The Periodic Deviation from the Schottky Line

The width of the potential hump traversed by thermions moving between parallel plates depends upon the strength $E$ of the external field at the cathode. Partial reflection at this hump, analogous to the partial reflection of light passing through a thin plate, may account for the small deviations from the Schottky line, depending in a periodic manner on $\surd E$, observed by Phipps, Seifert and Turnbull. A calculation based on this analogy shows rough agreement between the theory and the data. An approximate solution of the wave equation yields a small term of suitable period, but to start the theory, one needs a really accurate solution probably best obtained by mechanical integration.