Improved calibration of rf cavities for relativistic electron beams: Effects of secondary corrections and experimental verification

In the aspect of longitudinal beam bunching, bunching strength can be controlled by RF cavity phase and voltage. However, these machine parameters are different from those that interact with itself. order to gain control beam-cavity interaction, calibration must performed. Furthermore, it relies on fitting energy versus a function. Under conventional assumption relativistic conditions, function is first harmonic sinusoidal (a period 2{\pi}). this expression insufficient for high-voltage cavity. Due acceleration inside cavity, an bias second should included modify function, even electron beam. paper, we will derive modification provide comparison both Coherent Electron Cooling Experiment IMPACT-T simulation, respectively.