Miles: a new nonperturbative formalism to calculate the invariant spin field in circular accelerators
- 作者：Mane ; S.R.
- 关键词：29.27.Hj ; 29.20.&minus ; c ; 41.75.Lx ; 02.60.Lj ; Polarized beams ; Storage rings ; Dynamical systems
- 刊名：Nuclear Instruments and Methods in Physics Research Section A ; Accelerators ; Spectrometers ; Detectors and Associated Equipment
- 出版年：2003
- 期刊代码：41_01689002
- 类别：ph
- 出版时间：February 11, 2003
- 卷：498
- 期：1-3
- 页码：1-15
- 文件大小：218 K
摘要
We describe a new nonperturbative algorithm called Miles 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.