Townsend discharge

Townsend put forward the hypothesis that positive ions also produce ion pairs, introducing a coefficient ${\displaystyle \alpha _{p}}$ 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

${\displaystyle {\frac {I}{I_{0}}}={\frac {(\alpha _{n}-\alpha _{p})e^{(\alpha _{n}-\alpha _{p})d}}{\alpha _{n}-\alpha _{p}e^{(\alpha _{n}-\alpha _{p})d}}}\qquad \Longrightarrow \qquad {\frac {I}{I_{0}}}\cong {\frac {e^{\alpha _{n}d}}{1-({\alpha _{p}/\alpha _{n}})e^{\alpha _{n}d}}}}$

since ${\displaystyle \alpha _{p}\ll \alpha _{n}}$, 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.

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 ${\displaystyle \epsilon _{i}}$; the average number of electrons released from a surface by an incident positive ion, according to the following formula:

${\displaystyle {\frac {I}{I_{0}}}={\frac {e^{\alpha _{n}d}}{1-{\epsilon _{i}}\left(e^{\alpha _{n}d}-1\right)}}.}$

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.

In the presence of a magnetic field, the likelihood of an avalanche discharge occurring under high vacuum conditions can be increased through a phenomenon known as Penning discharge. This occurs when electrons can become trapped within a potential minimum, thereby extending the mean free path of the electrons [Fränkle 2014].

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.

Neon lamp/cold-cathode gas diode relaxation oscillator

The occurrence of Townsend discharge, leading to glow discharge breakdown shapes the current–voltage characteristic of a gas-discharge tube such as a neon lamp in a way such that it has a negative differential resistance region of the S-type. The negative resistance can be 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

${\displaystyle f\cong {\frac {1}{R_{1}C_{1}\ln {\frac {V_{1}-V_{\text{GLOW}}}{V_{1}-V_{\text{TWN}}}}}},}$

where

• ${\displaystyle V_{\text{GLOW}}}$ is the glow discharge breakdown voltage,
• ${\displaystyle V_{\text{TWN}}}$ is the Townsend discharge breakdown voltage,
• ${\displaystyle C_{1}}$, ${\displaystyle R_{1}}$ and ${\displaystyle V_{1}}$ are respectively the capacitance, the resistance and the supply voltage of the circuit.

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.

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.

Plot of variation of ionisation current against applied voltage for a co-axial wire cylinder gaseous radiation detector.

Townsend avalanche discharges are fundamental to the operation of gaseous ionisation detectors such as the Geiger–Müller tube and the proportional counter in either detecting ionising radiation or measuring its energy. The incident radiation will ionise atoms or molecules in the gaseous medium to produce ion pairs, but different use is made by each detector type of the resultant avalanche effects.

In the case of a GM tube the high electric field strength is sufficient to cause complete ionisation of the fill gas surrounding the anode from the initial creation of just one ion pair. The GM tube output carries information that the event has occurred, but no information about the energy of the incident radiation.[1]

In the case of proportional counters, multiple creation of ion pairs occurs in the "ion drift" region near the cathode. The electric field and chamber geometries are selected so that an "avalanche region" is created in the immediate proximity of the anode. A negative ion drifting towards the anode enters this region and creates a localised avalanche that is independent of those from other ion pairs, but which can still provide a multiplication effect. In this way spectroscopic information on the energy of the incident radiation is available by the magnitude of the output pulse from each initiating event.[1]

The accompanying plot shows the variation of ionisation current for a co-axial cylinder system. In the ion chamber region, there are no avalanches and the applied voltage only serves to move the ions towards the electrodes to prevent re-combination. In the proportional region, localised avalanches occur in the gas space immediately round the anode which are numerically proportional to the number of original ionising events. Increasing the voltage further increases the number of avalanches until the Geiger region is reached where the full volume of the fill gas around the anodes ionised, and all proportional energy information is lost.[1] Beyond the Geiger region the gas is in continuous discharge owing to the high electric field strength.