M iles: a new nonperturbative formalism to calculate the invariant spin field in circular accelerators

We describe a new nonperturbative algorithm called M iles to calculate the invariant spin field in circular accelerators. It is a map-based algorithm, based exclusively on the field-theoretic transformation of a vector field under the flow in the orbital phase-space. We employ the method to derive t...

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Bibliographic Details
Published inNuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment Vol. 498; no. 1; pp. 1 - 15
Main Author Mane, S.R.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2003
Subjects
Dynamical systems
Polarized beams
Storage rings
29.20.−c
29.27.Hj
41.75.Lx
02.60.Lj
Polarized beams
Storage rings
Dynamical systems
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ISSN0168-9002
1872-9576
DOI10.1016/S0168-9002(02)01992-7

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Summary:We describe a new nonperturbative algorithm called M iles to calculate the invariant spin field in circular accelerators. It is a map-based algorithm, based exclusively on the field-theoretic transformation of a vector field under the flow in the orbital phase-space. We employ the method to derive the exact analytical solution for a model of a planar ring with one Siberian Snake and a single resonance driving term. This model is in some sense the classic problem in the field. The solution contains new types of mathematical functions, which we call “sine-factorial” and “sine-Bessel” functions. We also display the exact analytical solutions for several other storage ring models, including rings with two or more Snakes. We compare our method against other formalisms, including numerical tracking programs.
ISSN:0168-9002
1872-9576
DOI:10.1016/S0168-9002(02)01992-7