Problems in Obtaining Polarized E+ and E- Beams and Perspectives for Pep*

BSTRACT A matrix formalism for polarization calculation, as well as its omparison with other methods, is briefly discussed. The prediction for PEAR is compared with experimental measurements. An estimate is offered or the transverse polarization for PEP. Various schemes for obtaining he longitudinal polarization in PEP are studied. \ITRODUCTION As we know, PEP has now been officially dedicated to do high energy nysics experiments. Beam polarization, among other things, will soon be aasured. It is perhaps useful to summarize what we expect theoretically >r the polarization before we make the measurements. I will first describe a matrix method that is used in our polariza-ion calculation. This method is applied to give estimates of the polari-ation expected for SPEAR and PEP. The SPEAR results are compared with ne existing experimental data. Conditions for obtaining a significant cansverse polarization in PEP are discussed. Also included is a study f a few longitudinal polarization schemes as they are applied to PEP. XARIZATION AND DEPOLARIZATION The spin polarization of a stored beam can potentially reach a level E 92%. The mechanism1 for this is that, during the process of synchro-ron radiation in a magnetic field, the spin transition rate from the up tate to the down state is not equal to the transition rate from the down tate to the up state. The beam accumulates a net polarization as a esult. It turns out that the very mechanism that gives rise to polarization, amely the synchrotron radiation, is also the main cause for depolariza-ion. 2y3p4 As an electron emits a synchrotron photon, it receives a ecoil perturbation which excites its subsequent oscillatory orbital mo-ions. The electron then sees a perturbing electromagnetic field, which s modulated by these orbital oscillation frequencies, causing its spin 3 precess. Summing over the uncorrelated photon emission events results n a diffusion of spin direction and hence a depolarization of the elec-ron. This depolarization is especially strong when the spin motion is oupled to the oscillatory orbital motions under resonant conditions. The achieved level of polarization is determined by an equilibrium etween the Polarizing and the depolarizing effects of the synchrotron adiation. The strength of the polarizing effect is already well-kn0wn.l he depolarization strength, torage ring operation. on the other hand, depends on details of the ne needs to know how the In order to calculate the depolarization strength spin and orbital degrees of freedom of an