Electron Flow in Gas Diodes. I. Transition from Inertia-Limited Flow to Mobility-Limited Flow

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Abstract
The transition from inertia‐limited flow (vacuum) to mobility‐limited flow (high pressure) in gas‐filled diodes is studied theoretically by taking velocity moments of the Boltzmann equation for the electron‐velocity distribution function. It is shown that the momentum‐transfer equation can be integrated when νc(C), the frequency of elastic collisions between electrons and gas atoms, is independent of the electron speed c, and the hydrostatic‐pressure term is neglected. The resulting current‐voltage (J‐V) curve, which is valid for all gas pressures, reduces to the proper vacuum law (J ∝ V3/2) at extremely low gas pressure and to the proper high‐pressure law (J ∝ V2) at high gas pressure, while it is a mixture of the two laws for intermediate gas pressures. The importance of the ratio νc/νp, where νc is the average value of νc(C) and νp is the electron‐plasma frequency, is emphasized. It is shown that the current is inertia limited for νc/νpc/νp>1. It is shown further that mobility‐limited flow divides naturally into two cases, according to whether the electrons retain the energy imparted to them by the electric field or whether this energy is given up in elastic collisions with atoms. The former situation, called the low‐pressure case, prevails when (m/M)1/2νc/νp1, where m/M is the ratio of electron mass to atom mass.