Investigation of spin resonance crossing in proton circular accelerators

The general approach to the problem of the symplectic integration of Hamilton´s equations and which uses only the common properties of Lie groups, is developed to obtain the numerical tracking methods for both orbital and spin motions. The integration step of these methods is an explicit canonical map (we use the term “canonical” instead “symplectic” for the systems with the spin Poisson brackets). Some methods are realized in the computer code VasiLIE. With help of this code it is possible to study the dynamics of the polarization during acceleration. The numerical simulation of crossing the depolarizing resonances depending on the different parameters was performed for a lattice under study for the TRIUMF KAON Factory Booster. The effect of nonlinear elements is also discussed