Beam Optics Ramping in Under-Constrained Lattice Design: Application to Electron-Ion Collider Hadron Storage Ring Cooling Section

Abstract

This paper presents the lattice design and optics ramping strategy for the cooling section of the Hadron Storage Ring (HSR) at the Electron-Ion Collider (EIC). The main challenge is that available tuning knobs exceed beam-optics constraints. Independently optimized injection and top-energy optics often yield disconnected solutions, making interpolation impossible. To address this, we propose two new methods. The first is a midpoint-penalty scheme that ensures ramping path continuity by penalizing constraint violations at intermediate state. The second is a top-down approach that adapts high-energy optics to low energy, guided by an adaptive weighting scheme to balance injection and ramping constraints. The solutions meet all beam dynamics and hardware limits. The two methods offer a general strategy for ramping in systems where the solution space is under-constrained and the starting and target configurations are far apart.

arXiv comment10 pages, 10 figures