Modelling of polarized protons dynamics in electrostatic storage rings

Electric dipole moment of elementary particles (such as deuterons or protons) is a very small quantity and measurement of such small value which requires long term beam evolution (about $10^9$ turns) to accumulate enough statistical data. To develop optimal accelerator lattice one needs to do numerical modelling for polarized beam evolution during $10^{12}$ integration steps. Also such class of dynamic systems requires considering additional constraints (like symplecticity and energy conservation) during the integration period. To search electric dipole moment horizontal polarization has to be conserved during long time. Polarized beam dynamics in electrostatic accelerators was modelled. The article discussed different methods to solve T–BMT equation numerically, analytical estimations being made as well. Different programs to simulate spin orbit motion of polarized beam were used. It was shown, that spin coherence time could be increased up to several thousand seconds using customly shaped deflectors with sextupole fields. Bibliogr. 17. Il. 4.