Spin Echo and Interference in Synchrotrons

Spin dynamics in crossing a single depolarization resonance is a well-studied subject. One well-known example is that of Froissart and Stora in 1960. More is needed to complete the understanding, particularly of the transient effects, when crossing a single resonance, but question arises what happens if we cross two resonances or cross a single resonance twice. When a resonance is crossed twice, the particle's spin dynamics encounters two additional phenomena. First, the two crossings will interfere with each other, leading to an interference effect. Second, there will be a spin echo effect. We discuss these two effects in this report. Two proposals to test these effects experimentally are made at the end.