We recently studied the proton beam polarization in the Indiana University Cyclotron Facility Cooler Ring at five energies. We found that the Gy=2 imperfection depolarizing resonance occurred about 1.9 MeV below the expected resonance energy of 108.4 MeV. This energy shift could be due to a shift of about +0.0036 in the spin tune v,, which is the number of spin rotations in each turn around the ring. We then demonstrated that this spin tune shift is consistent with the Cooler Ring containing a partial type-3 Siberian snake, which is apparently caused by the magnets that confine the electron and proton beams in the cooling region.High-energy polarized proton collisions provide important information about the fundamental nature of strong interactions. However, it is difficult to accelerate polarized protons above about 20 GeV because of the many depolarizing resonances [I]. Siberian snakes [21 should allow the acceleration of polarized proton beams to very high energy by preserving the protons' spin polarization along some stable spin direction during acceleration through the many depolarizing resonances. To confirm the Siberian-snake concept, we have been studying various properties of Siberian snakes and depolarizing resonances [3,41. We recently found a new type of Siberian snake, whose existence explains some interesting aspects [5-71 of our earlier studies.The various types of depolarizing resonances can be described in terms of the spin tune v,, which is the number of spin precessions in each turn around a circular accelerator. An imperfection depolarizing resonance 131 occurs whenever the spin tune, which is normally equal to Gy, becomes equal to an integer n: v s = G y 5 n ,where G = ( g -2)/2 = 1.7928 in the anomalous part of the proton magnetic moment and y is the relativistic energy factor. An intrinsic depolarizing resonance [41 occurs whenever v , = G y s m P f v,.,where m is an integer, P is the ring's periodicity, and v, is the vertical betatron tune. More generally a depolarizing resonance occurs whenever the spin tune satisfies v.? = n + m P +qv, + r v , iTsvSy, ,where m, n, q, r, and s are integers, vsy, is the synchrotron tune, and v, is the horizontal betatron tune. A synchrotron depolarizing resonance I41 occurs when s is nonzero. Polarized proton beams were successfully accelerated to 44 R1361
