A critical analysis of the conventional theory of spin resonances in storage rings

Abstract

We present a critical assessment of the conventional theory of spin resonances in storage rings. We show that an application of the rigorous formula for the locations of spin-resonant orbits, using the nonperturbative off-axis solution for the spin tune, frequently fails to correctly identify the locations of depolarization. We use recently discovered analytical solutions for the invariant spin field and spin tune in several storage ring models, to obtain a general overview of the spin dynamics and also of the polarization. We calculate the long-term polarization and the depolarizing spin resonances for each model. In particular, we present a detailed examination of the so-called “Snake resonances”. We also compare our analytical solutions against the results of numerical simulations. We consider various measures of the degree of long-term polarization and point out fallacious tacit assumptions in the conventional literature. We also present some new mathematical results linking the so-called sine-Bessel functions to the complete elliptic integral of the first kind.