Generic conditions for suppressing the coherent synchrotron radiation induced emittance growth in a two-dipole achromat

The effect of the coherent synchrotron radiation (CSR) becomes evident, and leads to increased beam energy spread and transverse emittance dilution, as both the emittance and bunch length of the electron beams are continuously pushed down in present and forthcoming high-brightness light sources and linear colliders. Suppressing this effect is important to preserve the expected machine performance. Methods of the R-matrix analysis and the Courant-Snyder formalism analysis have been proposed to evaluate and to suppress the emittance growth due to CSR in achromatic cells. In this paper a few important modifications are made on these two methods, which enable us to prove that these two methods are equivalent to each other. With the modified analysis, we obtain explicit and generic conditions of cancelling the CSR-driven emittance excitation in a single achromat consisting of two dipoles of arbitrary bending angles. In spite of the fact that the analysis constrains itself in a linear regime, based on the assumption that CSR-induced particle energy deviation is proportional to both theta and rho(1/3), with theta being the bending angle and rho the bending radius, it is demonstrated through ELEGANT simulations that the conditions derived from this analysis are still effective in suppressing the emittance growth when a more detailed one-dimensional CSR model is considered. In addition, it illustrates that the emittance growth can be reduced to a lower level with the proposed conditions than with the other two approaches, such as matching the beam envelope to the CSR kick and setting the cell-to-cell betatron phase advance to an appropriate value.