Stored polarized beams: Miles, Limes, Smile, sine-Bessels and Sodom2 too

摘要

The fundamental theory underlying several computational algorithms for the spin dynamics of stored polarized beams is analyzed Particular attention is paid to the consequences of the use of finite-dimensional matrices and/or Fourier series. The single resonanc model with a pair of diametrically opposed nonorthogonal pointlike Siberian Snakes is analyzed in detail to clarify several point pertaining to the above algorithms, and more generally to the spin dynamics of stored polarized beams in rings with Snakes. Ne analytical results are also presented, e.g. for the spin tune shift in the nonorthogonal Snakes model, and the sine-Bessel functions for th orthogonal Snakes model. Many results are derived using multiple algorithms, which serves as a check on their mutual consistency.