Structure study of a dielectric laser accelerator with discrete translational symmetry

The dielectric laser accelerator (DLA) is a promising technology for achieving high-gradient acceleration in a compact design. Its advantages include ease of cascading and an energy gain per unit distance which can exceed that of conventional accelerators by two orders of magnitude. This paper establishes rules for efficient particle acceleration using dielectric structures based on basic equations, proposes a design principle for DLA structures with clear physical images and verifies the accuracy of the corresponding formula for energy gain. DLA structures with different specifications, materials and geometric shapes are constructed, and the achievable acceleration gradient is calculated. Our results demonstrate that effective acceleration can be achieved when the electric field sensed by particles in the acceleration cavity has zero frequency, which provides a powerful method for designing such devices. Furthermore, we demonstrate that the simplified formula for calculating energy gain presented in this paper can accurately determine the energy gain of particles during the design of acceleration structures using a dielectric accelerator.