Longitudinal single-bunch instability driven by high-frequency impedance is a major challenge for achieving optimal performance in fourth-generation synchrotron light sources and future electron-positron colliders. Accurate simulations of this instability are critical, yet computationally intensive, often requiring millions of macro-particles and fine slicing to resolve bunch density distributions. To address this, we have developed a GPU-accelerated tracking code that enables efficient simulations of longitudinal single-bunch instability. Our solution is specifically designed to run on a desktop computer equipped with a high-performance GPU, providing an accessible and cost-effective alternative to computing clusters.

The in-vacuum undulator (IVU) exhibits exceptionally strong trapped-mode impedance due to its distinctive ridge-loaded waveguide structure and narrow magnetic gap design, which may lead to beam instability issues. This study primarily use the CST wakefield solver to investigate the trapped-mode impedance of the IVUs of the Hefei Advanced Light Facility (HALF). The trapped-mode impedance in the vertical direction is evaluated for both structures, with and without pump ports. Based on the impedance results, two mitigation strategies are proposed: ferrite damping and transition section optimization. Simulation results demonstrate that both strategies effectively reduce the impedance, with the transition section optimization strategy showing superior suppression performance.

In high-intensity storage rings, long-range transverse resistive-wall (RW) wakefield is a dominant source of coupled-bunch instability. Conventional particle tracking algorithms handling this wakefield equire storing bunch-by-bunch and turn-by-turn centroid position histories, resulting in excessive memory consumption, which leads to computational inefficiency. This study proposes fitting the long-range transverse RW wakefield through a sum of exponentials. This method eliminates the need for bunch centroid histories during tracking computations while facilitating GPU-based parallel implementation, thereby significantly enhancing computational efficiency. This work demonstrates the dependence of the fitting performance on the number of exponential functions and the fitting interval.

NSRL recently proposed a future plan to further upgrade the HLS to an EUV diffraction-limited storage ring, named HLS-III. To improve the Touschek lifetime and suppress beam instabilities, HLS-III will employ a bunch-lengthening harmonic cavity system. Based on theoretical analysis, this work evaluates the bunch lengthening performance under five distinct double RF configurations involving different frequencies and harmonic orders, identifies the required harmonic cavity voltage to achieve the target bunch lengthening, and quantifies the corresponding improvement factor in Touschek lifetime. These findings provide valuable guidance for the selection of RF frequencies and the design of harmonic cavity parameters for HLS-III.