Modern Concepts of the Mechanism of Electrical Breakdown in High Vacuum

L. V. Tarasova

Introduction

At the present time, the insulating properties of vacuum are widely used in science and technology. Charged-particle accelerators, X-ray tubes, electron-beam tubes, electron microscopes, vacuum capacitors—this is by no means a complete list of devices whose operation is connected with the electrical strength of a vacuum gap. In this connection it has become necessary to study and explain the mechanism of the initiation and development of an electrical discharge in high vacuum.

When the gas pressure is reduced (usually at \(p < 10^{-3}\)—\(10^{-4}\) mm Hg), the mean free path of molecules and charge carriers—electrons and ions—becomes greater than the dimensions of the interelectrode gap. Under these conditions electrons and ions practically do not collide with molecules of the residual gas in the volume; ionization does not occur and avalanche processes necessary for the formation of a gas discharge do not develop. Experiments show, however, that such a high-vacuum interlayer is not an ideal insulator. Under certain conditions a discharge inevitably arises. Just as in the breakdown of gas gaps at high pressure, the currents during breakdown of a vacuum gap may be regarded as limited only by the resistance of the current-source circuit. Most experimental data indicate that the breakdown voltage of a vacuum gap is independent of any further lowering of the pressure of the residual gas in the discharge volume. Consequently, all carriers of electricity arise either at the electrodes or at the walls of the device.

Vacuum, like any real insulator, possesses a certain conductivity. If one disregards the negligible influence of residual gases in the volume, as well as thermionic-emission currents, which are insignificant at normal temperature, then the stable conductivity

of the vacuum can be regarded as due to the phenomenon of cold emission. The formula for the current density of cold emission is derived on the basis of the ideas of quantum mechanics, taking into account the image electric force. If \(E\) is the electric-field strength at the cathode in volts per centimeter and \(\varphi\) is the work function in electron-volts, then the current density from the cathode \(j\), in amperes per square centimeter, is expressed as follows:

\[ j = 1.55 \cdot 10^{-6}\,\frac{E^{2}}{\varphi}\, e^{-\frac{6.85 \cdot 10^{7}\varphi^{3/2}}{E}}\, \psi\!\left(\frac{3.78 \cdot 10^{-4}\sqrt{E}}{\varphi}\right). \tag{1} \]

The values of \(\psi\!\left(\dfrac{3.78 \cdot 10^{-4}\sqrt{E}}{\varphi}\right)\) are found from special tables or graphs.

Experimental verification confirms the validity of formula (1). Analysis of this formula shows that, at field strengths below \(10^{7}\ \mathrm{V/cm}\), cold-emission currents are very small; as the field strength is increased, the current density rises rapidly. Usually, in real structures, cold-emission currents become measurable already at fields of the order of \(10^{6}\ \mathrm{V/cm}\), and sometimes \(10^{5}\ \mathrm{V/cm}\). However, these field strengths are calculated without taking into account the roughness of the cathode surface. At microroughnesses the fields are larger, and the emission is determined not by the entire cathode surface but by the microroughnesses. Therefore, when calculating the current density from a real surface, it is necessary to take into account the roughness factor and the area of the emitting surface.

Cold-emission currents, calculated theoretically and measured experimentally for voltages close to the breakdown voltages for a vacuum gap, are several orders of magnitude lower than the currents that can develop during breakdown. Consequently, there exist other processes that ensure the rapid release of a large number of charge carriers in the vacuum gap and large currents during breakdown.

Experimental investigations show that the development of breakdown in high vacuum can be divided into two stages. The first stage is characterized by low pressure, directed motion of electrons and ions, and the presence of X-radiation. In the first stage the principal processes determining the development of breakdown take place: the release of charge carriers, gas, and metal vapors from the electrodes and the walls of the vacuum chamber. The first stage ends with a rapid rise in current and a drop in voltage across the vacuum gap.

The second stage—the burning of the “vacuum arc”—is characterized by increased pressure in the interelectrode gap, low voltage, and large current. The duration and mode of burning of the “vacuum arc” depend mainly on the parameters of the external electrical circuits.

It has been established that the phenomena observed at relatively low voltages in small vacuum gaps differ from the phenomena occurring at high voltages and large gaps. The mechanism of breakdown of a vacuum gap in a uniform electric field and in strongly nonuniform fields is also substantially different. In real systems, the presence of an adsorbed gas layer on the electrode surfaces and their contamination have a great influence on the development of breakdown. The presence, near the electrodes, of an insulator—which is an indispensable part of any electrovacuum device—strongly changes the breakdown voltage of a vacuum gap.

Over recent decades, a considerable number of works have appeared in the literature devoted to the study of the mechanism of the initiation and development of breakdown in high vacuum. Numerous attempts have been made to explain the phenomena observed during breakdown of various vacuum gaps and with various electrode shapes. Extensive experimental material has been accumulated.

The present work is devoted to presenting the most important experimental data and hypotheses explaining the mechanism of the development of breakdown in high vacuum. We have limited our task to questions associated with the first stage of breakdown in the simplest two-electrode systems. The work does not consider vacuum breakdown initiated by a triggering spark in high vacuum. Nor are the phenomena occurring in the second stage of breakdown discussed (the burning of a “vacuum arc”).

I. ELECTRICAL BREAKDOWN IN HIGH VACUUM

1. Experimental data

The breakdown voltage of a vacuum gap depends strongly on the experimental conditions. Since the charge carriers that provide the breakdown currents are emitted from the boundary surfaces of the vacuum gap, the breakdown voltage is determined by the configuration of the electrodes and of the tube walls, by their characteristics, and by the state of the surfaces. The better the electrode surface is polished, cleaned, and degassed, the higher the breakdown voltage. Breakdown of a vacuum gap occurs at a higher voltage in the case of fields close to uniform.

The breakdown voltage depends on the material of the electrodes. Table I presents Anderson’s data on the influence of the electrode material on the breakdown voltage of a vacuum gap of length 1 mm for fields close to uniform.\(^1\)

As the distance between the electrodes increases, the breakdown voltage of the vacuum gap also increases. However, only at small distances (hundredths of a millimeter) and low voltages (up to 20–50 kV) can this dependence be considered proportional.

for fields close to uniform. In this case the field strength corresponding to breakdown does not change as the distance between the electrodes increases \(^{2,54}\).

A different course of the curve is observed at large distances and high voltages, even for fields close to uniform. The experimental curves in this case agree satisfactorily with the formula \(^{3}\)

\[ U=(Cd)^{1/2}, \]

where \(U\) is the breakdown voltage of the vacuum gap, \(d\) is the distance between the electrodes, and \(C\) is a constant. Thus, the field strength corresponding to breakdown decreases with increasing distance between the electrodes, and breakdown depends not only on the field strength at the cathode, but also on the total voltage across the vacuum gap.

Table I

Breakdown voltage of a vacuum gap with electrodes made of various materials

At sufficiently high voltages and distances between the electrodes, the stable conductivity of the vacuum turns out to be of a different nature. Anderson \(^{1}\) investigated prebreakdown currents up to voltages of \(120\ \text{kV}\) under conditions of fields close to uniform. The magnitude of these currents proved to be of the order of \(10^{-8}\)—\(10^{-7}\ \text{A}\). It was established that in this case the prebreakdown currents are determined not only by the field strength at the cathode, i.e., by cold emission, but also by the total voltage between the electrodes. Anderson assumes the participation in the conduction of positive ions from the anode. The ions, bombarding the cathode, can knock out from it a certain number of electrons that maintain the conductivity of the vacuum.

The release of metal ions from the anode at high interelectrode voltages is confirmed by the following Anderson experiment. The electrodes of the vacuum gap were made of two different metals: copper and steel. The interelectrode gap was held for several minutes at a voltage close to the breakdown voltage. After this, the material of the anode (copper) was found in appreciable quantity on the steel cathode.

In the case of a poorly degassed anode, positive ions arise as a result of gas evolution from the anode and its ionization. The effects of the formation of gas ions under the action of electron bombardment of a nondegassed anode surface and a nondegassed glass surface were investigated in the works of Bennet \(^{4,5}\).

Numerous experiments by various authors show that the breakdown voltage may be regarded as independent of the pressure of residual gases if the mean free path of the molecules is greater than the dimensions of the vessel. The experiments were carried out in the pressure range \(10^{-3}\)—\(10^{-7}\) mm Hg. However, the pressure of residual gases is closely connected with the degree of degassing of the electrodes, with the amount of gas adsorbed on the surfaces of the electrodes and the walls of the tube, and the breakdown voltage depends strongly on the degree of degassing. Consequently, the pressure of residual gases also has some influence on the breakdown voltage\(^{6,7,8}\).

Recently, some indications have appeared of an increase in the electric strength of a vacuum gap with increasing pressure of the residual gases. Thus, according to the data of Mack Kibben and Boyer\(^{9}\), in a sectionalized accelerating tube of diameter 200 mm and length approximately 560 mm the breakdown voltage increased sharply when the pressure rose to \(1 \cdot 10^{-4}\) mm Hg. According to Tarner\(^{10}\), the addition to the residual gas of hydrogen, helium, nitrogen, and argon in definite proportions limits phenomena associated with breakdown.

Linder and Christian\(^{11}\), investigating the operation of a radioactive high-voltage generator at 365 kV, found a dependence of the limiting voltage of the generator on the pressure of the residual gas in the chamber. In the interval \(10^{-6}\)—\(10^{-4}\) mm Hg the limiting voltage of the generator remains constant. With a further increase in pressure, the voltage rises and reaches a maximum at approximately \(10^{-3}\) mm Hg. A further increase in pressure leads to a rapid drop in the limiting voltage.

At approximately the same pressures (\(10^{-3}\)—\(10^{-2}\) mm Hg for helium, air, and argon), Kustova and Reichrudel\(^{12}\) observed certain features in the development of the discharge both in tubes with a triggering spark and in two-electrode systems. In particular, the integral intensity of the x-ray radiation in this pressure region has a maximum. The authors relate the appearance of the maximum to an increase in the formation time of the discharge, owing to the appearance in this pressure region of a transitional stage between the first phase of the discharge (a directed stream of electrons) and the second phase (plasma). In the transitional stage, gas focusing of the electron beam takes place. The appearance of a gas-focused beam is confirmed both by the authors’ calculations and by their additional experiments.

Investigations of the development of processes during breakdown of a vacuum gap in time were carried out by various methods: oscillographic recording of voltages and currents during breakdown, measurement of the time of the x-ray flash, and scanning of light phenomena during breakdown with the aid of a rotating mirror. Some idea of the time of development of breakdown can be obtained by knowing the pulse coefficient

for a vacuum gap, i.e., the ratio of the breakdown voltage for pulses of a specified duration to the breakdown voltage under constant voltage.

Experimental data show that, under various conditions in a vacuum gap, the time characteristics of breakdown are different.

According to Spivak and Dubinina ^13, at small distances between electrodes (hundredths of a millimeter) and low voltages, the transition from static voltage to pulsed voltage (rectangular pulses of duration \(1—10\ \mu\text{sec}\)) greatly increases the breakdown voltage. If, under static voltage, breakdown occurred at \(300\ \text{V}\), then under pulsed voltage it occurred at more than \(2\ \text{kV}\). Such a large impulse coefficient indicates that, under these conditions, the time of development of breakdown in high vacuum is of the order of several microseconds. Under approximately the same conditions, Boyle, Kisliuk, and Germer ^54 measured breakdown development times of the order of a microsecond. Significant impulse coefficients were also observed by Meson ^2 for pulse durations of the order of microseconds, small distances between electrodes, and voltages up to \(60\ \text{kV}\).

Impulse coefficients of the order of \(1.5—2\) and higher are also observed for the case of breakdown along insulation in vacuum with pulses of microsecond duration and voltages of tens of kilovolts. This effect is used in pulse oscillography ^14.

An impulse coefficient different from unity for breakdown of a vacuum gap has also been found at high voltages. In Hollern’s work ^15 a vacuum gap \(5\ \text{cm}\) long withstood a pulsed high-frequency voltage of \(2000\ \text{kV}\). The voltage was applied at a frequency of \(3000\ \text{MHz}\) with a pulse duration of \(2\ \mu\text{sec}\). Under constant voltage, an analogous gap breaks down at a voltage not exceeding \(800\ \text{kV}\).

Dyke and Trolan ^7 oscillographically recorded currents and voltages during breakdown of a vacuum gap in the case of a sharp cathode opposite a plane anode at voltages of several tens of kilovolts. Under these conditions, a time of about \(1\ \mu\text{sec}\) is required for breakdown to develop.

A breakdown development time of about \(2 \cdot 10^{-7}\ \text{sec}\) was obtained in the works of Warmoltz ^16 (\(15\ \text{kV}\), tungsten spheres at a distance of \(0.25\ \text{mm}\)) and of Sheffer ^17 (\(28\ \text{kV}\), breakdown between oscilloscope plates at a distance of \(15\ \text{mm}\)).

Hall and Buerger ^18 established that, with a distance between tungsten electrodes of about \(2\ \text{mm}\) and a voltage up to \(100\ \text{kV}\), the transition to an arc in metal vapor takes place in less than \(10^{-7}\ \text{sec}\).

The time sweep of the luminous phenomena accompanying breakdown in high vacuum was studied by Snoddy ^19 and Childs ^20 using a camera with a rotating mirror. It was established that, except for

with the exception of rare cases, the glow first appears at the anode, and only after some time \((1—2\cdot 10^{-7}\ \text{sec.}\) according to Snoddy, or \(1.3—9.3\cdot 10^{-8}\ \text{sec.}\) according to Chiles) does the region near the cathode begin to glow. Chiles also measured the propagation velocities of the luminous cloud of metallic vapor from the anode to the cathode for various anode materials. These velocities lie in the range \(5.0—8.9\cdot 10^{5}\ \text{cm/sec.}\)

2. Electrical breakdown in a high vacuum at small distances between electrodes and relatively low voltages

In the case of fields close to uniform, small distances between the electrodes (down to hundredths of a millimeter), and low voltages (up to \(20—50\ \text{kV}\)), the mechanism of electrical breakdown in vacuum is considered known. Experimental data \(^{2,1,6,54}\) show that in this case the field strength at the cathode surface before breakdown is sufficient for the onset of cold emission from microroughnesses of the cathode. The electrons of cold emission are accelerated in the interelectrode gap to high velocities and bombard the anode. The anode surface is locally heated to high temperatures; in this process a considerable quantity of gas and metal vapors is released. The high vacuum is disrupted, and breakdown occurs in the gas or metal vapors. Thus, in the case of small distances between the electrodes and low voltages, electrical breakdown occurs when the field strength at the cathode \(E\) exceeds the critical field strength \(E_{\mathrm{cr}}\), leading to the appearance of noticeable cold-emission currents:

\[ E \gg E_{\mathrm{cr}}. \tag{2} \]

A more exact criterion of electrical breakdown at small distances and low voltages was derived in the work of Boyle, Kisliuk, and Germer \(^{54}\). Experiments carried out at pressures of the order of \(10^{-9}\ \text{mm Hg}\) with two crossed tungsten wires \(0.75\ \text{mm}\) in diameter, with a distance between them of less than \(8\cdot 10^{-4}\ \text{cm}\) and a breakdown voltage below \(2.2\ \text{kV}\), confirmed the breakdown mechanism described above. At voltages below the breakdown voltage, steady and pulsed cold-emission currents from \(10^{-8}\) to \(10^{-2}\ \text{A}\) were detected and measured. The breakdown voltage as a function of distance varied approximately according to a linear law, i.e., the breakdown field strength for different distances remained practically constant.

On the basis of the experimental data, it was calculated that the power released at the anode due to bombardment by cold-emission electrons, even allowing for heat removal by thermal conduction, is sufficient to evaporate the anode metal. The metallic vapor is partially ionized by the electron current from the cathode,

L. V. TARASOVA

but the ionic current, according to the authors’ calculations, is several orders of magnitude smaller than the electronic current.

The authors’ approximate calculation, using simplified formulas, makes it possible to determine the current density of cold emission from the cathode, \(j_E\), under the action of the field \(E=E_A+E^+\), where \(E_A\) is the applied field and \(E^+\) is the field produced by ions. For \(j_E\) the following relation is derived:

\[ j_E=j_0 e^{M j_E^2}, \]

where \(j_0\) is the current density of cold emission without taking into account the influence of positive ions, and \(M\) is a constant. A graphical solution of this equation and an investigation of stability lead to the breakdown condition:

\[ \frac{j_E}{j_0}=\sqrt{e}\approx 1.65, \tag{3} \]

i.e., electrical breakdown between electrodes in a high vacuum occurs when the space charge of positive ions is sufficient to increase the cold emission of electrons by 65% in comparison with the emission that would exist without the ionic space charge.

After the field has increased to a value sufficient to cause breakdown, for approximately \(1\ \mu\mathrm{sec}\) there is still no noticeable increase in current. This time is necessary for heating and evaporation of the anode material. The authors’ approximate estimate agrees with the experimental data. Following evaporation of the anode material there is a rapid growth of current, occurring in a time less than \(10^{-8}\) sec.

With an increase in the distance between the electrodes, the described breakdown mechanism is gradually replaced by the breakdown mechanism at high voltages and large interelectrode distances \(^{21}\). Mason \(^{2}\), Hall and Borger \(^{18}\) observed, at somewhat larger distances and voltages, a breakdown mechanism associated with cold emission and evaporation of the anode surface.

In the work of Chiles \(^{20}\), at voltages of \(55\)—\(120\ \mathrm{kV}\), electrode dimensions of the order of \(1\ \mathrm{mm}\), and approximately the same interelectrode gaps, a mixed breakdown mechanism was observed. In his view, the cold-emission currents heat the anode, and a cloud of vapor is released, moving toward the cathode. It is greatly outstripped by positive ions. Bombardment of the cathode by positive ions and the increase in field strength at the cathode as the positive ions approach it cause additional emission of electrons. Such bombardment of the cathode by positive ions is accompanied by luminescence of the cathode surface. The appearance of luminescence on the electrodes and the motion of the vapor cloud from the anode to the cathode were observed by Chiles with the aid of a camera with a rotating mirror.

Mason’s experimental data \(^{2}\) for interelectrode distances from \(0.2\) to \(0.7\ \mathrm{mm}\) show that the pulse coefficients

in this case can be explained on the basis of the mechanism described above, if the velocity of the vapor stream leaving the anode is approximately \(10^5\ \text{cm/sec}\). Such velocities have been measured experimentally for the case of a mercury anode in an atmosphere of hydrogen, independently of the pressure\(^{22}\). Similar values of the velocities were also obtained in Child’s work.

3. Electrical breakdown in high vacuum at large distances between the electrodes and high voltages

As is seen from the curves of Fig. 1, when the distance between the electrodes is increased the breakdown voltage rises much more slowly than is required by condition (2), and the field strength near the cathode corresponding to breakdown steadily decreases\(^{6}\). For example, at a breakdown voltage of \(650\ \text{kV}\) the gradient at the cathode is less than \(100\ \text{kV/cm}\); at such a gradient no appreciable cold-emission currents can arise capable of ensuring the development of breakdown. Thus, the breakdown voltages at large distances between the electrodes are determined not only by the field strength, but also depend on the total voltage across the vacuum gap.

Fig. 1. Breakdown voltages (crosses) and field strengths (circles) at breakdown in high vacuum between a steel sphere 25.4 mm in diameter (anode) and a flat steel disk 50.8 mm in diameter\(^{6}\).

Various considerations have been put forward concerning possible causes determining the breakdown of a vacuum gap at high voltages. The two hypotheses most clearly formulated are: the mechanism of exchange of charged particles and photons, and the mechanism of detachment of large particles of matter from the surfaces of the electrodes. We shall consider each of them in more detail.

a) Mechanism of mutual exchange of electrons, ions, and photons between the cathode and the anode. To explain the processes occurring in the breakdown of long vacuum gaps at high voltages, Trump and Van de Graaff\(^{6}\) considered a breakdown mechanism that takes into account the influence of the total voltage between the electrodes on the electric strength

of the possibility of breakdown. This is the mechanism of mutual exchange of charged particles and photons between cathode and anode. From the ideas of Trump and van de Graaff it follows that breakdown can develop from one or several electrons that happen to be in the discharge gap. Electrons moving from the cathode are accelerated by the electric field to high velocities. Upon collision with the anode, positive ions and X-ray photons are released from the latter. The ions and photons, striking the cathode, cause further electron emission. When the conditions in the discharge gap become such that the mutual exchange builds up, breakdown occurs.

For a quantitative formulation of the breakdown condition, let us introduce the following notation:

$A$ — the average number of ions knocked out of the anode by one electron;

$B$ — the average number of secondary electrons knocked out of the cathode by one of these ions;

$C$ — the average number of X-ray quanta emitted by the anode upon the impact of one electron;

$D$ — the average number of secondary electrons emitted from the cathode under the action of one of these quanta.

Then the breakdown condition may be written in the following form:

\[ AB + CD \geq 1. \tag{4} \]

It should be expected that the coefficients $A$, $B$, $C$, and $D$ must increase with increasing accelerating voltage between the electrodes. In addition, they depend on the gradients at the electrode surfaces, as well as on the electrode material and the condition of their surfaces. However, the available experimental data show that the left-hand side of relation (4) is always less than unity. The values of the coefficient $A$, determined as early as in the first work of Trump and van de Graaff, were $2\cdot 10^{-4}$—$2\cdot 10^{-3}$ for voltages up to $230\ \mathrm{kv}$. Later, Philosopho and Rostagni^23 subjected these measurements to serious criticism. In their experiments the number of ions per one electron reaching the anode at voltages up to $70\ \mathrm{kv}$ proved to be 200–2000 times smaller than in the experiments of Trump and van de Graaff*). The effective values of the coefficient $A$ may be increased somewhat at the expense of secondary electron emission. According to the measurements of Trump and van de Graaff^6,24, the coefficient of secondary electron emission in the voltage range $30$–$340\ \mathrm{kv}$ does not exceed 8 (tungsten anode).

The value of the coefficient $B$ (the number of electrons per one positive ion) has been measured by many authors^6,25,26,27,28,29,30,31,32

*) Philosopho and Rostagni believe that the overestimated values of the coefficient $A$ in the experiments of Trump and van de Graaff are connected with the presence of adsorbed oil vapors on the anode surface. In the experiments of Philosopho and Rostagni the oil vapors were frozen out.

under various conditions for different ions. According to these data, the coefficient \(B\) does not exceed 25. Thus, even if one adopts the maximum value of the coefficient \(A\) according to Trump and Van de Graaff and takes into account the possible maximum secondary electron emission, the value of the term \(AB\) in relation (4) will be less than 0.4.

Interesting observations of the exchange mechanism have recently been published by Bourne \(^{33}\). The powers released at the electrodes by negative and positive particles of pre-breakdown currents in high vacuum at voltages of about \(100\ \mathrm{kv}\) were determined separately from the change in temperature of the corresponding electrode. Comparison of the data obtained in this way made it possible to establish that the current of positive ions amounts to tenths of a percent of the total current. Bourne believes that the magnitude of the pre-breakdown current is determined mainly by cold-emission electron currents. Because of the small values of the coefficient \(B\), the observed pre-breakdown currents cannot be explained by exchange processes.

The second term of relation (4)—the product \(CD\)—is very small even in the opinion of the authors of the hypothesis. No experimental determinations of the coefficients \(C\) and \(D\) were specially made. An approximate calculation shows, however, that, at least for voltages up to \(1000\ \mathrm{kv}\), this term does not exceed hundredths. Föhner experimentally established that irradiation of the vacuum gap by an intense X-ray flash has no effect on its electric strength \(^{21}\).

The mechanism of electron-ion exchange is also inconsistent with data on the electric strength of a vacuum gap under short-duration application of voltage. At frequencies of \(3000\ \mathrm{Mc}\) and voltages of \(2000\ \mathrm{kv}\) \(^{15}\), even the lightest ion will not have time to traverse an interelectrode gap \(5\ \mathrm{cm}\) long in the time corresponding to half the voltage period.

These data and calculations show that, in its original form, the mechanism of exchange by charged particles and photons is not confirmed experimentally. Recently attempts have been made to supplement this hypothesis by considerations concerning the participation of negative ions in the exchange process \(^{28,31,32}\). It is assumed that positive ions, upon striking the cathode surface, knock out not only electrons but also negative ions. The coefficient of secondary emission of positive ions under bombardment by negative ions is undoubtedly much greater than under bombardment by electrons. In this case the probability of the occurrence of an exchange mechanism increases substantially.

A noticeable influence of negative ions on the breakdown process was established by the experiments of MacKibben and Boyer \(^{9}\). The magnetic field applied in the interelectrode gap was calculated so as to deflect electrons while practically not changing the trajectories of negative ions. The electrons did not reach the anode (the X-ray

radiation is absent). However, the breakdown voltage of the gap did not change. This indicates the undoubted participation of negative ions in the breakdown process.

b) Mechanism of particle detachment from electrodes. In 1952, Cranberg^3 proposed the following hypothesis to explain the mechanism of electrical breakdown in high vacuum. He assumes that breakdown occurs owing to the detachment of particles from the surface of one of the electrodes. These particles are regarded as electrically bound to the electrode, and their detachment is caused by the action of electrostatic repulsive forces. In the interelectrode field the charged particles are accelerated to high energies and, upon striking the opposite electrode, produce very high local temperatures. According to the hypothesis, this should lead to the development of breakdown.

For a quantitative formulation of the hypothesis Cranberg introduces the following notation:

\(W\) — the energy per unit area imparted to the electrode when a particle strikes;

\(C'\) — a certain energy constant characterizing the given pair of electrodes.

Then the breakdown condition is written in the form

\[ W \geq C'. \]

But \(W = \sigma U\), where \(\sigma\) is the surface density of charge on the particle, and \(U\) is the voltage between the electrodes. If \(E\) is the field strength at the electrode surface before the particle is detached, then for an approximate estimate one may take \(\sigma \sim E\). Then the breakdown criterion is written as

\[ UE \geq C \qquad (C \text{ — constant}). \tag{5} \]

In the case of a uniform field \(E = \dfrac{U}{d}\), and the final breakdown criterion has the form

\[ U \geq (Cd)^{1/2}, \tag{6} \]

i.e., the voltage that a vacuum gap can withstand in the case of a uniform field is proportional to the square root of the gap length for a given pair of electrodes.

For an experimental verification of relation (6), Cranberg processed the literature data on the dependence of the breakdown voltage on the distance between the electrodes for fields close to uniform. These data, on a logarithmic scale, are presented in Fig. 2. All the experimental points (with the exception of three points from Gleikhauf’s results) lie on straight lines with tangent of the angle of inclination approximately equal to \(1/2\). Thus, the available experimental data over a wide range of voltages, \(20\)—\(7000\) kV, with distances varying from tenths of a millimeter to \(6\) m, agree with this formula. The value of the con-

stant \(C\) is a function of the state of the electrodes and is usually approximately \(10^{11}\ \mathrm{V}^2/\mathrm{cm}\).

For nonuniform fields, formula (6) is no longer valid, but relation (5) must be preserved, i.e., electrical breakdown

Fig. 2. Dependences of the breakdown voltages of a vacuum gap on the distances between the electrodes for fields close to uniform, processed by Cranberg: 1—steel spherical anode of diameter 25.4 mm, steel disk of diameter 50.8 mm\(^6\); 2—pulse voltage with rise front \(3 \cdot 10^{-7}\) sec; 2a—tungsten hemispheres of diameter 50 mm; 2b—copper hemispheres of diameter 50 mm\(^ {34}\); 3a—aluminum plates; 3b—steel planes; 3c—aluminum ring opposite the steel anode plate (section of an electrostatic-generator tube)\(^ {35}\); 4a—plane electrodes with rounded edges, of Kovar (cathode) and steel; 4b—plane electrodes with rounded edges, of copper, with a hole at the center of the anode\(^ {36}\); 5—molybdenum spheres\(^ {37}\); 6a—molybdenum spheres of diameter 1 cm, degassed; 6b—molybdenum spheres of diameter 1 cm, un-degassed\(^ {33}\); 7—aluminum electrodes; 8—Robinson’s data (unpublished); 9—aluminum electrodes; 10—steel electrodes; 11—steel electrodes.

is determined by the magnitude of the product of the voltage and the field strength at the electrode surface. From Table II it is seen that the values of \(C\) for nonuniform fields are close to the values of \(C\) for uniform fields. This, in Cranberg’s opinion, indicates the validity of the particle-detachment mechanism also in the case of nonuniform fields.

On the basis of this mechanism, the conditioning effect (increase of the breakdown voltage under repeated discharges), the transfer of anode material to the cathode, and the difficulty of reproducing identical conditions in the discharge gap (scatter of breakdown-voltage values) are readily explained.

In breakdown along the surface of a cylindrical dielectric between plane electrodes, the breakdown voltage is also proportional to \(d^{1/2}\), but the value of \(C\) is smaller (approximately \(3 \cdot 10^9\ \mathrm{V}^2/\mathrm{cm}\)).

With the aid of an orienting calculation, Kränberg attempts to estimate the local temperatures on the target electrode that arise upon impact of the particles, as well as the velocities of these particles before impact. The energy released as a result of the impact is expressed as follows:

\[ W' \approx Q U, \]

where \(Q\) is the charge of the particle. Using the relations \(Q = \sigma \cdot \pi r^2\) (\(r\) is the particle radius), \(E = 4\pi\sigma\), \(E = \frac{U}{d}\), and \(U = (Cd)^{1/2}\), we obtain:

\[ W' \approx \frac{C r^2}{4}. \]

This energy falls on a region of the target electrode with area

Table II

\(\pi r^2\) and a depth of \(n\) atomic layers, i.e., to the number of atoms

\[ \frac{\pi r^2 n}{a^2}, \]

where \(a\) is the interatomic distance. Then one may write:

\[ W' \simeq \frac{3}{2} kT \frac{\pi r^2 n}{a^2} \simeq \frac{Cr^2}{4}, \]

where \(k\) is Boltzmann’s constant, \(T\) is the absolute temperature. Hence the local temperature arising upon impact of the particles is

\[ T \simeq \frac{1}{6\pi}\frac{Ca^2}{kn}. \tag{7} \]

Substituting the values of \(C\), \(a\), \(k\), we obtain, for \(n=1\), \(T \simeq 10^6\,^\circ\mathrm{K}\). Consequently, even for several hundred atomic layers one may expect a temperature exceeding the melting temperatures of metals.

If the particles are regarded as spherical, with radius \(r\) and density about 1, then their velocity at the end of the path can be found from the relation \(\frac{mv^2}{2}=W'\), where \(m\) is the mass of the particle:

\[ v \simeq \sqrt{\frac{1}{8}\frac{C}{r}}. \tag{8} \]

For particle radii from \(10^{-2}\) to \(10^{-6}\,\mathrm{cm}\), the particle velocity lies within the range \(10^4\)—\(10^6\,\mathrm{cm/sec}\). Thus, according to Cranberg, the breakdown development time must be greater than \(1\,\mu\mathrm{sec}\) for gaps larger than \(1\,\mathrm{cm}\). This is not in agreement with most experimental data.

Cranberg’s mechanism cannot explain the occurrence of the X-ray flash accompanying the development of breakdown. It is also unclear what particles Cranberg has in mind. If they are foreign particles, then this is not the general case; with appropriate treatment of the electrodes they may be absent. If they are metallic particles of the electrodes, then the mechanisms of their adhesion to the electrode and detachment are unclear.

The principal value of Cranberg’s work lies in the systematization of a large number of experimental results (Fig. 2, Table II). In addition, it may be considered proven that if, under a sufficiently long application of voltage, a particle is torn away from some electrode, this will lead to breakdown. However, it does not seem possible, in the general case, to explain the development of breakdown of a vacuum gap by the mechanism of particle detachment.

4. Electrical breakdown in a strongly nonuniform field

In the case of a strongly nonuniform field, breakdown in high vacuum, even for considerable distances between electrodes, occurs at a comparatively low voltage. In this case the potential gradients at one or both electrodes are large (point—plane…

sharp edge—sharp edge, thin wire—cylinder, etc.). In the early works the magnitudes of the gradients were not determined, since the exact profile of the edge or wire was not known. It is difficult to judge the mechanism of breakdown from such experiments.

Figure 3 gives curves of the dependence of the breakdown voltage on the distance between the electrodes for the electrode configuration needle—plane, obtained in 1947 by Hashimoto \(^{41}\). The radius of curvature of the edge is unknown. The three lower curves correspond to a negative needle, the three upper ones to a positive one. It is seen that with a negative needle breakdown develops at considerably lower voltages. The dependence of the breakdown voltage on distance follows an approximately linear law. In the same work interesting photographs are presented of the surface of a plane electrode after breakdowns under various conditions, but the patterns of these surface changes are not explained in any way.

Fig. 3. Breakdown voltages for the electrode configuration needle—plane in vacuum. The three upper curves correspond to a positive needle, the three lower ones to a negative one \(^{41}\).

There is a supposition \(^{42}\) that a discharge in high vacuum with a sharp anode opposite a plane or a wire-anode in a cylinder develops due to the ejection by the anode of positive ions under the action of strong fields. The breakdown voltage increases when the anode is heated, the whole tube is annealed, or several discharges are passed. However, in Loeb’s opinion \(^{43}\), such a mechanism is hardly possible, since emission of ions under the action of strong fields has never been observed.

Breakdown in high vacuum in the case of a negative edge opposite a plane has been studied in detail by Dyke and Trolan \(^{7}\). In these experiments the cathode was a tungsten needle, the anode a molybdenum plane at a distance of \(5\ \mathrm{mm}\) from the cathode. The profiles of the cathodes were investigated with the aid of an electron microscope before and after breakdown. The electrodes were in a sealed-off bulb with sputtered getter at a pressure of chemically active gases \(\sim 10^{-12}\ \mathrm{mm}\) Hg. At such a pressure the surfaces of thoroughly degassed electrodes may be considered free of residual gases. The experiments were carried out with pulsed voltages from 2 to \(35\ \mathrm{kV}\), with pulse durations of 2 or \(1/2\ \mu\mathrm{sec}\). The pulse shapes were close to P-shaped.

For several tungsten cathodes, curves were taken of the dependence of the current on the voltage between the electrodes. At dens-

MECHANISM OF ELECTRICAL BREAKDOWN IN HIGH VACUUM

At current densities at the cathode from 6 to \(6\cdot 10^6\ \mathrm{A/cm^2}\), the experimental data coincide with the values of the currents calculated from the formula for cold emission (1). At current densities from \(6\cdot 10^6\) to \(1\cdot 10^7\ \mathrm{A/cm^2}\), the calculated values prove to be overestimated in comparison with the experimental ones. This is explained by the influence of the space charge of electrons near the tip on the emission currents. At a current density exceeding \(1\cdot 10^7\ \mathrm{A/cm^2}\), breakdown occurs. The radius of curvature of the tip before breakdown is fractions of a micron, and the measurement results are reproducible. After breakdown the tip is melted; its radius increases to tens of microns.

The process of transition from cold-emission currents to a vacuum arc was investigated oscillographically. At comparatively small pulse voltages, the current oscillogram has a constant plateau of duration approximately \(1\ \mu\mathrm{sec}\). These are cold-emission currents. Increasing the voltage leads to an increase of the current during the pulse. When the pulse voltage is increased by still approximately \(1\%\), during the first microsecond of the pulse the current rises slowly (as in the preceding case), then increases abruptly by approximately two orders of magnitude (breakdown, transition to a “vacuum arc”). The abrupt transition lasts less than \(5\cdot 10^{-8}\ \mathrm{sec}\); the field strengths at the cathode necessary for breakdown are approximately \(8\cdot 10^7\ \mathrm{V/cm}\).

The authors conceive the mechanism of breakdown as follows. Cold-emission currents, reaching high densities, heat the thin tip of the cathode. Heating occurs because of the small cross section of the tip and its high electrical resistance. Thermoelectron emission arises, leading to an increase of the current during the pulse. As the current increases, the temperature of the tip also increases, up to evaporation and the development of electrical breakdown between the electrodes in the metal vapor of the cathode tip.

In the work of Dyke, Trolan, et al.\(^{44}\), with the aid of a simple electron-optical device, photographs were taken of portions of the cathode emitting electrons. The work was carried out with pulses of duration \(1\ \mu\mathrm{sec}\). Analysis of the photographs shows that cases of an increase of current during the pulse correspond to a more uniform distribution of emission over the cathode surface and a larger emitting area. These effects confirm the influence of space charge on emission from the cathode. The current density immediately before breakdown is greater than the current density calculated from the cold-emission formula for the given electric field; consequently, thermoelectron emission also takes part in the processes. A theoretical calculation of the temperature of the tip, taking into account the thermal conductivity of the metal, gives values sufficient for thermoelectron emission.

The authors prove that, in the case of a sharp cathode opposite a plane anode, bombardment of the negative tip by ions or by particles from the anode is insignificant for the development of breakdown. Breakdown can

develop over times insufficient for an ion or particle to traverse the interelectrode distance (for example, breakdown with a pulse of duration \(1/2\ \mu\text{sec}\) at a voltage below \(10\ \text{kV}\) and a distance between the electrodes of \(8.5\ \text{cm}\)).

Against the participation of ions and particles from the anode in breakdown there is also the circumstance that the breakdown voltage depends only on the density of the electron current from the cathode, i.e., on the field strength at the cathode, and does not depend on the total voltage between the electrodes. This has been verified in the voltage range from 5 to \(60\ \text{kV}\). However, with a poorly degassed anode, positive ions take an active part in the breakdown mechanism. Electrons arising as a result of cold emission from the sharp cathode, upon striking the anode, cause gas evolution and its ionization \(^{4}\).

II. THE INFLUENCE OF A SOLID DIELECTRIC ON BREAKDOWN IN HIGH VACUUM

Electrodes in vacuum are always separated by an insulator that bounds the vacuum volume. In practice, in most high-voltage designs, the surfaces of insulators play a decisive role in the development of the breakdown process. In vacuum high-voltage devices with glass envelopes (for example, in X-ray tubes), breakdown is usually accompanied by an intense flash of the glass, indicating the participation of the glass surface in the breakdown process. The breakdown voltage of such a device depends on the shape of the envelope and its properties (purity, degree of degassing, surface electrical conductivity) and is much lower than the breakdown voltage of the vacuum gap. Under certain conditions one can observe flashes of the glass or luminous spots on the glass that are not accompanied by breakdown \(^{45}\). All these effects on the glass envelopes of X-ray tubes are usually explained by bombardment of the glass by both primary and secondary electrons \(^{8}\).

High-voltage conditioning has a large influence on the electrical strength of the finished product. It usually consists in a gradual increase of the voltage as the discharges in the device cease. With such conditioning it is possible to increase the electrical strength of a tube by more than 100% \(^{8}\). However, if the conditioning is carried out improperly, the electrical properties of the vacuum device can also be considerably worsened. This is observed in the case when, during conditioning breakdowns, excessively large currents pass through the tube. Intense gas evolution, damage to the electrode surfaces, and their sputtering onto the bulb often even lead to failure of the tubes. Therefore, during conditioning of the product and during its operation (if possible), limiting resistances must be placed in the current-source circuit. It has been found experimentally that the magnitude of the limiting resistances is more...

...part should be of the order of \(1\ \Omega\) per \(1\ \mathrm{V}\) of voltage for instruments operating in the range \(30\text{--}200\ \mathrm{kV}^{8}\).

Of all the many forms of insulators, only the simplest case may be regarded as studied: a cylindrical insulator in a uniform electric field (the generator of the cylinder is situated along a field line). Surface breakdown of various insulators of this form under constant voltage up to \(100\ \mathrm{kV}\) was studied by Gleikhauf \(^{46,36}\). Various insulating materials were investigated in the form of rods (or tubes) about \(13\ \mathrm{mm}\) in diameter and approximately \(23\ \mathrm{mm}\) long.

The author found no dependence of the breakdown voltage on the residual-gas pressure in the volume over the interval from \(5\cdot 10^{-3}\) to \(10^{-7}\ \mathrm{mm\ Hg}\). Nor was any dependence of the breakdown voltage on the electrode material (stainless steel, copper, magnesium, aluminum) found for insulators made of Pyrex glass and fused quartz.

Fig. 4. Dependence of the breakdown voltage on insulator length for hollow Pyrex cylinders 51 mm in diameter with wall thickness \(1.9\ \mathrm{mm}^{36}\).

Figure 4 presents the dependence of the breakdown voltage on insulator length for the case of hollow Pyrex cylinders \(51\ \mathrm{mm}\) in diameter with wall thickness \(1.9\ \mathrm{mm}\). The breakdown voltage increases with length nonlinearly, as in the case of a vacuum gap, but the absolute voltage values are substantially lower.

Table III illustrates the dependence of the breakdown voltage on the insulator material. Analyzing these experimental data, Gleikhauf concludes that the breakdown voltage does not depend on the elasticity of the insulator vapors, its dielectric constant, or its density, but is determined chiefly by the specific surface resistance of the insulator. As the surface resistance decreases, the breakdown voltage falls. A roughly treated matte surface of glass or quartz corresponds to a breakdown voltage increased by approximately \(40\%\). The breakdown voltage is especially affected by the roughness of the cylindrical surface of the insulator near the cathode; roughness at the anode end has little effect. Gleikhauf especially emphasizes the importance of the conditions at the cathode and near the cathode for the development of breakdown. According to his data, the quality of the contact between the insulator and the cathode and coating the cathode with a thin layer of glass noticeably affect the breakdown voltage.

To elucidate the mechanism of breakdown along the surface of a dielectric, Gleikhauf investigated the pre-breakdown stage, i.e., the nature and magnitude of the currents flowing in the given construction at voltages below the breakdown voltage. Indirect measurements of pre-breakdown currents were made by detecting X-ray quanta with a Geiger counter, which was placed on the outside of the vacuum chamber. With this method only the electron current in the vacuum was measured, and leakage currents did not interfere with the measurements. The paper presents curves of the dependence of the magnitude of the pre-breakdown current in the interval \(10^{-11}—10^{-8}\ a\) on the voltage (\(40—65\ \mathrm{kV}\)). Despite the very large scatter of the points, there is a general tendency for the current to increase with voltage.

Table III

Surface breakdown voltage of various insulators in vacuum

A large scatter of points was also observed for vacuum gaps without an insulator. Conditioning the gap with high voltage (without breakdown) noticeably reduces the scatter.

It was natural to expect that breakdown occurs after the pre-breakdown currents reach a certain critical value. However, in the experiment no such critical value was found; breakdown occurred at pre-breakdown currents varying by several orders of magnitude (from \(5\cdot 10^{-11}\) to \(5\cdot 10^{-7}\ a\)). Gleikhauf believes that the pre-breakdown currents are due to cold emission.

In addition to registration of X-radiation by Geiger counters, investigations were carried out using a camera obscura with filters. This made it possible to determine the place where the X-radiation arose and to assess its hardness.

It turned out that at the beginning of breakdown the insulator is charged negatively and deflects electrons; therefore the sites of the main, hardest

MECHANISM OF ELECTRICAL BREAKDOWN IN HIGH VACUUM

radiation on the anode are somewhat removed from the insulator. Near the insulator, only low-velocity electrons reach the anode at the moment when the development of the breakdown has led to a considerable decrease in the voltage between the electrodes.

Oscillographic investigations have shown that, during breakdown, the voltage between the electrodes drops from 10–15 kV to hundreds of volts (sometimes to 2.5 kV). The low-voltage arc that is ignited as a result of breakdown cannot burn at a current of less than 1 A either for a gap with an insulator or for a vacuum gap without an insulator. If the external resistances of the current-source circuit do not permit such currents in the circuit, then during breakdown only a discharge of the interelectrode capacitance occurs.

Leikhauf also describes the conditioning effect—the increase in breakdown voltage during successive breakdowns—both for a vacuum gap and for a gap with a dielectric (glass, fused quartz). During successive breakdowns of a gap with a dielectric, the value of the breakdown voltage, despite a large scatter, increases substantially. Apparently, conditioning affects both the state of the electrode surface and the dielectric itself. If, after such conditioning, the voltage is not applied for some time, the breakdown voltage decreases, but nevertheless remains above the initial value. A similar decrease is also observed after keeping the specimen at atmospheric pressure; in this case the duration of the exposure is not important.

From the experimental data on the conditioning of vacuum gaps, gaps with a dielectric, and high-voltage vacuum devices with glass bulbs, one may conclude that during conditioning both irreversible and reversible processes take place. The irreversible processes should include, first of all, melting of points on the electrode surface and burning out of accidental foreign particles (for example, dust particles) and contaminants both on the electrodes and on the dielectric. An improvement of the vacuum is also possible—hardening of the tube. During breakdowns, gas or ions are released from the electrodes and from the parts of the dielectric participating in the breakdown. All this is actively absorbed by the more remote parts of the tube. As a result, the most highly stressed regions of the tube are additionally degassed. This last process may be regarded as partly reversible. Finally, charging of the dielectric surface and high-voltage polarization could (but only for certain designs) increase the electric strength by producing a more favorable redistribution of the fields. Such effects are undoubtedly reversible.

It is possible that the processes occurring during conditioning are not exhausted by those listed above. It is impossible to picture clearly the mechanism of conditioning in all its details so long as many processes in breakdown in high vacuum and the participation of dielectrics in these remain unexplained.

processes. Neither Gleichauf nor the authors of other works who observed the behavior of dielectrics in vacuum during breakdowns address the mechanism of the processes that occur in this case.

Whatever the form of the dielectric (rods between electrodes, tube walls, etc.), its influence distorts and redistributes the electric fields between the electrodes both in the case of a gas[^47] and in the case of a vacuum. Such a redistribution of fields is indicated by the data obtained by Gleichauf with the aid of a camera obscura. Such a change must undoubtedly be reflected in the electric strength of the gap.

The following causes of field redistribution may be indicated:

1. The dielectric constant of an insulator is always greater than the dielectric constant of vacuum; therefore, when an insulator is introduced, the field strength in the vacuum layer between the insulator and the electrode increases. This effect of distributed capacitances plays a decisive role in the case of alternating or pulsed voltage, when leakage over the insulator and the formation of surface charges do not have time to manifest themselves.

2. The surface resistance of the insulator may be nonuniform at different places; then, with leakage along the surface, different potential drops will arise in different regions.

3. Field distortion may arise because of surface charges on the insulator due to prebreakdown radiation in the tube or due to preceding discharges.

4. When there are inclusions in the dielectric with a smaller dielectric constant (for example, loose contact of the insulator with the electrode—an “inclusion” of vacuum), the potential drop across this inclusion is increased and a local breakdown may occur. The spark in such a breakdown serves as the initiating cause for a general flashover of the insulator. Similar sparking at the places where the insulator joins the electrode is often observed[^45].

Fig. 5. Voltage distribution in quartz.

1. The fields at the electrodes may change under the action of high-voltage polarization of the dielectric—the accumulation of space charges in the near-electrode regions[^48]. The duration of this process is measured in minutes, and therefore for alternating and pulsed voltage high-voltage polarization need not be taken into account when estimating the fields at the electrodes. Figure 5 gives the potential distribution in quartz[^48]. The straight line corresponds to the potential distribution immediately after the voltage is applied. The dashed and heavy curves were taken at subsequent instants of time. It is seen that, in the case of quartz, layers of charges are formed near both electrodes, pro-

MECHANISM OF ELECTRICAL BREAKDOWN IN HIGH VACUUM

opposite in sign to those supplied to the electrodes from an external source. For some dielectrics a charged layer can form only at one of the electrodes (for example, in the case of calcite—at the cathode).

These effects are explained by the displacement of impurity ions or of dielectric components under the action of the electric field. For example, when glass is formed, the highly mobile alkali ions move toward the cathode, while a layer of quartz remains at the anode12. In this case the electrical conductivity of individual regions of the dielectric also changes owing to the change in its composition; this likewise increases the nonuniformity of the field distribution between the electrodes.

In contrast to the polarization described above, sometimes called “internal polarization,” under certain conditions layers may arise whose charge has the same sign as the charge of the corresponding electrode. This so-called “external polarization” is found in all dielectrics if the applied field exceeds a certain threshold value (for glass, 9 kV/cm). In “external polarization,” charges are either generated on the dielectric–electrode interface or pass into the dielectric from the electrode3. The time for which high-voltage polarization charges are retained after the voltage is switched off varies under different conditions: usually it is of the order of several hours or days.

Thus, introducing a dielectric into a vacuum gap substantially distorts the electric field. This distortion depends on the properties of the dielectric, its shape, the shape of the electrodes, and the duration and magnitude of the applied voltage. But the participation of the dielectric in the breakdown of a vacuum gap apparently is not limited to distortion of the fields of that gap. Insulators also supply charge carriers needed for breakdown. This may occur either under the action of high voltage (cold emission from the dielectric), or under the action of bombardment of the insulator by electrons and ions (secondary emission of electrons and ions, gas evolution).

When choosing the correct design and dimensions of a high-voltage vacuum device, it must be remembered that the breakdown voltage increases more slowly than the dimensions of the insulator (see Fig. 4). Beginning with a certain voltage, increasing the dimensions of the device does not lead to a noticeable increase in electrical strength. Therefore, the manufacture of tubes for voltages greater than 200–300 kV is associated with great difficulties. For such voltages, sectionalized tubes are usually used, in which a number of intermediate electrodes (sections), at various intermediate potentials (usually up to 100 kV per section), are placed between the cathode and the anode. The potentials on the sections are set either forcibly (for example, by means of a potentiometer), or, under alternating or pulsed voltages, division of the potential difference between

cathode and anode according to the capacitances of the sections. In sectioned tubes the distribution of potential along the envelope is more uniform; therefore the electric strength is considerably higher. The dependence of the flashover voltage of the insulating part of a section on its length was studied by Noert$^{52}$.

There is also another original solution to the problem of the electric strength of the article: the creation of a semiconducting layer on the surface of the dielectric. Blodgett$^{53}$ describes in detail the technology for preparing such a semiconducting coating. A farphor cylinder was coated on the inside with lead-silicate glass. By means of a special hydrogen treatment, lead atoms were reduced in the surface layer and a considerable surface electrical conductivity arose (the resistance of the surface layer was $\sim 160$ megohms per square centimeter). To protect the semiconducting layer and increase its stability, a thin film of quartz was used, formed on the surface of the lead-silicate glass by etching in hydrochloric or nitric acid.

When a high voltage was applied to the ends of the cylinder, the potential along it was distributed uniformly, and the charges formed in the discharge volume did not accumulate on the walls but flowed along the semiconducting layer. When such semiconducting layers are used, for a static voltage of $140\ \mathrm{kV}$ an insulator length of $38\ \mathrm{mm}$ is sufficient.

It should be noted that, according to Gleikhauf’s data, dielectrics with greater surface electrical conductivity have poorer qualities when a high voltage is applied. Blodgett, on the contrary, by increasing the electrical conductivity of the surface, improved the electrical properties of the insulator. Here, apparently, the mechanism of electrical conductivity is such that no high-voltage polarization arises, and the potential is in fact distributed uniformly along the generatrix of the cylinder, whereas in Gleikhauf’s measurements greater surface electrical conductivity corresponded to greater high-voltage polarization and a greater distortion of the uniform field between the electrodes.

Blodgett’s results, namely a breakdown field strength along the surface of the insulator of $3.5\ \mathrm{kV/mm}$, are the best of those published. In modern high-voltage tubes operating in the voltage range $100$–$200\ \mathrm{kV}$, the field strengths along the surface of the glass usually do not exceed $1\ \mathrm{kV/mm}$.

CONCLUSION

The experimental data and hypotheses described above show that at present there is no sufficiently clear conception of the whole variety of phenomena occurring during breakdown in high vacuum. However, for a number of specific conditions the basic processes developing during vacuum breakdown may be regarded as clarified. Such

Such cases include breakdown of small vacuum gaps (down to hundredths of a millimeter) at relatively low voltages (up to 20–50 kV), when breakdown develops as a result of heating of the anode surface by cold-emission currents.

The mechanism of breakdown in strongly nonuniform fields, in the case of a sharp cathode and a plane anode with well-degassed electrodes in a very high vacuum, has also been satisfactorily explained. The experimental regularities observed under such conditions agree well with the hypothesis of heating and evaporation of the cathode tip under the action of cold-emission currents.

In the more general and practically important case of large distances and high voltages, a satisfactory theory does not yet exist. Under certain conditions, a mechanism involving the detachment of particles from the electrodes may occur. However, this hypothesis does not explain many phenomena that occur during breakdown of a vacuum gap (the X-ray flash, the time of breakdown development). The mechanism of exchange of charged particles between the electrodes may prove to be more universal if the participation of negative ions in the exchange is taken into account. None of these mechanisms is capable of explaining breakdown of a vacuum gap under short-time application of voltage.

A dielectric in a vacuum gap redistributes the electric fields of the interelectrode gap and participates in the supply of electrons and ions necessary for breakdown. However, the mechanism by which the dielectric affects breakdown in high vacuum cannot be regarded as sufficiently clear. Coating the dielectric with a semiconducting layer substantially increases the electric strength of vacuum high-voltage devices. Further work in this direction will evidently make it possible to reduce the dimensions of such products while maintaining their electric strength at a high level.

In conclusion, the author expresses deep gratitude to Doctor of Technical Sciences V. A. Tsukerman for a detailed discussion of the questions touched upon in the present work and for valuable advice.

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