Calculations of the Focusing Properties of a 7% Partical Snake Helical Magnet with Variable Helicity
The main function of the 5% partial snake [1, 2] which is currently installed in the ring of the AGS synchrotron, is to help overcome the imperfection spin resonances. The solenoidal field of the 5% partial snake introduces beam coupling that enhances the strength of the spin coupling resonances which is the cause of some polarization loss of the accelerated proton beam. Experiments performed with polarized proton beams in AGS have shown  that the beam coupling introduced by the solenoidal
... eld of the partial snake increases the strength of the spin coupling resonances, resulting in some polarization loss. Calculations have shown that the beam coupling introduced by the solenoidal field of the 5% partial snake is higher than the coupling introduced by the helical magnetic field[4,5,6] of a 7% partial snake. In a recent experiment 1 performed in AGS with polarized protons, the 5% partial snake of the AGS was set at 11.4%, and successfully overcome the Gγ=0+ν y intrinsic spin resonance in AGS. Additional calculations  have shown that a 7% helical dipole partial snake in conjunction with a 20% superconducting helical snake  can be used in the AGS to overcome not only the imperfection resonances but also the intrinsic ones. Based on these calculations [4, 8] and the experimental results[3,7] two helical dipole partial snakes have been designed to be placed in the AGS ring. One, helical dipole, 7% partial snake has already been constructed to be placed in the straight section E20 of the AGS synchrotron and another 20% superconducting helical dipole partial snake is under construction to be placed in the A20 straight section of the AGS. This technical note describes in details the 3D modeling of a 7% helical dipole partial snake, the calculation of its focusing properties, and its effect on the proton spin. The design of the helical dipole partial snake which is the subject of this technical note is similar but not exactly the same as the one which has been built to be installed in AGS. The purpose of the this technical note is two fold first to report details on the results of the study on the 7% helical dipole partial snake , and second to use these results as a prerequisite of a feasibility study for a proposed method, to measure experimentally the focusing properties of a magnet  .