Spin Motion and Resonances in Accelerators and Storage Rings Page: 2 of 19
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Spin Motion and Resonances
in Accelerators and Storage Rings
E D Courant
Some of the basic aspects of the spin dynamics of accelerators and storage rings are reviewed.
Since the components of spin parallel and perpendicular to the particle velocity behave different-
ly it is desirable to reformulate the equations of spin motion in a frame of reference that exhibits
this difference explicitly. The conventional treatment employs a coordinate system derived from
a reference orbit. An alternate coordinate system, based on the actual trajectory of the particle,
leads to simplified equations of spin motion but, contrary to a conjecture presented in a previous
note, resonance strengths calculated by the conventional and the revised formalisms are identic-
al, as pointed out by Kondratenko. Resonances induced by radiofrequency dipoles or solenoids
are also treated; with rf dipoles it is essential to consider not only the direct effect of the dipole
but also the contribution from oscillations induced by it.
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Courant,E. Spin Motion and Resonances in Accelerators and Storage Rings, report, January 1, 2008; United States. (https://digital.library.unt.edu/ark:/67531/metadc896004/m1/2/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.