J un 2 00 0 1 Polarized Protons in HERA
Polarized proton beams at HERA can currently only be produced by extracting a beam from a polarized source and then accelerating it in the three synchrotrons at DESY. In this paper, the processes which can depolarize a proton beam in circular accelerators are explained, devices which could avoid this depolarization in the DESY accelerator chain are described, and specific problems which become important at the high energies of HERA are mentioned. At HERA’s high energies, spin motion cannot be accurately described with the isolated resonance model which has been successfully used for lower energy rings. To illustrate the principles of more accurate simulations, the invariant spin field is introduced to describe the equilibrium polarization state of a beam and the changes during acceleration. It will be shown how linearized spin motion leads to a computationally quick approximation for the invariant spin field and how to amend this with more time consuming but accurate non-perturbative computations. Analysis with these techniques has allowed us to establish optimal Siberian Snake schemes for HERA.
Precession of the Polarization of Particles Moving in a Homogeneous Electromagnetic Field
The problem of the precession of the “spin” of a particle moving in a homogeneous electromagnetic field — a problem which has recently acquired considerable experimental interest — has already been investigated for spin ½ particles in some particular cases.1 In the literature the results were derived by explicit use of the Dirac equation, with the occasional inclusion of a Pauli term to account for an anomalous magnetic moment. On the other hand, following a remark of Bloch2 in connection with the nonrelativistic case, the expectation value of the vector operator representing the “spin” will necessarily follow the same time dependence as one would obtain from a classical equation of motion. To solve the problem for arbitrary spin in the relativistic case, it will thus suffice to produce a consistent set of covariant classical equations of motion. Such equations have been indicated a long time ago by Frenkel3 and are discussed by Kramers.4 These authors use an antisymmetric tensor M as the relativistic generalization of the intrinsic angular momentum observed in the rest-frame of the particle. A formulation in terms of the (axial) four-vector s which describes the polarization in a covariant fashion5 — though basically equivalent — is however much more convenient for our problem. We shall therefore derive first the equations of motion directly in terms of this four-vector s.
The Soviet Home Front, 1941-1945: A Social and Economic History of the USSR in World War II
List of tables and maps Preface Acknowledgements Abbreviations and technical terms Part 1: On the Eve 1. Building Socialism 2. The Great Patriotic War 3. The State in Wartime Part 2: Soviet Society at War 4. Mobilisation 5. Subsistence and Survival 6. The Social Order Part 3: The Productive Effort 7. Fortress of the Rear 8. Labour: The 'Ultimate Bottleneck' 9. 'In Labour as in Combat' 10. Production: The Power of Victory 11. Planning: 'The Military-Economic Staff' Epilogue Tables Important dates References Maps Index