Physics of Limiting Phenomena in Superconducting Microwave Resonators: Vortex Dissipation, Ultimate Quench and Quality Factor Degradation Mechanisms
Superconducting niobium accelerating cavities are devices operating in radio-frequency and able to accelerate charged particles up to energy of tera-electron-volts. Such accelerating structures are though limited in terms of quality factor and accelerating gradient, that translates--in some cases--in higher capital costs of construction and operation of superconducting rf accelerators. Looking forward for a new generation of more affordable accelerators, the physical description of limiting mechanisms in superconducting microwave resonators is discussed. In particular, the physics behind the dissipation introduced by vortices in the superconductor, the ultimate quench limitations and the quality factor degradation mechanism after a quench are described in detail. One of the limiting factor of the quality factor is the dissipation introduced by trapped magnetic flux vortices. The radio-frequency complex response of trapped vortices in superconductors is derived by solving the motion equation for a magnetic flux line, assuming a bi-dimensional and mean free path-dependent Lorentzian-shaped pinning potential. The resulting surface resistance shows the bell-shaped trend as a function of the mean free path, in agreement with the experimental data observed. Such bell-shaped trend of the surface resistance is described in terms of the interplay of the two limiting regimes identified as pinning and flux flow regimes, for low and large mean free path values respectively. The model predicts that the dissipation regime--pinning- or flux-flow-dominated--can be tuned either by acting on the frequency or on the electron mean free path value. The effect of different configurations of pinning sites and strength on the vortex surface resistance are also discussed. Accelerating cavities are also limited by the quench of the superconductive state, which limits the maximum accelerating gradient achievable. The accelerating field limiting factor is usually associate d to the superheating field, which is intimately correlated to the penetration of magnetic flux vortices in the material. Experimental data for N-doped cavities suggest that uniform Ginzburg-Landau parameter cavities are statistically limited by the lower critical field, in terms of accelerating gradient. By introducing a Ginzburg-Landau parameter profile at the cavity rf surface--dirty layer--the accelerating gradient of superconducting resonators can be enhanced. The description of the physics behind the accelerating gradient enhancement as a consequence of the dirty layer is carried out by solving numerically the Ginzburg-Landau equations for the layered system. The enhancement is showed to be promoted by the higher energy barrier to vortex penetration, and by the enhanced lower critical field. Another serious threat to the quality factor during the cavity operation is the extra dissipation introduced by the quench. Such quality factor degradation mechanism due to the quench, is generated by the trapping of external magnetic flux at quench spot. The purely extrinsic origin of such extra dissipation is proven by the impossibility of decrease the quality factor by quenching in a magnetic field-free environment. Also, a clear relation of the dissipation introduced by quenching to the orientation of the applied magnetic field is observed. The full recover of the quality factor by re-quenching in compensated field is possible when the trapped flux at the quench spot is modest. On the contrary, when the trapped magnetic flux is too large, the quality factor degradation may become irreversible by this technique, likely due to the outward flux migration beyond the normal zone opening during the quench.