Townsend coefficient first

It is postulated that a, the first Townsend coefficient, is a function of E/P, the ratio of the electronic field in V/cm over the pressure of the filling gas in Torr, and that. 

The two electrons produced by the process axe accelerated by the electrical field and may ionise other gas molecules. An avalanche is formed. The frequency of the ionisation process is characterised by the first Townsend coefficient a. This coefficient depends on the reduced electrical field E/p, where p is the pressure of the gas. The increase dn of the n electrons after a distance dx is given by ... 

One of the earliest models for the first Townsend coefficient was given by Rose and Korff [96] in 1941 and later standardised by Zastawny [134] in 1997 ... 

Figure 2.8 First Townsend coefficient a for argon, hydrogen, air, and nitrogen. Plotted using data from [134].

An electron avalanche occurs in a medium when the drifting electron attains sufficient energy from the electric field to effect collisional ionization. In dilute gases, this process is described by the first Townsend coefficient, a, which is defined as... 

In solids, electronic breakdown is observed in semiconductors (Seeger, 1973). At a sufficiently high electric field strength, electrons from the valence band can tunnel directly into the conduction band. This effect is also called internal field emission and it forms the basic principle of the tunnel diode. A necessary condition for this type of electronic breakdown is a narrow band gap (1 to 2 eV) and a high electron mobility. Avalanche breakdown takes place in the depletion layer of a reversed p-n junction where electric field strengths up to 10 V/cm are obtained. Collisional ionization by electrons (and holes) across the band gap takes place. Here we only consider the effect of the electrons. The relative increase of the number of charge carrier pairs per unit of length is called the ionization rate, a (the first Townsend coefficient of the gas phase), defined as... 

At longer gap distances, the distribution is characterized by two time lags which are summarized in Table 2. Analysis of the data with a single electron avalanche model (see Section 2.8) gave a first Townsend coefficient of a = 6.4 x 10 cm" at 3.5 MV/cm (Arii et al, 1979). This value is one order of magnitude higher than data estimated by Haidara et al., (Haidara and Denat, 1991) for cyclohexane and propane (see Section 8.2). 

Table 3. First Townsend coefficient a in LXe as a function of the electric field strength. 

No attempts to calculate those limiting surface field intensities or gradients for small particles have been reported in the literature. However, point-to-plane corona has been studied in detail. Loeb (L8) has proposed a method for calculating positive corona threshold limits making use of established values of the Townsend first ionization coefficient. Loeb s threshold formula is... 

In seeking a quantitative interpretation of the rate coefficient for the formation of water, Pwa/n, Kirby invoked the theory of electron-impact reaction formulated first by Townsend (85, 86). In terms of the account given earlier in this paper, the formal statement of that early theory can be seen to approach closely Formulae 2 and 12 when the following qualifications are made ... 

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