Spin with two snakes and overlapping resonances

The authors study the effect of multiple spin depolarization resonances on the spin of the particles with two snakes. They found that (1) When two resonances are well separated, the polarization can be restored in passing through these resonances provided that the snake resonances are avoided. (2) When two resonances are overlapping, the beam particles may be depolarized depending on the spacing between these two resonances. If the spacing between these two resonances is an odd number for two snakes, the beam particles may be depolarized depending on the strength of the resonance. When the spacing becomes an even number, the spin can tolerate a much larger resonance strength without depolarization. Numerical simulations can be shown to agree with the analytic formula. (3) However the spin is susceptible to the combination of an intrinsic and an imperfection resonances even in the present of the snakes. Numerical solutions indicates that the spin can be restored after the resonances provided that imperfection strength is less than 0.1 if intrinsic strength is fixed at 0.745