A well-corrected lattice is essential for the performance of any modern synchrotron light source. Beyond the standard motivations -- such as preserving optimized nonlinear dynamics and maintaining sufficient dynamic and momentum acceptance -- accurate lattice correction is particularly important in APS-U for achieving the predicted emittance reduction associated with insertion-device radiation. In APS-U, lattice characterization relies on response-matrix fitting. Simulations performed during the design phase indicated that the achievable accuracy of such measurements would be limited to the few-percent level, thereby constraining the ultimate lattice correction precision. This paper presents the typical results of the APS-U lattice correction, examines approaches to improving lattice measurement accuracy, and discusses the long-term stability of the corrected lattice.

The Advanced Photon Source (APS) continues to advance short-period superconducting undulator (SCU) technology using NbTi, Nb₃Sn, and 2G-HTS. Recent 16.5-mm-period NbTi SCUs (K ≈ 1.63) incorporate design changes to improve coil-to-ground insulation and enhanced quench protection, enabling training up to 500 A with fewer than fifteen quenches in 1.5-m magnets, ensuring reliable operation at about 430 A. Mechanical shimming reduced RMS phase errors below 5°. Eight new NbTi SCUs are planned for the APS, with two being assembled for installation in May 2026. The first (λu=18 mm) Nb₃Sn SCU successfully delivered high-energy X-rays for three months, demonstrating suitability for user operations. Building on this, a 14-mm-period, conduction-cooled, cryogen-free Nb₃Sn SCU (K > 2) is under development using a modified cryostat. Short 0.15-m prototypes have been fabricated, are being quench trained in liquid helium, and will be tested in a small helium-free test cryostat before scaling to longer lengths. In parallel, force-balanced 2G-HTS SCU concepts (K > 1.5) with λu ~10 mm are being explored to achieve higher magnetic fields. This presentation will highlight recent APS SCU developments.

Precise reconstruction of the beam sigma matrix is critical for transport-line modeling and injection optimization. Our earlier work demonstrated that the differentiable simulation framework Cheetah enables gradient-based recovery of the 5×5 transverse sigma matrix at the APS-U BTS transport line using quadrupole scans. In this paper, we extend the method to improve efficiency and robustness. We introduce a generalized formulation that incorporates multi-screen measurements, providing increased stability in realistic lattice configurations. The differentiable-tracking approach yields physically consistent reconstructions while remaining computationally scalable. These developments form a practical framework for sigma-matrix determination in complex transport lines and support future real-time model calibration and tuning at the APS-U and similar facilities.