Determination of detector frequency ranges for an electron bunch length monitor for AWAKE Run 2c

The AWAKE 150 MeV electron beamline at CERN is used to provide a witness bunch for plasma wakefield acceleration, with a bunch length shorter than the plasma wavelength to ensure efficient capture and acceleration. To accomplish this, a real-time, non-invasive bunch length monitor is essential. A monitor is being studied to calculate the RMS bunch length by measuring coherent Cherenkov diffraction radiation with three Schottky diodes across different frequency ranges. In this paper, we present theoretical bunch length calculations based on the polarization current approach (PCA) to determine the appropriate frequency ranges for the Schottky diodes. Results show that while higher frequencies are more sensitive to variations in bunch length, they are also influenced by the skewness of a Gaussian longitudinal bunch profile.