Beam Energy Re-calibration of Beijing HI-13 Tandem Accelerator

The Beijing HI-13 Tandem Accelerator is a national scientific facility for nuclear physics research in China, characterized by an extremely small beam-energy spread with a resolution reaching 0.02%. The analyzing magnet with a high momentum resolution is a key component of the tandem accelerator for achieving a high energy resolution. Due to the uniformity of the magnetic field and installation errors of the magnet, as well as variations in measurement positions, there may be a significant deviation between the actual deflection radius and the theoretical value, which therefore requires a calibration experiment to determine the magnet constant K with high precision and accuracy. After the accelerator was installed, it underwent the first calibration in 1994 and the second calibration in 2007. Since 2007, the accelerator has undergone several upgrades and modifications, especially the installation of the superconducting linear post-accelerator in 2019, wherein the analyzing magnet was disassembled and reassembled, and the magnetic field measurement instrument was changed from the previous nuclear magnetic resonance frequency meter to a Gauss meter. These changes may alter the K of the analyzing magnet, thereby affect the accuracy of the beam energy. Therefore, it is necessary to re-calibrate the analyzing magnet. The resonance nuclear reactions of the p+¹²C system were selected for this purpose. The main advantage of this system is that the compound nucleus ¹³N has an extremely-narrow resonant state at 15.064 6 MeV with a width of 0.93 keV, allowing for a precise calibration of the K. Additionally, the corresponding beam energy 14.231 MeV is almost in the middle energy range provided by the tandem accelerator. Two wider energy levels of 6.364 and 10.360 MeV were selected as well for preliminary calibration, allowing for a quick determination of a rough K and thus saving beam time. To test the stability of the K over a wider energy range, measurements were also conducted at a higher energy level of 18.961 MeV. The experiment was carried out at the R60º nuclear reaction terminal of the Beijing HI-13 Tandem Accelerator at the China Institute of Atomic Energy. Proton beam bombarded a ¹²C target with a thickness of 25 μg/cm², scanning near four energies of 4.793, 9.127, 14.231, and 18.460 MeV, respectively. The product counts from each reaction channel were normalized by the beam-current integrator to obtain the excitation functions. By fitting the excitation functions, the magnetic field corresponding to the resonance peak position can be determined, which in turn allows us to calculate the K of the analyzing magnet. At the most accurate energy point of 14.231 MeV, the K is determined to be （803.95±0.09） keV·u/kGs², 1.835% higher than the calibration result in 2007, with an energy resolution rate of （7.6±5.4）×10⁻⁵. This provides a basis for the precise determination of energy in subsequent experiments on the accelerator. Considering the four energy points, the K shows a weak linear positive correlation with beam energy: K（keV·u/kGs²）= 800.612+2.054×10⁻⁴E（keV）, which is similar to the result in 1994.