Transition radiation on a superlattice in finite thickness plate generated by two acoustic waves

Forward transition radiation from relativistic electrons is investigated in an ultrasonic superlattice excited in a finite thickness plate by two acoustic waves. In the quasi-classical approximation formulae are derived for the vector potential of the electromagnetic field and for the spectral-angular distribution of the radiation intensity. Zone structures appear in the plate, which makes it possible (by an appropriate choice of the frequencies of the two acoustic waves) to control the spectral-angular distribution of the radiation through changes in the parameters of the medium. The acoustic waves generate new resonance peaks in the spectral and angular distribution of the radiation intensity. The heights of the peaks can be tuned by choosing the parameters of the acoustic waves. Numerical examples are presented for a plate of fused quartz.