= 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, $dn_e/dx=\alpha n_e$ 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>.<A Generalized Townsend's Theory for Paschen Curves in Planar, Cylindrical, and Spherical Geometries in Planetary Atmospheres by Jeremy A. Riousset and others>[Townsend ionization coefficient and planar breakdown criterion]{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.
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