Longitudinally Polarized Colliding Beams

The feasibility of experiments with the polarized colliding beams expands significantly possibilities of getting information on fundamental interactions. Even the use of the transversely polarized beams enables getting the more reliable and clear definition of spins for the intermediate states and final particles,1p2 as well as to introduce the precise absolute energy scale.3-s But only the use of the longitudinally polarized colliding beams with particles of certain helicities, enables one to get basically new information. This circumstance forced us, in Novosibirsk, commencing from 1969, to develop the principles and structures of the storage rings which provide at a given azimuth the stability of any spin direction needed, including longitudinal direction617 (see also Refs. 8 and 9). 1. In the storage ring of "conventional" type which magnetic field along the equilibrium closed orbit has a constant, for example, vertical z-direction (the field sign can vary) the spin orientation conserved from turn to turn is z-direction. In other words, when particles are moving along the equilibrium orbit their spins precess around this direction and the spin projection on this direction is constant. For example, if initially the particle spin has z-projection +k, this value does not change with time (of course, unless either dissipative or diffusional processes will affect). The projection -f will be conserved just the same way. This statement is valid if the precession frequency (because of anomalous part of a particle magnetic moment) is not resonant to the frequency of orbital rotation along the equilibrium orbit. The similar situation became valid also for the case of the storage ring with arbitrary oriented magnetic fields.6p7 Namely, along any closed orbit there always is such a unit vector $(e), the projection on which of the spins of particles moving along this orbit has a constant value. In particular, if the particle spin is oriented along I, at some initial azimuth 8,, this spin will be oriented along (different in direction) z,(e) at any other azimuth 0 at any turn. Selecting the shape of closed orbit which curve at any azimuth unambiguously determine the transverse magnetic field value for this azimuth and (or) introducing the azimuthal distribution of the longitudinal magnetic field one can achieve the required orientation Go for the necessary azimuth; this orientation is the same at the sections with zeroth magnetic field on the closed orbit. In particular, one can achieve the longitudinal orientation z. at the storage ring sections where colliding beam interactions are occurred. In this case, if the means are made polarized one can obtain interaction of particles with certain helicities. Varying the polarization sign for one or both beams one can consequently vary helicities of interacting particles. Let us note that for studying, for exampie, the interactions which do not conserve the spatial parity, in principle, it is enough to have even one of interacting beams polarized (with the controllable level of polarization). Though, of course, experiments can be performed with better purity if there is a possibility to control the polarization in its sign and level for both beams. 2. Having in mind the possibility to achieve the desired behavior of the spin along the equilibrium orbit the first question is to find the spin motion while the particle motion deviates from the equilibrium one, i.e. in the presence of energy and betatron oscillations in the beam. This problem is "dynamic" part of the general question of conservation of the beam polarization level in a storage ring. The particle motion with deviation of their orbital motion g(t), determined by initial conditions, from the equilibrium motion described by $,[0(t)] can be presented by