  The coherent synchrotron radiation (CSR) effect in a bending path plays an
important role in transverse emittance dilution in high-brightness light
sources and linear colliders, where the electron beams are of short bunch
length and high peak current. Suppression of the emittance growth induced by
CSR is critical to preserve the beam quality and help improve the machine
performance. It has been shown that the CSR effect in a double-bend achromat
(DBA) can be analyzed with the two-dimensional point-kick analysis method. In
this paper, this method is applied to analyze the CSR effect in a triple-bend
achromat (TBA) with symmetric layout, which is commonly used in the optics
designs of energy recovery linacs (ERLs). A condition of cancelling the CSR
linear effect in such a TBA is obtained, and is verified through numerical
simulations. It is demonstrated that emittance preservation can be achieved
with this condition, and to a large extent, has a high tolerance to the
fluctuation of the initial transverse phase space distribution of the beam.
