  This paper consists of two main parts regarding Coherent Synchrotron
Radiation (CSR). The first part extends the CSR theory of two particle
interaction from a system of one bending magnet to two bending magnets, where
the wake can leak from the first to the second. The new theory agrees well with
the established simulation code Bmad. The second part of the paper presents the
CSR simulation results on CBETA, the Cornell BNL Energy-Recovery-Linac (ERL)
Test Accelerator, in which the magnets are so close to each other and the new
extended theory becomes important. CBETA is the first multi-turn ERL with
Superconducting Radio Frequency (SRF) accelerating cavities and a Fixed Field
Alternating gradient (FFA) beamline. Simulations show that CSR causes phase
space dilution that becomes more significant as the bunch charge and the number
of recirculation passes increase. Potential ways to mitigate the CSR effects,
including adding vacuum chamber shielding and increasing bunch length, are
being investigated.
