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Description
High-intensity hadron linear accelerators transporting a 1 A deuteron beam operate in regimes dominated by severe space-charge forces, where preserving beam emittance and suppressing halo formation represent critical design challenges. In fixed-geometry superconducting lattices, strong initial space-charge tune depression is accompanied by evolving phase advances along the acceleration path. A transverse space-charge-depressed 4D matching optimization (𝛼𝑥,𝛽𝑥,𝛼𝑦,𝛽𝑦) was performed using the Nelder-Mead simplex algorithm coupled with the 3D PIC code TRACK, demonstrating robust transverse control.
To resolve longitudinal bunching instabilities and unconfined phase excursions, a tailored parabolic synchronous phase profile 𝜙𝑠(𝑧) was implemented. This phase smoothing effectively mitigates non-adiabatic transitions, stabilizes longitudinal motion, and significantly suppresses halo formation. By mapping the depressed transverse (𝜎𝑡) and longitudinal (𝜎𝑙) tunes onto Hofmann stability diagrams, residual emittance evolution is shown to originate from space-charge-driven structural resonance crossings (primarily 𝜎𝑡=𝜎𝑙). This coupling drives continuous energy exchange between planes, causing the longitudinal-to-transverse equipartition ratio to increase steadily towards the exit. These results demonstrate that combining precise 4D core matching with tailored RF phase profiles offers a robust framework for high-current LINAC design, paving the way for future magnetic tapering strategies.