Some models of spin coherence and decoherence in storage rings
Abstract
I present some simple exactly solvable models of spin diffusion caused by synchrotron radiation noise in storage rings. I am able to use standard stochastic differential equation and FokkerPlanck methods and I thereby introduce, and exploit, the polarization density. This quantity obeys a linear evolution equation of the Bloch type, which is, like the FokkerPlanck equation, universal in the sense that it is independent of the state of the system. I also briefly consider Bloch equations for other local polarization quantities derived from the polarization density. One of the models chosen is of relevance for some existing and proposed low energy electron (positron) storage rings which need polarization. I present numerical results for a ring with parameters typical of HERA and show that, where applicable, the results of my approach are in satisfactory agreement with calculations using SLIM. These calculations provide a numerical check of a basic tenet of the conventional method of calculating depolarization using the naxis. I also investigate the equilibrium behaviour of the spin ensemble when there is no synchrotron radiation. Finally, I summarize other results which I have obtained using the polarization density and which will be published separately.
 Publication:

arXiv eprints
 Pub Date:
 September 1997
 DOI:
 10.48550/arXiv.physics/9709025
 arXiv:
 arXiv:physics/9709025
 Bibcode:
 1997physics...9025H
 Keywords:

 Physics  Accelerator Physics;
 Mathematical Physics
 EPrint:
 93 pages, 13 Postscript figures, Latex