کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1897979 1044617 2007 19 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Polarization fields and phase space densities in storage rings: Stroboscopic averaging and the ergodic theorem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Polarization fields and phase space densities in storage rings: Stroboscopic averaging and the ergodic theorem
چکیده انگلیسی

A class of orbital motions with volume preserving flows and with vector fields periodic in the “time” parameter θθ is defined. Spin motion coupled to the orbital dynamics is then defined, resulting in a class of spin–orbit motions which are important for storage rings. Phase space densities and polarization fields are introduced. It is important, in the context of storage rings, to understand the behavior of periodic polarization fields and phase space densities. Due to the 2π2π time periodicity of the spin–orbit equations of motion the polarization field, taken at a sequence of increasing time values θ,θ+2π,θ+4π,…θ,θ+2π,θ+4π,…, gives a sequence of polarization fields, called the stroboscopic sequence. We show, by using the Birkhoff ergodic theorem, that under very general conditions the Cesàro averages of that sequence converge almost everywhere on phase space to a polarization field which is 2π2π-periodic in time. This fulfills the main aim of this paper in that it demonstrates that the tracking algorithm for stroboscopic averaging, encoded in the program SPRINT and used in the study of spin motion in storage rings, is mathematically well-founded. The machinery developed is also shown to work for the stroboscopic average of phase space densities associated with the orbital dynamics. This yields a large family of periodic phase space densities and, as an example, a quite detailed analysis of the so-called betatron motion in a storage ring is presented.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica D: Nonlinear Phenomena - Volume 234, Issue 2, 15 October 2007, Pages 131–149
نویسندگان
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