scholarly journals Reevaluation of spin-orbit dynamics of polarized e+e− beams in high energy circular accelerators and storage rings: An approach based on a Bloch equation

2020 ◽  
Vol 35 (15n16) ◽  
pp. 2041003 ◽  
Author(s):  
Klaus Heinemann ◽  
Daniel Appelö ◽  
Desmond P. Barber ◽  
Oleksii Beznosov ◽  
James A. Ellison
Keyword(s):  
Spin Polarization ◽  
High Energy ◽  
Bloch Equation ◽  
Storage Rings ◽  
Spin Orbit ◽  
High Energy Electron ◽  
Numerical Work ◽  
Electron Storage ◽  
Electron Storage Rings ◽  
And Storage

We give an overview of our current/future analytical and numerical work on the spin polarization in high-energy electron storage rings. Our goal is to study the possibility of polarization for the CEPC and FCC-ee. Our work is based on the so-called Bloch equation for the polarization density introduced by Derbenev and Kondratenko in 1975. We also give an outline of the standard approach, the latter being based on the Derbenev–Kondratenko formulas.

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

2019 ◽  
Vol 34 (36) ◽  
pp. 1942032 ◽  
Author(s):  
Klaus Heinemann ◽  
Daniel Appelö ◽  
Desmond P. Barber ◽  
Oleksii Beznosov ◽  
James A. Ellison
Keyword(s):  
Mathematical Model ◽  
Spin Diffusion ◽  
Spin Dynamics ◽  
High Energy ◽  
Bloch Equation ◽  
Storage Rings ◽  
Electron Storage ◽  
Model Based ◽  
Spin Flip ◽  
Electron Storage Rings

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.

Sign in / Sign up

Export Citation Format

Share Document