Spin decoherence rate in a homogenous all-electric ring

I derive analytical expressions for the spin decoherence rate for motion in a homogenous weak focusing all-electric storage ring. Canonical dynamical variables are employed throughout. I treat on-energy betatron oscillations and off-energy dispersion orbits. I obtained exact solutions for the spin decoherence rate, for the off-energy dispersion orbits and for motion in a vertical spiral in a logarithmic potential. I also reproduce, with kind permission, Koop׳s elegant analysis of motion in a vertical spiral in a logarithmic potential. I have also recently published the exact solution for the spin precession in the relativistic Kepler problem (inverse square law), and I verify that it confirms the perturbative solution. The appendices present some comments on other published work in the field, including a discussion of conceptual and quantitative errors therein.