Systematic integer spin resonances

In a plane electron ring like LEP, the depolarization arises from the parasitic horizontal magnetic fields due to misalignments and field imperfections. We show in this paper that their statistical properties are an important factor that must be taken into account in the computation of the asymptotic polarization level. It is found indeed that random magnetic defects only drive a subset of spin resonances, grouped around ''systematic'' integer resonances. After closed orbit correction, the horizontal spurious fields, including orbit correctors, are highly correlated; they then drive all spin resonances. For LEP, the polarization level before a specific polarization optimization is divided by two when taking into account a proper orbit spectrum. A hint is given for a simple improvement of existing polarization programs to better simulate a corrected closed orbit