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TY - CONF AU - Heinemann, K.A. AU - Appelö, D. AU - Barber, D.P. AU - Beznosov, O. AU - Ellison, J.A. ED - Schaa, Volker RW ED - Makino, Kyoko ED - Snopok, Pavel ED - Berz, Martin TI - Spin Dynamics in Modern Electron Storage Rings: Computational and Theoretical Aspects J2 - Proc. of ICAP2018, Key West, FL, USA, 20-24 October 2018 CY - Key West, FL, USA T2 - International Computational Accelerator Physics Conference T3 - 13 LA - english AB - In this talk we present some numerical and analytical results from our work on the spin polarization in high energy electron storage rings. Our work is based on the initial value problem of what we call the full Bloch equations (FBEs). The solution of the FBEs is the polarization density which is proportional to the spin angular momentum density per particle in phase space and which determines the polarization vector of the bunch. The FBEs take into account spin diffusion effects and spin-flip effects due to synchrotron radiation including the Sokolov-Ternov effect and its Baier-Katkov generalization. The FBEs were introduced by Derbenev and Kondratenko in 1975 as a generalization of the Baier-Katkov-Strakhovenko equations from a single orbit to the whole phase space. The FBEs are a system of three uncoupled Fokker-Planck equations plus two coupling terms, i.e., the T-BMT term and the Baier-Katkov term. Neglecting the spin flip terms in the FBEs one gets what we call the reduced Bloch equations (RBEs). The RBEs are sufficient for computing the depolarization time. The conventional approach of estimating and optimizing the polarization is not based on the FBEs but on the so-called Derbenev-Kondratenko formulas. However, we believe that the FBEs offer a more complete starting point for very high energy rings like the FCC-ee and CEPC. The issues for very high energy are: (i) Can one get polarization, (ii) are the Derbenev-Kondratenko formulas satisfactory at very high energy? If not, what are the theoretical limits of the polarization? Item (ii) will be addressed both numerically and analytically. 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. Seco PB - JACoW Publishing CP - Geneva, Switzerland SP - 127 EP - 133 KW - polarization KW - storage-ring KW - electron KW - radiation KW - synchrotron DA - 2019/01 PY - 2019 SN - 978-3-95450-200-4 DO - DOI: 10.18429/JACoW-ICAP2018-MOPLG03 UR - http://jacow.org/icap2018/papers/moplg03.pdf ER -