Townsend (unit)

The townsend (symbol Td) is a physical unit of the reduced electric field (ratio E/N), where $$E$$ is electric field and $$N$$ is concentration of neutral particles.

It is named after John Sealy Townsend, who conducted early research into gas ionisation.

Definition
It is defined by the relation

$$1 \, {\rm Td} = 10^{-21} \, {\rm V\cdot m^2} = 10^{-17} \, {\rm V\cdot cm^2}.$$

For example, an electric field of

$$E = 2.5 \cdot 10^{4} \, {\rm V/m}$$

in a medium with the density of an ideal gas at 1 atm, the Loschmidt constant

$$n_0 = 2.6867811 \cdot 10^{25} \, {\rm m^{-3}}$$

gives

$$E/n_0 \approx 10^{-21} \, {\rm V \cdot m^{2}}$$,

which corresponds to $$1 \, {\rm Td}$$.

Uses
This unit is important in gas discharge physics, where it serves as scaling parameter because the mean energy of electrons (and therefore many other properties of discharge) is typically a function of $$E/N$$ over broad range of $$E$$ and $$N$$.

The concentration $$N$$, which is in ideal gas simply related to pressure and temperature, controls the mean free path and collision frequency. The electric field $$E$$ governs the energy gained between two successive collisions.

Reduced electric field being a scaling factor effectively means, that increasing the electric field intensity E by some factor q has the same consequences as lowering gas density N by factor q.