The basic setup of Townsend's early experiments investigating ionization discharges in gases consisted of planar parallel plates forming two sides of a chamber filled with a gas. A direct current high voltage source was connected between the plates, the lower voltage plate being the cathode while the other was the anode. Forcing the cathode to emit electrons using the photoelectric effect, by irradiating it for example with an X-ray source, Townsend found that the current I flowing through the chamber depends on the electric field between the plates in such a way that gas ions seemed to multiply as they moved between them. He observed currents varying exponentially over ten or more orders of magnitude with a constant applied voltage when the distance between the plates was varied. He also discovered the importance of the pressure of the gaseous medium, and was able to generate ions in gases at low pressure with a much lower voltage than that required to generate a spark. This overturned conventional thinking about the amount of current that an irradiated gas could conduct.[2]

The experimental data obtained from his experiments are described by the following formula

\frac{I}{I_0}=e^{\alpha_n d}, \,

where

I is the current flowing in the device,

I_0 is the photoelectric current generated at the cathode surface,

e is Euler's number

\alpha_n is the first Townsend ionization coefficient, expressing the number of ion pairs generated per unit length (e.g. meter) by a negative ion (anion) moving from cathode to anode,

d is the distance between the plates of the device.

The almost constant voltage between the plates is equal to the breakdown voltage needed to create a self-sustaining avalanche: it decreases when the current reaches the glow discharge regime. Subsequent experiments revealed that the current I rises faster than predicted by the above formula as the distance d increases: two different effects were considered in order to explain the physics of the phenomenon and to be able to do a precise quantitative calculation.

Gas ionization caused by motion of positive ions Edit

Townsend put forward the hypothesis that positive ions also produce ion pairs, introducing a coefficient \alpha_p expressing the number of ion pairs generated per unit length by a positive ion (cation) moving from anode to cathode. The following formula was found

\frac{I}{I_0}=\frac{(\alpha_n-\alpha_p)e^{(\alpha_n-\alpha_p)d}}{\alpha_n-\alpha_p e^{(\alpha_n-\alpha_p)d}}

\qquad\Longrightarrow\qquad \frac{I}{I_0}\cong\frac{e^{\alpha_n d}}{1 - ({\alpha_p/\alpha_n}) e^{\alpha_n d}}

since \alpha_p \ll \alpha_n, in very good agreement with experiments.

The first Townsend coefficient ( α ), also known as first Townsend avalanche coefficient is a term used where secondary ionization occurs because the primary ionization electrons gain sufficient energy from the accelerating electric field, or from the original ionizing particle. The coefficient gives the number of secondary electrons produced by primary electron per unit path length.

Cathode emission caused by impact of ions Edit

Townsend, Holst and Oosterhuis also put forward an alternative hypothesis, considering the augmented emission of electrons by the cathode caused by impact of positive ions. This introduced Townsend's second ionization coefficient \epsilon_i; the average number of electrons released from a surface by an incident positive ion, according to the following formula:

\frac{I}{I_0}=\frac{e^{\alpha_n d}}{1 - {\epsilon_i}\left(e^{\alpha_n d}-1\right)}.

These two formulas may be thought as describing limiting cases of the effective behavior of the process: either can be used to describe the same experimental results. Other formulas describing various intermediate behaviors are found in the literature, particularly in reference 1 and citations therein.