Khan, D. Raubenheimer, T.O. JACoW Geneva, Switzerland 978-3-95450-179-3 10.18429/JACoW-FEL2017-TUP028 English 300-304 TUP028 ion electron FEL radiation synchrotron Contribution to a conference proceedings 2018 2018-02 https://doi.org/10.18429/JACoW-FEL2017-TUP028 http://jacow.org/fel2017/papers/tup028.pdf In this paper, we describe the development of simplified analytic expressions for the Coherent Synchrotron Radiation's (CSR) root-mean-square induced energy spread, typically found in the bending magnets of short bunch-length charged particle accelerators. The expressions are derived for a Gaussian longitudinal bunch distribution and compared with the full-rigor CSR wakefield integral expressions while entering, traversing and exiting a bending magnet. The validity of the expressions are then tested against ELEGANT with the simulation of an unchirped beam traveling across a bending magnet into a drift section, and the second stage bunch compressor (BC2) of the proposed LCLS-II beamline.