A Similarity Principle for Multipacting Discharges

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Abstract
A similarity principle is introduced for multipacting discharges in geometrically similar electrode configurations. For phase‐similar breakdowns, it is shown that the rf and dc voltages are proportional to (fl)2, the electron velocity is proportional to fl, and the rf and dc magnetic fields are proportional to f, where f is the frequency of the rf voltage and l is the characteristic length for similar configurations. If the electron kinetic energy is similar as well, fl must also be invariant. These similarity relations are applied to previous work in parallel plates, and it is shown that the results of the different multipacting cases can be unified under the similarity principle. A physical explanation is also given for the success of the constant vf/vi assumption, where vi and vf are the respective emission and impact electron velocities. When applied to geometries other than parallel plates, the similarity principle yields important scaling information and allows prediction of the breakdown behavior in these geometries, where analytical solutions are otherwise not available.