The purpose of the present work is the development of a method for searching the electric dipole moment (EDM) of the deuteron inside the storage ring environment using the frozen spin method. The 2D frozen spin method is a variation on the original frozen spin method proposed at Brookhaven National Laboratory, in which the beam polarisation vector freely precesses in the vertical plane. One distinguishing feature of the 2D frozen spin method, is that it uses the radial magnetic fields induced by the accelerator optical lattice's imperfections to drive the vertical plane precession. The net electric + magnetic dipole moment spin precession frequency is measured. The EDM estimator is constructed as the sum of the net frequency estimates in two cases: when the beam circulates clockwise (CW), and when it does counter-clockwise (CCW). For the deuteron, since the experiment is performed in a combined ring, the beam circulation direction change requires flipping the polarity of the guiding magnetic field. When this is done, the imperfection fields change their sign as well, and so does the magnetic dipole moment (MDM) component of the spin precession angular velocity vector. Therefore, theoretically, the MDM term cancels in the EDM estimator. The trick is to calibrate the MDM precession frequency with sufficient precision. For that purpose, the concept of the effective Lorentz factor was introduced. We try to prove that particles having equal values of the effective Lorentz factor have equal spin tunes (and invariant spin axis orientations as well), and therefore, by controlling a single parameter -- the effective Lorentz factor -- it is possible to calibrate the MDM component of the precession frequency. A special calibration procedure is numerically modelled, with the conclusion that it allows sufficiently precise MDM spin precession frequency reproduction. Three major systematic effects of spin dynamics have been analysed: 1) perturbations to the particle spin dynamics caused by betatron oscillations, 2) spin decoherence in the zero spin resonance (frozen spin) region, 3) properties of the machine imperfection MDM spin precession angular velocity. We conclude that the first systematic effect is negligible; analyse the sextupole field approach to suppressing spin decoherence, and find it effective; find that the imperfections systematic error is linear, but asymmetric with respect to the beam circulation direction, which is more motivation for using the effective Lorentz factor as the tool for calibrating the MDM spin precession frequency. Overall, we find the proposed method effective.
Particle Acceleration in Spherical Wave Fields
