A Realistic Proportional-Integral RF Feedback Model for Longitudinal Beam Dynamics Simulation

TL;DR

The paper presents a physics-based, GPU-accelerated RF feedback model for longitudinal beam dynamics in storage rings, implemented in STABLE_HTL. It discretizes the generator current into pulse charges and updates cavity voltage per RF cycle to capture realistic beam–cavity interactions. The model comprises a three-stage digital I/Q PI feedback chain (pre-PI averaging, discrete-time PI control, and post-PI current synthesis) with a finite system delay, enabling efficient parameter scans of PI gains and loop delays, and is applicable to single- and multi-RF configurations including harmonic cavities. This framework facilitates accurate stability studies and practical insights for designing DLLRF systems in modern fourth-generation light sources.

Abstract

Modern fourth-generation storage ring light sources predominantly utilize digital I/Q-based proportional-integral (PI) feedback for their radio-frequency (RF) systems. This paper introduces a dedicated PI feedback model implemented in the STABLE tracking code to enable accurate and fast longitudinal beam dynamics simulations. The model's key innovation lies in its treatment of the continuous generator current, which is discretized into electron-bunch-like charge pulses, while the cavity voltage is refreshed on an RF-cycle basis. This methodology offers a more physically accurate model of the beam-cavity-feedback coupling, providing a versatile tool for precise longitudinal beam dynamics studies in single- and multi-rf configurations.

Figures (3)

• Figure 1: Discretization of a cosine generator current into equivalent pulsed charges.
• Figure 2: Simplified block diagram of the RF system at SSRF xia2019transfer.
• Figure 3: Schematic of the modeled LLRF control system for simulation.