[en] I extend and update earlier work, summarised in an earlier paper (D.P. Barber, M. Voigt, AIP Conference Proceedings 1149 (28)), whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.

[en] A report on the status of the HERA project is presented. The machine, the proposed experiments and the plans for longitudinal polarization are described. (orig.)

[en] We extend the closed orbit correction formalism of an earlier paper (1985) to take into account the notion that the polarization in electron storage rings may be more sensitive to tilts, δn vector, of the equilibrium spin axis in some parts of the lattice than in others. This is achieved by means of a periodic weighting function. The formalism requires some modifications of the computer program already developed for implementing the ideas given in the cited paper. (orig./HSI)

[en] Here, and in a sequel, we invoke the invariant spin field to provide an in-depth study of spin motion at and near low order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarization at and near so-called snake resonances in proton storage rings. (orig.)

[en] The two real canonical spin variables α and β introduced in an earlier paper are combined with the six canonical variables of coupled synchro-betatron motion to form a system of eight canonical spin-orbit variables in which spin and orbital otion are treated on the same level. In these variables one turn maps are origin preserving and the usual techniques of canonical perturbation theory can be applied. By writing the Hamiltonian in normal form the spin detuning terms as well as the so called vector n-axis which is needed in the theory of radiative polarization can be constructed. The equations derived are valid for arbitrary velocity of the particles (below and above transition energy). (orig.)

[en] This article provides a pedagogical review of spin rotators and Siberian Snakes used in the manipulation and attainment of stored high energy spin polarized beams (SHESPB)

[en] We investigate the motion of protons of arbitrary energy (below and above transition energy) in a storage ring. The motion is described both in terms of the fully six-dimensional formalism with the canonical variables x, p_x, z, p_z, σ = s - v₀ . t, η = ΔE/E₀ = p_σ and in terms of a dispersion formalism with new variables x, p_x, z, p_z, σ, p_σ. Since the dispersion function is introduced into the equations of motion via a canonical transformation the symplectic structure of these equations is completely preserved. In this formulation it is then possible to define three uncoupled linear (unperturbed) oscillation modes which are described by phase ellipses. Perturbations manifest themselves as deviations from these ellipses. The equations of motion are solved within the framework of the fully six-dimensional formalism. (orig.)

[en] In the following report we begin to reformulate work by Derbenev on the behaviour of coupled quantized spin-orbit motion. To this end we present a classical symplectic treatment of linear and non-linear spin-orbit motion for storage rings using a fully coupled eight-dimensional formalism which generalizes earlier investigations of coupled synchro-betatron oscillations by introducing two additional canonical spin variables which behave, in a small-angle limit, like those already used in linearised spin theory. Thus in addition to the usual x-z-s couplings, both the spin to orbit and orbit to spin coupling are described canonically. Since the spin Hamiltonian can be expanded in a Taylor series in canonical variables, the formalism is convenient for use in 8-dimensional symplectic tracking calculations with the help, for example, of Lie algebra or differential algebra for the study of chaotic spin motion, for construction of spin normal forms and for the study of the effect of Stern-Gerlach forces. (orig.)

[en] Published in summary form only

[en] In the following report we investigate stochastic particle motion in electron-positron storage ring in the framework of a Fokker-Planck treatment. The motion is described by using the canonical variables χ, p_χ, z, p_z, σ = s - cxt, p_σ = ΔE/E₀ of the fully six-dimensional formalism. Thus synchrotron- and betatron-oscillations are treated simultaneously taking into account all kinds of coupling (synchro-betatron coupling and the coupling of the betatron oscillations by skew quadrupoles and solenoids). In order to set up the Fokker-Planck equation, action-angle variables of the linear coupled motion are introduced. The averaged dimensions of the bunch, resulting from radiation damping of the synchro-betatron oscillations and from an excitation of these oscillations by quantum fluctuations, are calculated by solving the Fokker-Planck equation. The surfaces of constant density in the six-dimensional phase space, given by six-dimensional ellipsoids, are determined. It is shown that the motion of such an ellipsoid under the influence of external fields can be described by six generating orbit vectors which may be combined into a six-dimenional matrix B(s). This 'bunch-shape matrix', B(s), contains complete information about the configuration of the bunch. Classical spin diffusion in linear approximation has also been included so that the dependence of the polarization vector on the orbital phase space coordinates can be studied and another derivation of the linearized depolarization time obtained. (orig.)