the discharge current. The form of the curves does not differ in any way from ordinary curves of this type, when, as the electrodes are brought closer together, the burning potential first falls (which corresponds to the “eating away” of the anodic parts of the discharge and of the positive column by the anode), reaches a minimum of the burning potential (which in the experiments of Spivak and Reichrudel is taken as the cathode potential fall), and then begins to rise, owing to the obstruction of the discharge. In each pair the solid curve corresponds to measurements without illumination, and the dotted curve to illumination of the discharge by external radiation. It is easy

Fig. 8.

Fig. 9.

one sees that the curve under illumination lies above the curve without illumination. The change in the cathode potential drop upon illumination of a discharge in pure neon is comparatively small. The effect of decreasing the concentration of metastable atoms by illumination reaches a considerable value when a small dose of argon is added to neon \((\Delta V = \text{up to } 12\mathrm{V})\). The increase of the cathode potential drop at constant current is connected with the need to compensate for the weakening of ionization by metastable atoms in the discharge, which occurs as a result of the decrease in their concentration under illumination, by strengthening ionization through direct collisions of atoms with electrons. The increase of \(\Delta V\) when argon is admixed with neon is explained by the fact that, in this case, substantial ionization of argon atoms by metastable neon atoms through collisions of the second kind becomes possible.

Fig. 10. 1 — c. p. d., 2 — n. g.

Spivak and Reichrudel succeeded in establishing that the quantity

\[ \frac{\Delta V}{i} \]

(the change in the potential drop under illumination, calculated per unit current) increases as the discharge current decreases. From this the authors conclude that the role of ionization by metastable atoms in the discharge increases as the current decreases. The ionizing action of metastable atoms proves especially large if conditions have been prepared in the discharge for its transition from one form into another, when the slightest change in ionization can cause this transition, often accompanied by a considerable change in the current strength and a noticeable change in the external appearance of the discharge. In particular, this influence on the ignition potential and on the extinction potential of the discharge is considerably greater than on the burning potential.

If the burning potential of the discharge is kept constant, one can observe a change in the current density under illumination. By observing, in parts, the influence of illumination of the cathode region of the discharge on the current strength, Spivak and Reichrudel established that the concentration of metastable atoms in the different parts of the cathode region is not the same. The greatest concentration occurs in the negative glow (Fig. 10). The negative glow is the radiation of excited atoms. Thus the place of greatest concentration for atoms excited to ordinary levels and for metastable atoms is one and the same—the negative glow. The study of the influence of metastable atoms on the cathode parts of the discharge in argon^47 leads to results consistent with those obtained by Spivak and Reichrudel

in the discharge in neon. The ionizing role of metastable atoms increases with rising gas pressure in the range from 0.8 to 4 mm Hg. In some cases illumination of the discharge may cause not a decrease in the discharge current at a constant potential difference on the electrodes, but an increase in it¹).

4. Non-self-sustained discharge

Very interesting data on ionization by metastable atoms were obtained by Kruithof and Penning¹⁸ in a non-self-sustained discharge in a mixture of neon with argon. The authors made a direct measurement of the quantity \(\eta=\frac{\alpha}{E}\), where \(\alpha\) is Townsend’s ionization coefficient and \(E\) is the electric field in the discharge gap, in pure neon and in a mixture of neon with argon. The most intense ionization for the mixture \(\mathrm{Ne}+\mathrm{Ar}\) occurs at \(\mathrm{Ne}+0.1\%\mathrm{Ar}\) and

\[ \frac{E}{p}=3.3\ \mathrm{V/cm}. \]

In this case \(\eta=\eta_{\max}=0.037\). For small values of \(\frac{E}{p}\), \(\eta\) decreases sharply as a result of increasing elastic losses. The excitation of neon and argon then becomes negligible. The decrease of \(\eta\) with increasing argon density above 0.1% is explained by the fact that at higher density the loss of energy to excitation of argon atoms increases.

On the other hand, when the argon density is reduced below 0.1%, ionization by metastable atoms by means of collisions of the second kind will decrease because of the shortage of argon atoms in the mixture.

Thus it turns out that the values

\[ \frac{E}{p}=3\ \mathrm{V/cm\cdot mm} \]

and an argon density of 0.1% are the most favorable for the development of ionization by collisions of the second kind in a non-self-sustained discharge in a mixture of neon with argon. With increasing \(\frac{E}{p}\) a small decrease of \(\eta\) is also observed. This is apparently due to the increase in losses of electron energy for excitation of higher unstable levels of neon, which occurs as the field increases. Kruithof and Druyvesteyn, using the experimental data, calculated the probability \(K\) that an excited neon atom will pass to a metastable level and ionize an argon atom. With ionization by collisions of an argon atom with excited atoms at an unstable level—

¹) In unpublished work by K. Panevkina, carried out under the direction of V. Fabrikant, data are presented on measurements of the concentration of metastable atoms in a neon discharge. These data show that the change in the concentration of metastable atoms under illumination is so small that it can hardly explain the observations of the electrical parameters described in this work. K. Panevkina’s work also shows, in agreement with the works mentioned here, the influence of discharge illumination by external radiation on its electrical parameters, so that the viewpoint of Found and Langmuir (C. Found and I. Langmuir, Phys. Rev., 39, 237, 1932)—that external radiation is of low effectiveness in destroying metastable atoms—is apparently not entirely correct.

if the flight time need not be taken into account. The probability of such collisions is insignificant. The probability \(K\) is a function of \(\frac{E}{P}\) and of the argon density. In Table 3 are given the calculated values of \(K\) (where \(a\) denotes the ratio of the argon pressure to the total pressure of neon and argon).

TABLE 3

Values of \(K\) as a function of \(a\) and \(\frac{E}{P}\)

From Table 3 it is seen that the largest value of the probability occurs at \(\frac{E}{P}=3.36\ \mathrm{V/cm}\) (in the experiments \(i_{\max}\) occurs at \(\frac{E}{P}=3.3\ \mathrm{V/cm}\)).

If the values of \(K\) are known, one can calculate the probability \(q\) that a neon atom excited to an arbitrary level will pass into a metastable state. It is known that the probability \(K\) may be represented as the product of two probabilities, \(K=q\pi\). The meaning of \(q\) is clear to us. \(\pi\) is the probability that a metastable neon atom, during its lifetime, ionizes an impurity atom. Druyvesteyn and Penning calculated \(q\) for a number of values of \(\frac{E}{P}\).

The action of metastable atoms in a non-self-sustained discharge was also studied experimentally by Glotov.^49 Glotov’s experiments make it possible to establish that the actions of metastable atoms in a non-self-sustained discharge, under certain experimental conditions, become significant. Moralev’s work^50 is devoted to taking into account ionization by collisions of the second kind in calculating the ionization coefficient \(\alpha\).

Conclusions

From what has been set forth it is clear that the results of a large number of experimental works point to the significant role of collisions of the second kind in gas discharge. Under known conditions the action of collisions of the second kind appears as the principal factor in explaining many phenomena connected with spectral and electri-

characteristic of the discharge. Therefore the study of collisions of the second kind is of not only theoretical but also practical interest.

However, a quantitative estimate of the effects of collisions of the second kind encounters considerable difficulties. These difficulties are connected, first of all, with the limited information on the excitation functions and, in part, also the ionization functions of atoms. The simplest, from the point of view of quantitative accounting of the phenomena, is the positive column. The phenomena in the cathode region are the most difficult to subject to quantitative analysis. The reason for this is, chiefly, the distortion of the electric field by space charges in front of the cathode. The question of the velocity distribution of electrons diffusing through a gas in a uniform electric field is also important, and its solution is necessary for estimating phenomena connected with collisions of the second kind.

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