Analytical model of the streaking process in a single split-ring resonator for sub-ps electron pulse

Abstract

The use of THz-driven split-ring resonator (SRR) for temporal characterization of sub-ps electron pulse has been proposed for a few years and was experimentally demonstrated recently. The dependence of the streaking performance on the dimensions of SRR is to be further discussed here. For SRRs with simple structures, the resonance frequency can be derived through an equivalent LC circuit, which reveals the quantitative dependence of the resonance frequency on its geometric dimensions. Besides, the geometric dimensions of SRR determine its streaking region and field enhancement factor, which have a substantial impact on the streaking process and the temporal resolution. We analyze the existing equivalent LC circuit model for SRRs and propose an analytical beam dynamics model to describe the streaking process of electron pulse. Formulas for the streaking angle, the post-streaking beam divergence, the spot size on the detector and the temporal resolution of SRR are derived. The analytical results are compared with the particle tracking simulation to discuss its applicability. The restriction of the bunch length measurement due to the space charge effect are discussed as a complement to the analytical model. This analytical model provides a link between the temporal resolution and the geometric dimensions of SRR, which can be utilized for performance evaluation and structural optimization.