Enabling arbitrary correlations in beam phase space via curve matching

Beam manipulations require precise control of phase space correlations. Gwanghui's previous work introduced a method for generating arbitrary correlations using Fourier series and cosine sums with transverse wigglers. However, accurately controlling the wigglers to match a desired correlation curve remains challenging, as it involves optimizing parameters like amplitude, phase, and period. Existing optimization methods are computationally intensive and prone to local minima. We address these limitations with a deterministic gradient-based optimization process. Using a differentiable error function, we efficiently perform gradient backpropagation to identify optimal parameters. To minimize the number of wigglers while maintaining accuracy, we adopt a recursive strategy: starting with a single wiggler and iteratively adding one at a time, using results from prior steps as seeds. This approach accelerates optimization and reduces computational demands. Building on this method, we design a feedback control strategy for real-time correlation generation with transverse wigglers, enabling precise, flexible beam manipulation and new possibilities in accelerator physics.