Parametric Analysis on Enhancement of THz Smith–Purcell Radiation by Two- Layer Grating Structure

Smith–Purcell radiation (SPR) is generated when an electron beam passes near a periodic structure. This study provides a parametric analysis on the enhancement of SPR by improving the coupling of evanescent waves with an electron beam using a two-layer grating structure. Previously, using particle-in-cell (PIC) simulations, two-layer gratings have been shown to enhance SPR growth rates and reduce the starting currents at certain grating parameters. However, our study shows such an enhancement is not universal and its effectiveness depends on the specific operating point and, significantly, the spatial growth rate, which is intricately tied to the grating parameters (e.g., width and heights). Theoretically, the operation frequency of SPR in a two-layer grating is obtained by its cold-tube dispersion relation, and the spatial growth rate is determined by the hot-tube dispersion relation. Higher spatial growth rate directly correlates with lower starting current, both of which show a similar scaling on the dependence of grating parameters. It is found that the use of a second-layer grating shifts the spatial growth rate band toward lower beam energies, enabling higher growth rates and facilitating starting current reduction in SPR for lower beam energies. Our parametric analysis identifies the domain in which a two-layer or a single-layer grating structure should be chosen to enhance SPR and reduce the starting current. This reduction in beam current yields several advantageous effects, such as minimizing beam loss, prolonging cathode lifetime, and mitigating the heating of beam-carrying components.