标题： 束流光学斜坡在欠约束晶格设计中的应用：电子-离子对撞机强子存储环冷却段 显示英文标题

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

摘要： 本文提出了重子储存环（HSR）在电子-离子对撞机（EIC）冷却部分的晶格设计和光学梯度提升策略。主要挑战在于可用的调节旋钮超出了光束光学约束。独立优化的注入和顶能量光学通常会产生不连贯的解决方案，使得插值变得不可能。为了解决这个问题，我们提出了两种新方法。第一种是一种中点惩罚方案，通过在中间状态惩罚约束违反来确保梯度路径的连续性。第二种是一种自上而下的方法，通过一种自适应加权方案来调整高能光学到低能，以平衡注入和梯度提升约束。这些解决方案满足了所有束流动力学和硬件限制。这两种方法为系统中的梯度提升提供了一种通用策略，在这些系统中解空间是欠约束的，并且起始和目标配置相距甚远。 显示英文摘要

摘要： 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.