Paschen's Law

Description

In standard conditions at atmospheric pressure, gas serves as an excellent insulator, requiring the application of a significant voltage before breaking down. In partial vacuum, this breakdown potential may decrease to an extent that two uninsulated surfaces with different potentials might induce the electrical breakdown of the surrounding gas. Paschen’s Law is an equation that gives, in a partial vacuum, the breakdown voltage, that is the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length.

Constants A and B depend on the surrounding gas. A is the saturation ionization in the gas at a particular E / p (electric field/pressure), and B is related to the excitation and ionization energies. Both are determined experimentally and have been found to be roughly constant over a restricted range of E / p for any given gas.

For example, air with an E / p in the range of 450 to 7500 V·(kPa·cm)−1, A = 112.50 (kPa·cm)−1 and B = 2737.50 V·(kPa·cm)−1.

Related formulas

Variables

VbThe breakdown potential ( DC) (V)
BConstant that depends on the surrounding gas (V/atm*m)
pThe pressure of the surrounding gas (atm)
dThe gap distance (m)
AConstant that depends on the surrounding gas (1/atm*m)
γse Secondary Electron Emission Coefficient (dimensionless)