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TY - CONF AU - Wang, G. AU - Blaskiewicz, M. AU - Litvinenko, V. ED - Petit-Jean-Genaz, Christine ED - Kim, Dong Eon ED - Kim, Kyung Sook ED - Ko, In Soo ED - Schaa, Volker RW TI - Analytical Studies of Ion Beam Evolution under Coherent Electron Cooling J2 - Proc. of IPAC2016, Busan, Korea, May 8-13, 2016 C1 - Busan, Korea T2 - International Particle Accelerator Conference T3 - 7 LA - english AB - In the presence of coherent electron cooling (CeC), the evolution of the longitudinal profile of a circulating ion bunch can be described by the 1-D Fokker-Planck equation. We show that, in the absence of diffusion, the 1-D equation can be solved analytically for certain dependence of cooling force on the synchrotron amplitude. For more general cases, we solved the 1-D Fokker-Planck equation numerically and the numerical solutions have been used to benchmark our simulation code as well as providing fast estimations of the cooling effects. PB - JACoW CP - Geneva, Switzerland SP - 1247 EP - 1249 KW - ion KW - electron KW - synchrotron KW - simulation KW - scattering DA - 2016/06 PY - 2016 SN - 978-3-95450-147-2 DO - 10.18429/JACoW-IPAC2016-TUPMR009 UR - http://jacow.org/ipac2016/papers/tupmr009.pdf ER -