Effect of non-uniform surface resistance on the quality factor of superconducting niobium cavity

• Take the effect of non-uniform surface resistance into consideration.
• A criterion where the non-uniform resistance need to be considered is given.
• The distribution of magnetic field in superconducting cavities is evaluated carefully.
• Thermal Feedback Model and Srimp Code is applied.

The formula Rs=G/Q0is commonly used in the calculation of the surface resistance of radio frequency niobium superconducting cavities. The applying of such equation is under the assumption that surface resistance is consistent over the cavity. However, the distribution of the magnetic field varies over the cavity. The magnetic field in the equator is much higher than that in the iris. According to Thermal Feedback Theory, it leads non-uniform distribution of the density of heat flux, which results in a different temperature distribution along the cavity inter surface. The BCS surface resistance, which depends largely on the temperature, is different in each local inner surface. In this paper, the effect of surface non-uniform resistance on the quality factor has been studied, through the calculation of Q0 in the original definition of it. The results show that it is necessary to consider the non-uniform distribution of magnetic field when the accelerating field is above 20 MV/m for TESLA cavities. Also, the effect of inhomogeneity of residual resistance on the quality factor is discussed. Its distribution barely affects the quality factor.