IPAC'25 - the 16th International Particle Accelerator Conferece

Computing spin-polarization in electron storage rings by a Galerkin method for integrating the Bloch equation of the polarization density

WEPS093

4 Jun 2025, 16:00

2h

Exhibiton Hall A _Salmon (TWTC)

Poster Presentation MC5.D02 Nonlinear Single Particle Dynamics Resonances, Tracking, Higher Order, Dynamic Aperture, Code Developments Wednesday Poster Session

Speaker

Klaus Heinemann (University of New Mexico)

Description

Here we report on one of our approaches to this problem where we model the evolution of the polarization density of an electron bunch by the so-called Bloch equation. The Bloch equation captures key effects like the radiative depolarization effect, the Sokolov-Ternov effect, the Baier-Katkov effect, the kinetic polarization effect and the intrabeam scattering effect. The Bloch equation is a PDE which we aim to integrate numerically using a Galerkin method which was proposed in O. Beznosov’s 2020 UNM dissertation* and is being studied in the ensuing years by K. Heinemann. The algorithm and results of a simple model will be presented.

Funding Agency

Supported by U.S. Department of Energy, Office of Science, under Award Numbers
DE-SC0018008 and DE-SC0025476

Footnotes

• O. Beznosov, PhD Dissertation, Department of Mathematics and Statistics, University of New Mexico, December 2020.