Induced Smith–Purcell radiation

Excitation of induced coherent Smith–Purcell (SP) radiation by relativistic magnetized electron beam in the absence of the resonator is considered within the framework of the dispersion equation. We have found that the dispersion equation for the SP instability is a quadratic equation for frequency. The first-step approximation for solution of the dispersion equation, giving the SP-spectrum of frequency, corresponds to the mirror boundary case, when the electron beam propagates above a plane metal surface (mirror). It was found that the conditions for both the Thompson and the Raman regimes of excitation do not depend on beam current and depend on the height of the beam above the grating surface. The growth rate of the instability in both cases is proportional to the square root of the electron beam current. No feedback is needed to provide the coherent emission.