dorsal/arxiv
View SchemaQuasiperiodic spin-orbit motion and spin tunes in storage rings
| Authors | D. P. Barber, J. A. Ellison, K. Heinemann |
|---|---|
| Categories | |
| ArXiv ID | physics/0412157 |
| URL | https://arxiv.org/abs/physics/0412157 |
| DOI | 10.1103/PhysRevSTAB.7.124002 |
| Journal | Phys.Rev.ST Accel.Beams 7 (2004) 124002 |
Abstract
We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. 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 and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.
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"abstract": "We present an in-depth analysis of the concept of spin precession frequency\nfor integrable orbital motion in storage rings. Spin motion on the periodic\nclosed orbit of a storage ring can be analyzed in terms of the Floquet theorem\nfor equations of motion with periodic parameters and a spin precession\nfrequency emerges in a Floquet exponent as an additional frequency of the\nsystem. To define a spin precession frequency on nonperiodic synchro-betatron\norbits we exploit the important concept of quasiperiodicity. This allows a\ngeneralization of the Floquet theorem so that a spin precession frequency can\nbe defined in this case too. This frequency appears in a Floquet-like exponent\nas an additional frequency in the system in analogy with the case of motion on\nthe closed orbit. These circumstances lead naturally to the definition of the\nuniform precession rate and a definition of spin tune. A spin tune is a uniform\nprecession rate obtained when certain conditions are fulfilled. Having defined\nspin tune we define spin-orbit resonance on synchro--betatron orbits and\nexamine its consequences. We give conditions for the existence of uniform\nprecession rates and spin tunes (e.g. where small divisors are controlled by\napplying a Diophantine condition) and illustrate the various aspects of our\ndescription with several examples. The formalism also suggests the use of\nspectral analysis to ``measure\u0027\u0027 spin tune during computer simulations of spin\nmotion on synchro-betatron orbits.",
"arxiv_id": "physics/0412157",
"authors": [
"D. P. Barber",
"J. A. Ellison",
"K. Heinemann"
],
"categories": [
"physics.acc-ph"
],
"doi": "10.1103/PhysRevSTAB.7.124002",
"journal_ref": "Phys.Rev.ST Accel.Beams 7 (2004) 124002",
"title": "Quasiperiodic spin-orbit motion and spin tunes in storage rings",
"url": "https://arxiv.org/abs/physics/0412157"
},
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