Field, frequency and temperature dependence of the surface resistance of nitrogen diffused niobium superconducting radio frequency cavities

We report the RF performance of several single-cell superconducting radio-frequency cavities subjected to low temperature heat treatment in nitrogen environment. The cavities were treated at temperature 120 - 165 $^{\circ}$C for an extended period of time (24 - 48 hours) either in high vacuum or in a low partial pressure of ultra-pure nitrogen. The improvement in $Q_0$ with a Q-rise was observed when nitrogen gas was injected at $\sim$300 $^{\circ} $C during the cavity cooldown from 800 $^{\circ}$C and held at 165 $^{\circ}$C, without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 GHz to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The Q-rise feature is similar to that achieved by nitrogen alloying Nb cavities at higher temperature, followed by material removal by electropolishing. The surface modification was confirmed by the change in electronic mean free path and tuned with the temperature and duration of heat treatment. The decrease of the temperature-dependent surface resistance with increasing RF field, resulting in a Q-rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of $\sim 0.95$~GHz above which the Q-rise phenomenon occurs at 2~K. Some of these results can be explained qualitatively with an existing model of intrinsic field-dependence of the surface resistance with both equilibrium and nonequilibrium quasiparticle distribution functions. The change in the Q-slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance.