Statistical study of undulator radiated power by a classical detection system in the mm-wave regime

The statistics of FEL spontaneous emission power detected with a detector integration time much larger than the slippage time has been measured in many previous works at high frequencies. In such cases the quantum (shot) noise generated in the detection process is dominant. We have measured spontaneous emission in the Israeli electrostatic accelerator FEL (EA-FEL) operating in the mm-wave lengths. In this regime the detector is based on a diode rectifier for which the detector quantum noise is negligible. The measurements were repeated numerous times in order to create a sample space with sufficient data enabling evaluation of the statistical features of the radiated power. The probability density function of the radiated power was found and its moments were calculated. The results of analytical and numerical models are compared to those obtained in experimental measurements.