Experimental modeling of multiwave diffraction radiation of weakly relativistic electron beam

Using the averaging method for investigations of the statistical characteristics of phase locking with a proportionally integrating filter in the presence of a harmonic signal and white Gaussian noise at the input is examined. A solution of the Fokker-Planck equation is obtained for the energy probability density distribution. Asymptotic formulas are found for the average time until interruption of tracking as well as the locking bandwidth and frequency characteristic of the asynchronous phase-locking operating mode in the presence of noise.