Spin decoherence rate in a weak focusing all-electric ring

Abstract

I previously derived the expression for the spin decoherence rate (for orbital and spin motion in the horizontal plane) in a weak focusing all-electric storage ring with a radial field (logarithmic potential, field index $n=0$). Here I generalize the calculation to an arbitrary field index $n\ge 0$. I also solve the model for the relativistic Kepler problem (field index $n=1$), where the solution for the orbit is known analytically, and I verify that it confirms the solution from perturbation theory.

arXiv comment57 pages, 4 figures. v2: I solved the model also for off-energy dispersion orbits. The dispersion orbits are circles and I calculated the spin decoherence rate exactly. v3: I solved the model also for vertical motion, for $n=0$ (logarithmic potential). I have also solved for the spin precession the Kepler problem (inverse square law) exactly; the paper is in press. Extra appendices have been added; in particular, Ivan Koop kindly gave permission to reproduce his elegant analysis of motion in a vertical spiral in a logarithmic potential. v4: Added synchrotron oscillations. arXiv admin note: substantial text overlap with arXiv:1403.5023

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