The townsend (symbol Td) is a physical unit of the reduced electric field (ratio E/N), where E {\displaystyle E} is electric field and N {\displaystyle 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 Td = 10 − 21 V ⋅ m 2 = 10 − 17 V ⋅ cm 2 . {\displaystyle 1\ {\text{Td}}=10^{-21}\ {\text{V}}\cdot {\text{m}}^{2}=10^{-17}\ {\text{V}}\cdot {\text{cm}}^{2}.}
For example, an electric field of
E = 2.5 ⋅ 10 4 V / m {\displaystyle E=2.5\cdot 10^{4}\ {\text{V}}/{\text{m}}}
in a medium with the density of an ideal gas at 1 atm and 0 °C, the Loschmidt constant
n 0 = 2.6867811 ⋅ 10 25 m − 3 {\displaystyle n_{0}=2.6867811\cdot 10^{25}\ {\text{m}}^{-3}}
gives
E / n 0 ≈ 10 − 21 V ⋅ m 2 , {\displaystyle E/n_{0}\approx 10^{-21}\ {\text{V}}\cdot {\text{m}}^{2},}
which corresponds to 1 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 {\displaystyle E/N} over broad range of E {\displaystyle E} and N {\displaystyle N} . The concentration N {\displaystyle N} , which is in ideal gas simply related to pressure and temperature, controls the mean free path and collision frequency. The electric field E {\displaystyle 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.
See also Electric glow discharge Vacuum arc
References
A. Banković; S. Dujko; R. D. White; J. P. Marler; S. J. Buckman; S. Marjanović; G. Malović; G. García; Z. Lj. Petrović (2012). "Positron transport in water vapour". New J. Phys. 14 035003. doi:10.1088/1367-2630/14/3/035003. hdl:1885/61498.