Townsend coefficient

The Townsend coefficient is a function of the local electric field, and the expression takes the more general form... 

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].

After ionising the gas molecules, the positive ions generated migrate to the cathode and can liberate secondary electrons. The efficiency of this secondary electron production is given by the second Townsend coefficient 7 which is the fraction of secondary electrons liberated. This coefficient depends on the material of the cathode and is typically in the range around 0.1 [14]. 

For Reaction R4 the rate coefficient Pxx+A computed from Formulae 2.1 and 10 agrees closely with the values found from experiment (usually denoted as a/n or a/p) and long known as the Townsend coefficient of ionization (24). For Reaction R5 and for similar reactions generating the radiative species H2 (a 3V) and N2 (C 3nu), a similar concordance is found between experiment and the predictions of theory (16, 58, 59, 61, 74). In discussing possible interpretations of Kirkby s data for positive column reaction, it is assumed that the Maxwellian form for /(E) is a valid approximation to the true distribution. 

Townsend coefficient - In a radiation counter, the number of ionizing collisions by an electron per unit path length in the direction of an applied electric field. 

Each primary electron generated near a cathode produces exp(Q f) -1 positive ions moving back to the cathode (Fig. 4-1). The ions lead to extraction of y [exp(aJ) -1] electrons from the cathode due to secondary electron emission characterized by the Townsend coefficient y (Section 2.4.3). Typical y-values in discharges are 0.01-0.1. Taking into account the current of primary electrons io and electron current due to the secondary electron emission from the cathode, the total electroiuc part of the cathode current /cath is... 

The current in the gap is non-self-sustained as long as the denominator in 4-3 is positive. When the electric field and Townsend coefficient a become high enough, the denominator... 

Table 4-1. Numerical Parameters A and B for Semi-Empirical Calculation of Townsend Coefficient a...

A distinctive feature of the dark discharge is the smallness of its current and plasma density, which keeps the external electric field unperturbed and is determined by Townsend breakdown condition (4-4). Relations between electron (y e), ion (/+), and total (J) ciurent densities in a dark discharge (distance between electrodes da, from cathode x Townsend coefficient a) (Fridman Keimedy, 2004) are... 

The avalanche-to-streamer transition in the APG DBD depends on the level of preionization. The Meek criterion (Section 4.1.3) is related to an isolated avalanche, whereas in the case of interrsive pre-ionizatiorr, avalanches are produced close to each other and interact. If two avalanches occm close enough, their transition to streamers can be electrostatically prevented and the discharge remains uniform (A. Fridman et al., 2005). A modified Meek criterion of the avalanche-to-streamer transition can be obtained by considering two simrrltaneously starting avalanches with maximum radius R, separated by the distance L (a is Townsend coefficient, d is distance between electrodes) ... 

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. 

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