Physics
Scientific paper
Jun 2001
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001aipc..570..889b&link_type=abstract
The fourteenth international spin physics symposium, SPIN2000. AIP Conference Proceedings, Volume 570, pp. 889-889 (2001).
Physics
Storage Rings, Polarized Beams, Beam Dynamics, Collective Effects And Instabilities
Scientific paper
We show how spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters. The spin tune on the closed orbit emerges as an extra frequency of the system which is contained in the Floquet exponent in analogy with the wave vector in Bloch wave functions for electrons in periodic atomic structures. We then show how to analyze spin motion on quasi-periodic synchro-betatron orbits in terms of a generalisation of the Floquet theorem and find that if small devisors are controlled by applying a Diophantine condition, a spin tune can again be defined and that it again emerges as an extra frequency in a Floquet-like exponent. We thereby obtain a deeper insight into the concept of ``spin tune'' and the conditions for its existence. The formalism suggests the use of Fourier analysis to ``measure'' spin tune during simulations of spin motion on synchro-betatron orbits. .
Barber Desmond P.
Ellison James
Heinemann K.
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