The electron beam instability in a one-dimensional cylindrical photonic crystal

TL;DR

This paper investigates the radiative instability of a relativistic electron beam in a cylindrical photonic crystal, revealing a sharp change in instability behavior that enhances radiation generation efficiency.

Contribution

It demonstrates a novel instability behavior near dispersion roots, leading to improved radiation amplification in photonic crystal systems compared to traditional devices.

Findings

Instability increment proportional to $ ho^{1/4}$ near degeneracy points.

Enhanced radiation generation efficiency in the studied system.

Numerical calculations confirm the theoretical predictions.

Abstract

The radiative instability of the relativistic electron beam in a periodic dielectric-filled cylindrical waveguide is considered. The dependence of the beam instability increment on the radiated wave frequency near the region of dispersion equation roots degeneracy is studied. It is shown that sharp change in the instability of the beam under the conditions of two-wave diffraction in Compton generation regime, making the increment proportional to the fourth root from the beam density $\rho^{1/4}$ in contrast to conventional law $\rho^{1/3}$, brings radiation generation (amplification) in the considered system to be essentially improved in comparison with conventional devices (BWO, TWT, FEL etc). Numerical calculations of the instability increment for various parameters of the system are performed.