Induced Smith–Purcell radiation

Abstract

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.

Diffusive radiation in the infrared region

“…Therefore, making a stack with such thin plates and vacuum within them will be very difficult. On the other hand, such a situation can be realized when a charged particle slides over a rough metallic surface [23][24][25][26][27]. In this case, the randomly located hills and valleys will serve as plates and vacuum spacing between them, respectively.…”

Smith–Purcell radiation amplifier

“…, where = ± ± ± p 0; 1; 2; 3, ..., and then integrating over coordinate x within the interval (0;d) we obtain an infinite system of algebraic equations for the partial amplitudes P n (see equation ( 13) of [8]): (13) with the following coefficients…”

“…In the next section, we present the basic equations that describe the periodic solutions for a self-consistent system of a couple of Maxwell equations and equations for the medium. Then in section III, as an important example of applications of our early derived results [8], we present a small signal gain of the SP FEL signal for the case of a rectangular grating. In section IV we discuss the obtained results.…”

“…In [8][9][10] it was found that the dispersion equation describing the induced SP instability is a quadratic equation for frequency; and the zero-order approximation for solution of the equation, which gives the SP spectrum of frequency, corresponds to the mirror boundary case, when the electron beam propagates above 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.…”