Nonlinear Microwave Effects and the Switching Speed of Superconducting Tin

The nonlinear response of various superconducting tin surfaces has been observed when both a high-amplitude rf magnetic field at 9200 Mc/sec and a dc bias field were applied to such surfaces. Harmonics at 18 400 Mc/sec were generated because of the change of the superconducting surface resistance with field during the rf cycle. Data are presented on the variation of this harmonic output with temperature, with dc bias magnetic field, and with the rf power level. Results are given for the surfaces of pure bulk specimens, of alloy bulk specimens, and of thin films of various thicknesses. The amount of harmonic power observed is never more than a few percent of that which is calculated under the assumption that the surface resistance changes instantaneously and completely from its superconducting value to its normal value when the total applied field changes from less than to more than the critical value. The conclusion is drawn that the switching between states is only partial or incomplete at such high frequencies. A discussion is given which appears to qualitatively account for most of the salient experimental facts. For the alloy and thin film specimens and for the pure specimens near $T_c$, this discussion is based on consideration of the Ginzburg-Landau order parameter. For the pure specimens at lower temperatures, a new approach is proposed which is based on spatial effects: The switching field is confined to such a small skin depth that the presence of the large amount of adjacent unswitched material inhibits the transition from taking place. In neither case is it found necessary to include any purely temporal limitation on the switching speed in order to explain the experimental observations.