Townsend discharge

The Townsend discharge is a gas ionization 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, and is also commonly known by practitioners as a "Townsend avalanche".

Contents

Quantitative description of the phenomenon

The basic setup of the experiments investigating ionization discharges in gases consist of a planar 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 multiply 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 experiments are described by the following formula

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

where

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 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<<\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

Townsend, 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 \epsilon_i, 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.

Avalanche

A Townsend avalanche is a cascade reaction involving electrons in a region with a sufficiently high electric field. This reaction must also occur in a medium that can be ionized, such as air. The positive ion drifts towards the cathode, while the free electron drifts towards the anode of the particular device. It accelerates in the electric field, gaining sufficient energy such that it frees another electron upon collision with another atom/molecule of the medium. The two free electrons then travel together some distance before another collision occurs. The number of electrons travelling towards the anode is multiplied by a factor of two for each collision, so that after n collisions, there are 2n free electrons.

Conditions

A Townsend discharge can be sustained over a limited range of gas pressure and electric field intensity. At higher pressures, discharges occur more rapidly than the calculated time for ions to traverse the gap between electrodes, and the streamer theory of spark discharge is applicable. In highly non-uniform electric fields, the corona discharge process is applicable. Discharges in vacuum require vaporization and ionization of electrode atoms. An arc can be initiated without a preliminary Townsend discharge; for example when electrodes touch and are then separated.

Applications

f\cong\frac{1}{R_1C_1\ln\frac{V_1-V_\text{GLOW}}{V_1-V_\text{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.

See also

References