Note on Paschen Law and Similarity Theorem in Gaps with Cylindrical and Plane Geometry

An expression for the increase of the minimum of breakdown voltage is derived for the transition from plane to cylindrical geometry. The resulting breakdown voltage as a function of the reduced distance between inner and outer electrode, (R2-R1) p shows that for values of (R2-R1) p above the minimum the breakdown voltage decreases by changing from plane to cylindrical geometry. The production of charges is described by the wellknown ionization coefficient α/p depending on the local electric field E/p. Further it is shown that violations of the similarity theorem can not be caused by non-equilibrium ionization as postulated by G. R. G. Raju and R. Hackam. Similarity only fails if certain volume or wall processes become predominant.