Numerical spin tracking in a synchrotron computer code Spink: Examples (RHIC)

In the course of acceleration of polarized protons in a synchrotron, many depolarizing resonances are encountered. They are classified in two categories: Intrinsic resonances that depend on the lattice structure of the ring and arise from the coupling of betatron oscillations with horizontal magnetic fields, and imperfection resonances caused by orbit distortions due to field errors. In general, the spectrum of resonances vs spin tune Gγ(G = 1.7928, the proton gyromagnetic anomaly, and y the proton relativistic energy ratio) for a given lattice tune ν, or vs ν for a given Gγ, contains a multitude of lines with various amplitudes or resonance strengths. The depolarization due to the resonance lines can be studied by numerically tracking protons with spin in a model accelerator. Tracking will allow one to check the strength of resonances, to study the effects of devices like Siberian Snakes, to find safe lattice tune regions where to operate, and finally to study in detail the operation of special devices such as Spin Flippers. A few computer codes exist that calculate resonance strengths Ek and perform tracking, for proton and electron machines. Most relevant to our work for the AGS and RHIC machines are the programs Depol and Snake. Depol, calculates the Ek's by Fourier analysis. The input to Depol is the output of a machine model code, such as Synch or Mad, containing all details of the lattice. Snake, does the tracking, starting from a synthetic machine, that contains a certain number of periods, of FODO cells, of Siberian snakes, etc. We believed the complexities of machines like the AGS or RHIC could not be adequately represented by Snake. Then, we decided to write a new code, Spink, that combines some of the features of Depol and Snake. I.E., Spink reads a Mad output like Depol and tracks as Snake does. The structure of the code and examples for RHIC are described in the following