On the Mechanism of Gas Breakdown in the Presence of Electron Emission

I. I. Kapralov

Introduction

The Townsend–Rogowski theory does not answer many questions concerning the features of gas breakdown. The experimentally established Paschen law does not fully enough determine the quantitative aspect of the complex process that breakdown represents.

In our opinion, this situation has arisen because an important discharge parameter—the pre-breakdown current—has almost always remained aside, outside the experimenter’s field of view. Figure 1 shows a typical curve of the permissible anode current of an ionic device having a hot cathode. The ignition point (breakdown) is determined by two parameters: the breakdown voltage (ignition voltage) and the pre-breakdown current. The slope of this curve to the abscissa axis determines the conductivity \(\rho(U_a)\). The conductivity of the gas under conditions of a low-current discharge increases rapidly not only with voltage, but also with thermionic emission of the cathode. According to the curve of permissible currents, the phenomenon of gas breakdown is prepared gradually, but occurs suddenly, like an explosion. The increase of current with voltage leads spontaneously to a process having a new quality—breakdown (ignition of the discharge). The ignition point differs from all other points in that at this point the process ceases to be reversible. Thus, in order to obtain a more complete picture of the pre-breakdown state of the gas, it is necessary to take into account not only the features of the course of the discharge, but also to record the parameters indicating the onset of this avalanche-like process. These must include: the pre-breakdown current, the ignition voltage, the shape and steepness of the permissible-current curve. The screened electrode system with an igniting filament and a grid developed by us (Fig. 2) can serve as a good model for studying the static process leading to gas ignition.

Fig. 1. OA—the curve of permissible current \([I_{0a}=f(V_a)]\)
\(*\)—ignition point
\(I_{\text{pre}}\)—pre-breakdown current
\(U_{a3}\)—ignition voltage.

It is clear from Fig. 2 that the ionized channel formed along the filament (use is made of the known property of discharge propagation along thin metallic wires—anodes [1, 2] with a self-limiting region of ionization) performs the role of an artificial breakdown channel and a localized plasma cathode. If to the anode \(A\), screened by the grid \(C\),

a voltage sufficient for impact ionization of the gas is applied, then the anode will ignite every time the electric field, sagging through the mesh diaphragm, draws from the head of the plasma channel a sufficient “ignition dose” of electrons from the distance \(d_{np}\), which will ensure optimal conditions for ionization. These “ignition doses” appeared to be capable of being accurately registered in the anode circuit, estimated from the magnitudes of the pre-breakdown anode current and the triggering current of the filament.

In the present work the ignition characteristics in this model were studied in order to establish:

a) the dependence of the triggering current \(I_n\) on the pre-breakdown current \(I_{apr}\);

Fig. 2. Diagram of the formation of the pre-breakdown stage of the discharge in a thyratron with a control filament. \(A\)—anode; \(C\)—grid; \(K\)—cathode; \(H\)—filament; \(PK\)—plasma cathode with a self-limiting ionization region; \(G.K.\)—head of the plasma cathode; \(d\)—breakdown distance. Arrows indicate the paths of electrons drawn from the cathode by the anode field.

Fig. 3. Experimental three-chamber thyratron (simplified design).

\(K_{pi}\)—preliminary-ionization chamber.
\(K_p\)—triggering chamber,
\(K_{pu}\)—starting chamber, \(A\)—anode, \(K\)—cathode, \(C\)—grid, \(H\)—filament, \(D.R.\)—deionization grid, \(G\)—getter. The arrows indicate the path of the discharge.

b) the basic condition for artificial triggering.

Solving these questions should reveal the picture of the mechanism of formation of the low-voltage arc and supplement our information on the operation of ion devices of the thyratron type operating with auxiliary triggering.

Experimental Setup

To solve the questions posed above, which characterize the stage of breakdown formation and gas ignition in the presence of thermionic emission, an experimental ion device was used, the design of which is shown in Fig. 3.

Using the properties of self-limitation of the auxiliary discharge and of its self-motion along the filament, it proved possible to trigger the main arc by introducing into the chamber of high electric-field strength certain recorded “ignition doses” of electrons. These “ignition doses”

formed in the anode circuit by the electrons of the plasma channel of the filament. The plasma channel gradually moved toward the starting chamber of the device as the filament current increased to its ignition value.

In principle, the experimental tube did not differ in any way from the design of Fig. 2. The apparatus was subjected to thorough vacuum treatment and filled with mercury vapor, and was then installed in the circuit of Fig. 4. The circuit was equipped with class 0.5 electrical measuring instruments. The control circuits of the apparatus were supplied from BAS-70 type batteries. In order to regulate

Fig. 4. Electrical circuit for studying the prestarting static regime of chamber thyratrons. Principal data of the apparatus:

\(p_1, p_2, p_3, p_4\) — single-pole switches; \(P_{\mathrm{p}}, P_{\mathrm{s}}\) — double-pole switches; \(p_{\mathrm{A}}, p_{\mathrm{K}}\) — double-pole knife switches; \(R_{\mathrm{p}}, R_{\mathrm{c}1}, R_{\mathrm{c}2}\) — wireless resistors of 20, 125, 510 kohm; \(R_{\mathrm{A}}\) — sliding rheostat 2250 ohm, 0.5 A; \(R_a\) — wire resistance 5 ohm; \(R_{\mathrm{T}}\) — sliding rheostat 1000 ohm, 0.2 A; \(P_{\mathrm{T}}\) — telephone relay; \(Dr\) — choke, 1 H; \(C\) — capacitance, 10 microfarads; \(B_{\mathrm{s}}, B_{\mathrm{p}}\) — power supplies for the grid and filament circuits; \(B_{\mathrm{m}}\) — oil bath of 7 liters capacity; \(M\) — stirrer with electric motor; \(t\) — thermometer; \(T_{\mathrm{KCh}}\) — thyratron under investigation; \(A_1\) — astatic ammeter, 0–2.5 A; \(A_2, A_4, A_6\) — magnetoelectric microammeters, 0–100 μA; \(A_3, A_5\) — magnetoelectric milliammeters, 0–15–3–7.5 mA; \(V_1\) — magnetoelectric voltmeter, 0–1500–3000 V; \(V_2\) — tube dc voltmeter, 0–5–10–50–100–500 V; \(V_3\) — magnetoelectric voltmeter, 0–10 A; \(A_7\) — magnetoelectric ammeter, 0–1.5–3, 7.5–15 A.

the pressure of mercury vapor in the apparatus, it was immersed in an oil bath of 7 liters capacity, heated by an electric furnace. The furnace was immersed near the bottom of the bath. The stirrer \(M\) produced a uniform distribution of the oil temperature throughout the entire volume of the bath. The pressure of the mercury vapor was determined from the oil temperature. The oil temperature was recorded by the thermometer \(t\). The microammeter of the anode circuit was protected from large currents by means of the relay \(P_{\mathrm{T}}\). The prestarting regime was investigated by the method of single ignitions of the apparatus. Before its ignition, the static prestarting currents and the filament ignition current were determined for the corresponding parameters of the anode circuit and gradual changes in the mercury-vapor pressure. The remaining data for the circuit apparatus are visible directly from the figure. The presence of discharge shielded chambers

determine the features of the device. We called it a chamber thyratron with a control grid and filament. In the present experiment the grid \(C\) was not used. It was connected directly to the cathode.

General picture of the similarity of the characteristics of ignition and pre-start currents

The measurement results are reflected in the curves of Figs. 5a, 6. Figure 6 shows the dependences of the currents \(I_{pz}\) and \(I_{apr}\) on the pressure of mercury vapor \(p\) at a constant anode ignition voltage \(U_{az}=700\) volts. They are constructed from the data of Figs. 5a, 6 and represent the type of curves of a large family. Similar curves can be constructed for any value of \(U_{az}\). They express the similarity of the currents \(I_{pz}\) and \(I_{apr}\) with variation of \(p\). In the same figure a curve is plotted showing the dependence of the ratio

Fig. 5a. Dependence of the ignition voltage on the pre-start currents \(I_{apr}\). Parameter: gas pressure \(p\) (experimental device, Fig. 3).

\(I_{pz}/I_{apr}=K\) on the pressure \(p\): it can be expressed by the equation of a straight line \(K-K_0=\tan\varphi \cdot p\). The coefficient \(K_0\) is obtained by extrapolating the straight line at \(p=0\). It reflects the law of current distribution in the anode and filament circuits for the given electrode design in vacuum. According to this definition, the coefficient \(K\) must reflect this same law for the pre-start regime. The tangent of the angle of inclination of the straight line \(K\) to the abscissa axis expresses the ignition condition of the anode chamber of the device when a beam of electrons from the plasma channel of the filament is introduced into it. This ignition condition of the device can be expressed as follows: for ignition of the device to occur at different pressures, it is necessary that the ratio of the difference of the distribution coefficients to the pressure be a quite definite quantity

\[ \frac{K-K_0}{p}=\tan\varphi=\mathrm{const}\quad \text{at } U_{az}=\mathrm{const}. \tag{1} \]

Thus, in order for gas breakdown to occur and for a plasma to form, a certain dose of electron pre-starting current is necessary. Since the discharge to the filament was used by us as a source and “transporter” of electrons from the region of weak into the region of strong electric fields, the magnitude of the pre-starting current will depend on the concentration of charges in the working head of the channel and on the level of its rise along the filament. All factors that affect the concentration of charges in the filament channel and the length of its propagation must also affect the pre-starting current. The igniting current gives rise to the pre-starting current. They are therefore organically connected and, on a certain scale, copy one another when the breakdown conditions change. The breakdown field strength of the anode field \(E_{pr}\) and the gas pressure \(p\) determine the limits of variation of these currents.

Fig. 5b. Influence of variation of the gas pressure \(p\) on the course of the starting characteristic of a chamber-type thyratron (Fig. 3).

Basic condition for gas ignition

As we have already shown earlier, gas breakdown is prepared gradually. The model of the ionic tube operating in the circuit made it possible to determine, from the anode and filament currents, the critical state of the gas before ignition of the anode. This state is reflected in curves of the form: \(I_{nz}=f_1(p)_{uaz=\mathrm{const}}\) and \(I_{anp}=f_2(p)_{uaz=\mathrm{const}}\) (Fig. 6).

Each point of the curves characterizes the conditions for the onset of the avalanche-like process. A detailed check of the course of the curves (Fig. 6) showed that the pre-starting anode current, with changing gas pressure \(p\) at constant anode voltage, varied according to a hyperbolic law (Fig. 7). The curve of variation of the igniting current with pressure is close to a hyperbola (Fig. 6). Consequently, one may write

\[ I_{anp}\cdot p=\mathrm{const}, \tag{2} \]

\[ I_{nz}\cdot p=\mathrm{const}\,(Ap+B), \tag{3} \]

where \(A\) and \(B\) are constant quantities. The validity of these statements is shown by the dependence of \(K\) on \(p\): \(K = I_{pz}/I_{apr} = Ap + B\) (straight line in Fig. 6).

If one takes into account that the saturated vapor pressure of mercury for the measured temperature interval is proportional to the concentration of gas particles [3], and that the current \(I_{apr}\) is proportional to the concentration of electrons ionizing the gas, then the expression for the prebreakdown current can be rewritten in the following form:

\[ I_{apr}\,p = A N n_e = \text{const}, \tag{4} \]

where \(A\) is a certain proportionality coefficient;
\(N\) is the concentration of gas particles;
\(n_e\) is the concentration of electrons.

Fig. 6. Dependence of the igniting current \(I_{pz}\) and the prebreakdown current \(I_{apr}\) on the gas pressure \(p\) at \(U_a = 700\) volts \(= \text{const}\). Dependence of \(k\) on \(p\) (experimental apparatus, Fig. 3).

Fig. 7. Dependence of the anode prebreakdown current \(I_{apr}\) on the gas pressure \(p\). Parameter: anode ignition voltage \(U_{az}\); 1, 2 are experimental curves; 3 is a hyperbola.

Proceeding from the kinetic theory of gases, for the critical number of collisions of particles of two different kinds one may write the expression:

\[ Z_{cr} = B N n_e Q c_e, \tag{5} \]

where \(Q\) is the effective cross section of all molecules contained in \(1\ \text{cm}^3\);
\(c_e\) is the mean relative velocity of the electrons.

Since the product \(Qc_e\) for mercury is an approximately constant quantity [3], it follows that

\[ Z_{cr} = B N n_e = \text{const}. \tag{6} \]

The last expression contains an important condition for gas ignition. Thus, gas breakdown and the formation of plasma occur when the number of collisions of electrons with gas atoms is determined by a constant quantity proportional to the product of the concentrations of electrons and gas particles.

Conclusion

The experiments carried out show that the chamber-type experimental tube with a heating filament that we have developed is a convenient instrument for studying the pre-breakdown state of a gas in the presence of thermionic emission.

Using the method of single ignitions of the tubes and measuring the magnitudes of the igniting and pre-trigger currents with changes in the anode voltages and gas pressures, it was established:

1. A similarity of the dependences of the anode ignition voltages on the igniting and pre-trigger currents at different gas pressures.

2. A similarity of the dependences of the igniting and pre-trigger currents on gas pressure at different anode ignition voltages.

3. The latter dependence obeys a hyperbolic law. From the hyperbolic law there follows the constancy of the products of the gas pressure by the igniting or pre-trigger current. These products reflect the basic condition for gas ignition: the number of collisions of electrons with gas particles leading to gas breakdown is a constant quantity and is proportional to the product of their concentrations.

This ignition condition will also hold under more complex conditions of discharge development, often encountered in practice: ignition of the main discharge by means of a pilot arc at different stages of its development, the presence of a hot or cold cathode, electrodes of complex shape, low gas pressure, different degrees of shielding of the electrodes, etc.

Literature

1. Vorob’ev A. V. Collection of Works on Technical Physics. Publishing House of the Academy of Sciences of the USSR, 189, 1947.

2. Knoll-Ollendorff-Rompl. “Gasentladungstabellen.” Berlin. Verlag von Z. Springer, 43, 1935.

3. Spivak G. V. and Stolyarova E. L. Vestnik MGU, No. 5, 31, 1952.

Novosibirsk, West Siberian Branch of the Academy of Sciences of the USSR.