Breakdown of a Gas at Microwave Frequencies

An electric field of sufficiently high frequency applied to electrons in a gas may deliver energy to the electrons without imparting to them any continuous drift motion resulting from the field. The criterion for breakdown of a low pressure gas at microwave frequencies is therefore that ionization by collision of electrons with neutral gas molecules replace loss by diffusion to the walls of the discharge tube. The condition is mathematically expressed as a simple boundary value problem. This breakdown principle is applied to converting microwave breakdown measurements into measurements of ionization rates as a function of the electric field strength, pressure, and frequency. A new ionization coefficient is introduced appropriate to the high frequency discharge conditions, and its relation to the d.c. Townsend coefficient is explained. The energy transfer from the electric field to the electrons at a given $\frac{E}{p}$ is shown to be most efficient when the pressure is high enough or the frequency low enough to result in many collisions of electrons with gas molecules per cycle. This maximum efficiency is equal to the d.c. energy transfer efficiency. When the pressure is lower or the frequency is higher, the electrons have an out-of-phase component of motion and do not receive energy so efficiently, resulting in lower ionization rates observed experimentally.