Townsend's early experimental apparatus 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 and the upper-voltage the
anode. He forced the cathode to emit electrons using the
photoelectric effect by irradiating it with
x-rays, and he found that the current flowing through the chamber depended on the
electric field between the plates. However, this current showed an exponential increase as the plate gaps became small, leading to the conclusion that the gas
ions were multiplying as they moved between the plates due to the high electric field. Townsend 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 that gas pressure influenced conduction: he was able to generate ions in gases at low pressure with a much lower voltage than that required to generate a spark. This observation overturned conventional thinking about the amount of current that an irradiated gas could conduct. The experimental data obtained from his experiments are described by the formula :\frac{I}{I_0}=e^{\alpha_n d}, \, where • is the current flowing in the device, • is the
photoelectric current generated at the
cathode surface, • is
Euler's number, • is the
first Townsend ionisation coefficient, expressing the number of
ion pairs generated per unit length (e.g. meter) by a negative ion (
anion) moving from
cathode to
anode, and • 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 rises faster than predicted by the above formula as the distance increases; two different effects were considered in order to better model the discharge: positive ions and cathode emission.
Gas ionisation caused by motion of positive ions 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 ionisation occurs because the primary ionisation electrons gain sufficient energy from the accelerating electric field, or from the original ionising particle. The coefficient gives the number of secondary electrons produced by primary electron per unit path length.
Cathode emission caused by impact of ions 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 ionisation coefficient'' \epsilon_i, the average number of electrons released from a surface by an incident positive ion, according to the 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. ==Conditions==