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| Title | Spin Dynamics in Modern Electron Storage Rings: Computational Aspects | |
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| Abstract | In this talk we present some numerical results from our work on the spin polarization in high energy electron storage rings. The motivation of our work is to understand spin polarization in very high energy rings like the proposed Future Circular Collider* (FCC-ee) and Circular Electron Positron Collider** (CEPC). This talk is a supplement to K. Heinemann’s talk and gives further numerical details and results. As discussed in Heinemann’s talk our work is based on the initial value problem of the full Bloch equations*** (FBEs) which in turn determines the polarization vector of the bunch. The FBEs take into account spin diffusion effects and spin-flip effects due to synchrotron radiation. The FBEs are a system of three uncoupled Fokker-Planck equations plus coupling terms. Neglecting the spin flip terms in the FBEs one gets the reduced Bloch equations (RBEs) which poses the main computational challenge. Our numerical approach has three parts. Firstly we approximate the FBEs analytically using the method of averaging, resulting in FBEs which allow us to use large time steps (without the averaging the time dependent coefficients of the FBEs would necessitate small time steps). The minimum length of the time interval of interest is of the order of the orbital damping time. Secondly we discretize the averaged FBEs in the phase space variables by applying the pseudospectral method, resulting in a system of linear first-order ODEs in time. The phase space variables come in d pairs of polar coordinates where d = 1, 2, 3 is the number of degrees of freedom allowing for a d-dimensional Fourier expansion. The pseudospectral method is applied by using a Chebychev grid for each radial variable and a uniform Fourier grid for each angle variable. Thirdly we discretize the ODE system by a time stepping scheme. The presence of parabolic terms in the FBEs necessitates implicit time stepping and thus solutions of linear systems of equations. Dealing with 2d + 1 independent variables p | |
| Footnotes & References | * See http://tlep.web.cern.ch ** See http://cepc.ihep.ac.cn *** See http://ipac2018.vrws.de/papers/thpak144.pdf |
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| Funding | This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0018008. | |
| Paper | download MOPAF04.PDF [0.570 MB / 5 pages] | |
| Slides | download MOPAF04_TALK.PDF [0.993 MB] | |
| Export | download ※ BibTeX ※ LaTeX ※ Text/Word ※ RIS ※ EndNote | |
| Conference | ICAP2018 | |
| Series | International Computational Accelerator Physics Conference (13th) | |
| Location | Key West, FL, USA | |
| Date | 20-24 October 2018 | |
| Publisher | JACoW Publishing, Geneva, Switzerland | |
| Editorial Board | Volker RW Schaa (GSI, Darmstadt, Germany); Kyoko Makino (MSU, East Lansing, MI, USA); Pavel Snopok (IIT, Chicago, IL, USA); Martin Berz (MSU, East Lansing, MI, USA) | |
| Online ISBN | 978-3-95450-200-4 | |
| Received | 20 October 2018 | |
| Accepted | 24 October 2018 | |
| Issue Date | 04 May 2019 | |
| DOI | doi:10.18429/JACoW-ICAP2018-MOPAF04 | |
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