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Evaluating the energy spread growth due to radiation is crucial for the design of steady-state microbunching (SSMB) insertion section. This study systematically benchmarks a classical analytical formula against three-dimensional numerical simulations to validate its accuracy under varying initial energy spreads. Our findings reveal that while the formula provides reliable estimations for beams with small initial energy spreads, its predictions deviate significantly as the initial energy spread increases. Such discrepancies arise because larger initial energy spreads amplify three-dimensional effects and nonlinear beam dynamics, which compromise the idealized analytical model. This study shows that
comprehensive 3D simulations are indispensable for robust and accurate SSMB insertion section design.
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