High-precision Beam Optics Calculation of the HIAF-BRing Using Measured Fields

The construction of the High Intensity heavy ion Accelerator Facility (HIAF) has been completed, with current efforts focused on subsystem commissioning. Beam commissioning is scheduled for autumn 2025, marking a critical milestone in the HIAF project. This paper presents high-precision optics calculations for the Booster Ring (BRing) of HIAF, a key component for achieving stable heavy-ion beam acceleration. Leveraging high-precision magnetic field data, each magnet is divided into hundreds of slices, thus establishing a high-precision sliced optics model for BRing. Detailed calculations of BRing’s optics are presented in this work. Critical parameters including tunes and betatron functions of the lattice based on the measured magnetic fields and those of the ideal lattice have been compared. The results highlight the impact of realistic magnetic field on beam dynamics and provide essential insights for accelerator tuning and optimization. These findings serve as a fundamental reference for beam commissioning and long-term operation, ensuring beam stability and performance reproducibility in HIAF.

💡 Research Summary

This paper presents a high‑precision beam optics study of the Booster Ring (BRing) of the High‑Intensity heavy‑ion Accelerator Facility (HIAF), focusing on the impact of measured magnetic fields on lattice parameters and the development of a sliced magnet model that faithfully reproduces real‑world field distributions. The authors begin by describing the BRing layout, which consists of three arc sections (each containing 16 dipoles and 16 quadrupoles) and three straight sections (each with 10 quadrupoles). Magnetic field measurements reveal that the effective lengths of both dipole and quadrupole magnets are generally longer than their design specifications, indicating that the nominal focusing strengths derived from design data would be inaccurate for beam commissioning.

To address this discrepancy, each magnet is longitudinally divided into hundreds of thin slices: dipoles are split into 200 slices of 18.762 mm length, while quadrupoles are divided into 182–200 slices with lengths of 10–15 mm depending on the magnet type. For dipoles, the bending angle of each slice is computed from the normalized magnetic flux intensity, ensuring that the sum of slice angles reproduces the design bending angle while preserving the total magnetic integral. The model also explicitly treats the 98 mm overlap region between adjacent dipoles, where the magnetic fields of the two magnets coexist, by packaging the slices of both magnets into a single “line”. This approach captures both fringe‑field effects and longitudinal field non‑uniformity.

Quadrupole modeling is performed in two ways. The first method calculates the focusing strength K of each slice directly from the measured field and then applies a correction factor (L/L_eff) to account for the longer effective length. The second method multiplies the slice‑wise K by the same correction factor, preserving the longitudinal field integral while simplifying the calculation of the required excitation current (GL). Both methods are implemented in MAD‑X, allowing the authors to construct several optics models: the ideal design lattice, a dipole‑only sliced model (D), a quadrupole‑only sliced model without correction (Q), a quadrupole‑only sliced model with correction (QC), an all‑magnets sliced model without correction (A), and an all‑magnets sliced model with correction (AC).

Optics calculations reveal systematic shifts in the working point caused by realistic field effects. When only dipoles are sliced (D), the horizontal tune drops from 9.470 to 9.461 (ΔQ_x ≈ ‑0.009) while the vertical tune rises slightly to 9.432 (ΔQ_y ≈ +0.002). This reflects the dipole fringe field weakening horizontal focusing and modestly enhancing vertical focusing. Slicing only quadrupoles without correction (Q) raises both tunes by about 0.08–0.09, because the longer effective length over‑estimates the focusing strength. Introducing the correction factor (QC) reverses this trend, reducing both tunes by roughly 0.027, which aligns the lattice more closely with the design values. When all magnets are sliced, the uncorrected model (A) shows an even larger increase in tunes (ΔQ_x ≈ +0.093, ΔQ_y ≈ +0.100), whereas the corrected model (AC) yields a decrease (ΔQ_x ≈ ‑0.036, ΔQ_y ≈ ‑0.024).

Table 3 summarizes tunes, chromaticities, and maximum β‑functions for each model; the QC and AC configurations produce the smallest deviations from the ideal lattice. Table 4 lists the new quadrupole focusing strengths (K) obtained after matching the tunes and chromaticities. Notably, the QC case exhibits the smallest spread in K values, indicating that applying the correction factor stabilizes the required magnet currents. Figures 5–8 illustrate β‑functions, horizontal dispersion, and the changes after matching. After the matching procedure, the β‑functions differ only marginally from the ideal case, and the horizontal dispersion in the straight sections is reduced to within ±0.1 m, essentially eliminating the fluctuations observed in the un‑matched sliced models.

The authors conclude that realistic magnetic field effects—particularly dipole fringe fields and quadrupole effective‑length extensions—significantly modify the lattice tunes and dispersion. Maintaining a constant longitudinal field integral while accounting for these effects is essential for accurate beam tuning. The high‑precision sliced model, combined with MAD‑X matching, enables precise control of tunes, β‑functions, and dispersion, providing a solid foundation for BRing commissioning in autumn 2025. Future work will extend the model to evaluate dynamic aperture, alignment tolerances, and long‑term stability, thereby offering a comprehensive tool for the design and operation of complex accelerator systems.