Analytical solutions for spin response functions in model storage rings with Siberian Snakes

I present analytical solutions for the spin response functions for radial field rf dipole spin flippers in models of storage rings with one Siberian Snake or two diametrically opposed orthogonal Siberian Snakes. The solutions can serve as benchmarks tests for computer programs. The spin response functions can be used to calculate the resonance strengths for radial field rf dipole spin flippers in storage rings.