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Title: The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects

Journal Article · · International Journal of Modern Physics A
 [1];  [2];  [3];  [1];  [1]
  1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA
  2. Department of Applied Mathematics, University of Colorado Boulder, Boulder, CO 80309-0526, USA
  3. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA; DESY, Hamburg 22607, Germany
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In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov–Ternov effect with its Baier–Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev–Kondratenko formulas. For our numerical and analytical studies of the FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

Research Organization:
Univ. of New Mexico, Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0018008
OSTI ID:
1803219
Journal Information:
International Journal of Modern Physics A, Vol. 34, Issue 36; ISSN 0217-751X
Publisher:
World Scientific
Country of Publication:
United States
Language:
English

References (9)

Nuclear Induction journal October 1946
Spin transport, spin diffusion and Bloch equations in electron storage rings journal May 2001
The method of averaging in beam dynamics conference January 1995
Planar undulator motion excited by a fixed traveling wave: Quasiperiodic averaging, normal forms, and the free electron laser pendulum journal September 2013
Evaluation of beam distribution parameters in an electron storage ring journal February 1979
Evaluation of radiative spin polarization in an electron storage ring journal February 1981
Spectral Methods book January 2006
A Practical Guide to Pseudospectral Methods book December 2009
Additive Runge–Kutta schemes for convection–diffusion–reaction equations journal January 2003

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Related Subjects

Physics