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