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

We investigate 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>120</a:mn><a:mi>–</a:mi><a:mn>165</a:mn><a:mtext> </a:mtext><a:mi>°</a:mi><a:mi mathvariant="normal">C</a:mi></a:mrow></a:math> for an extended period of time (24–48 h) either in high vacuum or in a low partial pressure of ultrapure nitrogen. The improvement in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi>Q</d:mi><d:mn>0</d:mn></d:msub></d:math> with a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>Q</f:mi></f:math> rise was observed when nitrogen gas was injected at <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mo>∼</h:mo><h:mn>300</h:mn><h:mtext> </h:mtext><h:mi>°</h:mi><h:mi mathvariant="normal">C</h:mi></h:mrow></h:math> during the cavity cooldown from <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mn>800</k:mn><k:mtext> </k:mtext><k:mi>°</k:mi><k:mi mathvariant="normal">C</k:mi></k:mrow></k:math> and held at <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mrow><n:mn>165</n:mn><n:mtext> </n:mtext><n:mi>°</n:mi><n:mi mathvariant="normal">C</n:mi></n:mrow></n:math>, without any degradation in accelerating gradient over the baseline performance. The treatment was applied to several elliptical cavities with frequency ranging from 0.75 to 3.0 GHz, showing an improved quality factor as a result of low temperature nitrogen treatments. The <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>Q</q:mi></q:math> 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 <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>Q</s:mi></s:math> rise, becomes stronger with increasing frequency and decreasing temperature. The data suggest a crossover frequency of <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mo>∼</u:mo><u:mn>0.95</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>GHz</u:mi></u:math> above that the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>Q</w:mi></w:math> 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 <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>Q</y:mi></y:math> slope below 0.95 GHz may result from masking contribution of trapped magnetic flux to the residual surface resistance.