Beam Stability and Wakefield Control in High-Energy Accelerators via the AMDCF Framework

This paper presents a novel particle physics application of the Adaptive Memory-Driven Coupling Framework (AMDCF). We model the longitudinal beam dynamics in the Large Hadron Collider (LHC) at CERN, specifically addressing energy deviation and beam emittance growth caused by wakefields and RF noise. The AMDCF controller utilizes a non-Markovian memory kernel to represent the historical wakefield effects and a dynamic safety valve to suppress beam blow-up. The simulation demonstrates that the AMDCF framework successfully stabilizes the beam energy (final deviation: -1.66 GeV vs. 4.68 GeV without control) and reduces beam spread by approximately 50% (final spread: 14.80 vs. 29.59). This framework offers a robust mathematical tool for next-generation accelerator control systems.