Study of spin resonances in the accelerators with snakes

Abstract

Spin resonances in the circular accelerators with snakes are studied to understand the nature of snake resonances. We analyze the effect of snake configuration, and the snake superperiod on the resonance. Defining the critical resonance strength εc as the maximum tolerable resonance strength without losing the beam polarization after passing through the resonance, we found that εc is a sensitive function of the snake configuration, the snake superperiod at the first order snake resonance, the higher order snake resonance conditions and the spin matching condition. Under properly designed snake configuration, the critical resonance strength εc is found to vary linearly with NS as 〈εc〉=(1/π)sin−1(cosπνz z‖1/2)NS, where νz and NS are the betatron tune and the number of snakes respectively. We also study the effect of overlapping intrinsic and imperfection resonances. The imperfection resonance should be corrected to a magnitude of insignificance (e.g., ε≤0.1 for two snakes case) to maintain proper polarization.