Paschen's law

Paschen's law relates the electrical breakdown voltage of a gas between electrodes to the product of gas pressure and electrode spacing. Its characteristic curve has a minimum breakdown voltage at an intermediate pressure–spacing product.

Townsend discharge: A gas discharge sustained by electron impact ionization and secondary electron emission from electrodes. Paschen's law describes the breakdown threshold at which a Townsend discharge becomes self-sustaining.
Electrical breakdown: The sudden transition of an insulating material or medium into a conductive state under an electric field. Paschen's law is a gas-specific account of breakdown between electrodes.
Paschen curve: A graph of gas breakdown voltage against the product of gas pressure and electrode spacing. It visualizes the minimum and the rising voltage on either side predicted by Paschen's law.
Field emission: The emission of electrons from a solid surface under a strong electric field, enabled by quantum tunneling. It can initiate breakdown without the gas-impact ionization assumed in the classical account.
Townsend ionization coefficient: The average number of ionizing collisions made by an electron per unit distance in a gas under an electric field. Its dependence on the reduced electric field helps determine breakdown voltage.
Mean free path: The average distance a particle travels between collisions with other particles. Pressure changes collision spacing, which controls whether electrons gain ionizing energy.
Vacuum arc: An electrical arc in a high-vacuum gap, often sustained by material emitted from electrode surfaces. At very low pressure, breakdown can depart from ordinary gas-discharge predictions and involve electrode material.
Corona discharge: A localized gas discharge around a conductor where the electric field is strongest, without bridging the full gap. It is a partial discharge, unlike the full-gap breakdown voltage described by Paschen's law.
Electron avalanche: An exponential multiplication of free electrons through successive impact-ionization events in a gas. Avalanche growth is the immediate process behind gas breakdown.
Gas pressure: The force per unit area exerted by gas particles through their collisions with surrounding surfaces. It is one factor in the pressure–spacing product governing breakdown voltage.

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