# 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.