Spin Motion and Resonances in Accelerators and Storage Rings

Some of the basic aspects of the spin dynamics of accelerators and storage rings are reviewed. Since the components of spin parallel and perpendicular to the particle velocity behave differently it is desirable to reformulate the equations of spin motion in a frame of reference that exhibits this difference explicitly. The conventional treatment employs a coordinate system derived from a reference orbit. An alternate coordinate system, based on the actual trajectory of the particle, leads to simplified equations of spin motion but, contrary to a conjecture presented in a previous note, resonance strengths calculated by the conventional and the revised formalisms are identical, as pointed out by Kondratenko. Resonances induced by radiofrequency dipoles or solenoids are also treated; with rf dipoles it is essential to consider not only the direct effect of the dipole but also the contribution from oscillations induced by it