The Amplitude Dependent Spin Tune and the Invariant Spin Field in High Energy Proton Accelerators

There is some ambiguity in the definitions and use of the concepts of spin tune and spin-orbit resonance on synchrobetatron orbits. We clarify these issues and provide a numerical illustration of the internal consistency of our definitions using the computer code SPRINT for HERA with a standard Siberian Snake arrangement. Furthermore, we demonstrate the calculation of the invariant spin field using adiabatic anti-damping of the orbital motion and compare with the spin field obtained by stroboscopic averaging. In addition we study polarization loss on accelerating through resonances.