In this paper we consider only discharges in gases at such low pressure that the mean free path of electrons is greater than the size of the vessel. Part I. The elementary theory of the starting of an electrodeless discharge in a gas at low pressure by a uniform high-frequency electric field has been given by Gill & von Engel (1948). It was shown that a discharge will start when the applied field is large enough to cause multiplication of electrons by secondary electron emission from the end-walls of the vessel; initially, gas ionization is absent. Multiplication occurs if an electron starting at one end-wall with a small energy and in a suitable phase of the applied field crosses the vessel in one half-cycle and hits the opposite wall fast enough to release more than one secondary electron. Secondary electrons usually start in a negative phase of the field, but escape from the wall because of their initial energy, unless the phase is more negative than a certain limiting value; this corresponds to the cut-off wave-length, i.e. the longest one at which a discharge can be started. Here, for the first time, the growth of the discharge is treated in detail, the calculations being based on known atomic data only. When secondary electrons leave an end-wall a positive wall charge is left behind, which retards the electrons. This is important only near the cut-off wavelength. These wall charges cause the phase at one wall to become increasingly negative until, finally, the electrons would fail to escape, and the multiplication would cease, which is contrary to experience. However, the growth can be explained by considering the velocity distribution of the secondary electrons. Then a distribution in phase ensues, which must be repeated in successive half-cycles for an avalanche to develop. During this first stage the current is therefore essentially controlled by secondary emission, and grows exponentially with time. At these low pressures electrons rarely collide with gas molecules. Thus the electrons must make many transits across the vessel to form a large number of positive ions. The ions remain almost stationary in the gas; they are nearly uniformly distributed although slightly concentrated at the centre of the vessel. A second stage in the growth of the discharge begins when the ion space charge first appreciably affects the motion of the electrons. Although electrons are still produced mainly at the end-walls, the rate steadily decreases as the ion space charge grows. The rate of production of ions and electrons in the gas also decreases, and losses of both ions and electrons due to self-repulsion become important. The current thus rises more slowly than it would if space charges did not develop, until it reaches a constant value. It is shown that at very low pressures this second stage may not be reached, because self-repulsion of the electrons stops the development earlier. The final equilibrium state for larger pressures is not included in this treatment. This theory predicts the dependence of the growth on the material of the walls, on the nature of the gas and its pressure, and the effect of a field greater than the starting field. Part II. A new experimental technique has been employed to measure the current actually flowing through the discharge. The large capacitative current flowing across the external electrodes is balanced out by a bridge method, the bridge becoming unbalanced when a current flows through the gas. The unbalanced component is proportional to the discharge current and is amplified, rectified and displayed on an oscilloscope. In order to measure the growth of this current with time, pulses of high-frequency potential are applied across the discharge vessel, and the time-base of the oscilloscope synchronized with the pulses. Oscillograms show how the growth of current depends upon the pressure (2 to 35//) and nature of the gas (hydrogen and helium), the excess voltage applied ( < 20 %) and the frequency of the applied field (10 to 20 Mc/s). The spatial distribution of light from the discharge in the final state is also measured, from which the motion of the electrons can be deduced, and compared with theory. Good agreement is obtained between theoretical predictions derived solely from atomic data, and experimental results. These investigations clearly demonstrate that at low pressure the properties of the wall mainly control the multiplication process in the initial stage and thus the starting field, whereas the properties of the gas become important in the later stages and so essentially determine the total time of growth of the discharge.
Venturi Wet Gas Flow Modeling Based on Homogeneous and Separated Flow Theory