Deflecting/crabbing cavities serve a variety of purposes in different accelerator applications, primarily in separating a single beam into multiple beams and in rotating bunches for head-on collisions at the interaction point in particle colliders. Deflecting/crabbing cavities are also used for transverse and longitudinal emittance exchange in beams, x-ray pulse compression, and for beam diagnostics. Compact superconducting deflecting/crabbing cavities are under development due to strict dimensional constraints and requirements for higher field gradients with low surface losses. The TEM-like superconducting parallel-bar cavity supports low operating frequencies, thus making the design favorable for many of the deflecting/crabbing cavity applications. The design of the parallel-bar cavity based on cylindrical straight loading elements and rectangular outer conductors has evolved and been adapted to improve the design properties by modifying the design geometry. The improved design with trapezoidalshaped loading elements and cylindrical outer conductor has attractive properties such as low and wellbalanced peak surface fields and high transverse shunt impedance. Additionally, the wide separation of modes in the higher-order mode spectrum and the absence of lower-order mode are advantageous in high current applications. The evolution of the parallel-bar geometry into an rf-dipole geometry is presented with a detailed analysis of the properties for each design.

We present a general method to derive the magnetic field dependence of the surface resistance of superconductors from the Q-curves obtained during the cryogenic tests of cavities. The results are applied to coaxial half-wave cavities, TM-like "elliptical" accelerating cavities, and cavities of more complicated geometries.