 Gas discharge

A gas discharge is electrical conduction through a gas containing mobile charged particles. An applied electric field accelerates electrons; collisions can cause ionization, generating additional electrons and ions. A sustained discharge requires charge-production and electrode-emission processes to offset losses, rather than merely the presence of a few initially charged particles.

In a uniform Townsend avalanche model, $d{n}_e/dx=\alpha n_e$ gives $n_e(d)=n_e(0)e^{\alpha d}$ across a gap $d$. If each arriving positive ion releases on average $\gamma$ electrons from the cathode, the self-sustaining threshold is $\gamma (e^{\alpha d}-1)=1$. Combining that condition with the field dependence of $\alpha$ gives the Paschen law.^[ref]

A motivating measurement fixes the gas, electrode material and gap, varies pressure and records the onset electric potential difference with a current-limited source. A pressure gauge and current measurement distinguish the breakdown threshold from the later conducting regime. At larger currents, space charge and heating can invalidate the uniform-field avalanche approximation.