Explicit symplectic orbit and spin tracking method for electric storage ring

We develop a symplectic charged particle tracking method for phase space coordinates and polarization in all electric storage rings. Near the magic energy, the spin precession tune is proportional to the fractional momentum deviation delta(m) from the magic energy, and the amplitude of the radial and longitudinal spin precession is proportional to eta/delta(m), where. is the electric dipole moment for an initially vertically polarized beam. The method can be used to extract the electron electric dipole moment of a charged particle by employing narrow band frequency analysis of polarization around the magic energy.