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# Townsend discharge

The Townsend discharge is a gas ionisation process where an initially very small amount of free electrons, accelerated by a sufficiently strong electric field, give rise to electrical conduction through a gas by avalanche multiplication: when the number of free charges drops or the electric field weakens, the phenomena ceases. It is a process characterized by very low current densities: in common gas filled tubes, typical magnitude of currents flowing during this process range from about 10 − 18A to about 10 − 5A, while applied voltages are almost constant. Subsequent transition to ionisation processes of dark discharge, glow discharge, and finally to arc discharge are driven by increasing current densities: in all these discharge regimes, the basic mechanism of conduction is avalanche breakdown. Townsend discharge is named after John Sealy Townsend.

## Quantitative description of the phenomena

The basic set-up of the experiments investigating ionisation discharges in gases consist of a plane parallel plate capacitor filled with a gas and a continuous current high voltage source connected between its terminals: the terminal at the lower voltage potential is named cathode while the other is named anode. Forcing the cathode to emit electrons (eg. by irradiating it with a X-ray source), Townsend found that the current I flowing into the capacitor depends on the electric field between the plates in such a way that gas ions seems to multilply as they moved between them. He observed currents varying over ten or more orders of magnitude while the applied voltage was virtually constant: the experimental data obtained from his (and his school) first experiments is 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
• $\alpha_n\,$ 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
• $d\,$ 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 phenomena and to be able to do a precise quantitative calculation.

### Gas ionisation caused by motion of positive ions

Townsend put forward the natural hypotesis that also positive ions produce ion pairs, introducing a coefficient αp expressing the number of ion pairs generated per unit length by a positive ion (cation) moving from cathode to anode. 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 β < < α, in very good agreement with experiments.

### Cathode emission caused by impact of ions

Townsend and Holst and Oosterhuis also put forward an alternative hypothesis, considering augmented emission of electrons by cathode caused by positive ions impact, introducing Townsends second ionization coefficient εi, the average number of electrons released from a surface by an incident positive ion, and working out 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: note that they can be used to well describe the same experimental results. Other formulas describing, various intermediate behaviors, are found in the literature, particularly in reference 1 and citations therein.

## Applications

• Avalanche multiplication during Townsend discharge is naturally used in gas phototubes, to amplify the photoelectric charge generated by incident radiation (visible light or not) on the cathode: achievable current is typically 10~20 times greater respect to that generated by vacuum phototubes.
• The starting of Townsend discharge sets the upper limit to the blocking voltage a glow discharge gas filled tube can withstand : this limit is the Townsend discharge breakdown voltage also called ignition voltage of the tube.

• The presence of Townsend discharge and glow discharge breakdown voltages shapes the VAIA characteristic of any gas diode or neon lamp in a way such that it has a negative differential resistance region of the S-type. This occurrence is typically used to generate electrical oscillations and waveforms, as in the relaxation oscillator whose schematic is shown in the picture on the right. The sawtooth shaped oscillation generated has frequency
$f\cong\frac{1}{R1C1\ln\frac{V1-V_{GLOW}}{V1-V_{TWN}}}$
where
Since temperature and time stability of the characteristics of gas diodes and neon lamps is low, and also the statistical dispersion of breakdown voltages is high, the above formula can only give a qualitative indication of what the real frequency of oscillation is.