Polarization control in spin-transparent hadron colliders by weak-field navigators involving lattice enhancement effect

Hadron polarization control schemes for Spin Transparent (ST) synchrotrons are analyzed. The spin dynamics and beam polarization in such synchrotrons are controlled by spin navigators (SN) which are special small insertions of weak magnetic fields. An SN stabilizes the beam polarization and allows for setting any desirable spin orientation at an interaction point in the operational regime, including a frequent spin flip. We present a general approach to design of SNs. We distinguish different types of SNs, namely, those not causing closed orbit perturbation as well as those producing local and global orbit distortions. In the second case, the concept of the spin response function in an ST synchrotron is applied and expanded to reveal the effect of the SN strength enhancement by magnetic lattice of the synchrotron. We provide conceptual schemes for SN designs using longitudinal and transverse magnetic fields allowing for polarization control at low as well as high energies. We also develop the ST concept for ultra-high energies. This development may enable and stimulate interest in polarized beam experiments in possible polarized collider projects such as Large Hadron Collider (LHC), Future Circular Collider (FCC) and Super Proton Proton Collider (SPPC).