NEW EXPERIMENTAL RESULTS FOR INTERMEDIATE- AND HIGH-ENERGY POLARIZATION ASYMMETRY

We review recent experimental data on polarization asymmetry at intermediate and high energies. We include phenomenological interpretations of the data. In this review we examine the present status of polarization physics at intermediate and high energies. Special attention is directed to controversial experimental results as well as interpretations of the data. Our objective is to contribute toward the planning of future experimental facilities and experiments. For more detailed description and discussion of various experiments and phenomenological interpretations, we provide extensive references. Polarized-beam programs at the SLC (Stanford Linear Collider), HERA (Hadron Electron Ring Accelerator, and EPC (Electron Positron Collider) are not included in this review. Neither do we discuss the technologies of polarized ion sources, polarized targets, polarized beams, or accelerators.

Linear stability analysis of a class of solutions of the filament model for a stationary field electron ring accelerator

The stability of two of the short time scale solutions obtained in the filament model for a stationary field electron ring accelerator is studied by means of a linearized perturbation on the electron and ion distribution functions. The Vlasov equations for the electrons and ions are coupled. The coupling of these equations results in a Fredholm integral equation which can be converted into an infinite system of linear equations. A stability criterion is then obtained from the zeros of the truncated determinants of the coefficients of the infinite system. One of the equilibrium solutions, for which the ion density in phase space is a monotonic non-increasing function of the unperturbed ion Hamiltonian, is entirely stable. The other solution, for which this monotonicity does not hold, may be unstable, but turns out to be stable provided that both the non-monotonicity parameter ∈ and the ratio of the ion period to the electron period are not too large. In the nonmonotonic case, the ion density in physical space also does not drop off to zero monotonically from the centre of the ring. For the unstable cases, the instability is driven by a ‘spike’ in the phase-space ion density located at the maximum value of the unperturbed ion Hamiltonian.

Filament model for a stationary field electron ring accelerator: the generalized Bernstein—Green—Kruskal problem

The longitudinal behaviour of the electron ion ring in a stationary electron ring accelerator (ERA) is studied by means of a filament model which neglects the radial thickness of the ring. There are two widely different time scales (short or STS of the order of a bounce time in the ring, and long or LTS) that characterize the system. The Vlasov equations for a system which is stationary on the STS can be solved in the ion-pickup region by an approximation in which each species of particle essentially sees only a potential well formed by the other species. This gives a generalization of the classical Bernstein–Greene–Kruskal (BGK) problem, in which both species move in the same potential. The conditions under which this generalized BGK problem is well defined are given, and broad classes of quasi-equilibria (i.e. equilibria on the STS) are obtained. The time dependence on the LTS of some of these quasi-equilibria is then obtained by invoking charge conservation, momentum conservation and the adtained invariance of longitudinal action integrals. The stability of these quasi-equilibria (i.e. their behaviour under time-dependent perturbations on the STS) is deferred to a subsequent paper.