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Abstract: To resolve the strong parameter coupling and competing objectives in high-intensity RFQ beam-dynamics design, this paper presents a hierarchical optimization framework based on the Covariance Matrix Adaptation Evolution Strategy. A 14-knot parameterization reduces the problem from more than 600 dimensions to a tractable 42-dimensional optimization problem.Piecewise Cubic Hermite Interpolating Polynomial is then used to ensure physically smooth and monotonic axial profiles. A multi-stage search strategy is employed, including Latin hypercube sampling with K-means clustering for global exploration, CMA-ES local refinement with IPOP restarts, narrow-range re-optimization, coordinate-descent fine-tuning, and Gaussian perturbation search. This framework is applied to design a 162.5 MHz RFQ which will accelerate the He²⁺ from 50 keV/u to 2 MeV/u with 120emA. The beam dynamics simulation results show that the beam transmission efficiency can be improved from 90% to 99% comparing with the conventional four-section design strategy. This work provides an efficient and automated tool for high-intensity RFQ design and can be extended to other high-current accelerator design.
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