Title: Beam Energy Measurement using a Bayesian Approach with the Stacked Foil Method Show Chinese title

Title: 基于堆叠箔方法的贝叶斯方法用于束流能量测量

Abstract: We present a practical method to measure the energy of proton beams at a medical cyclotron using the stacked foil technique in combination with a Bayesian inference method. By measuring the $^{48}$V activity induced in a stack of irradiated titanium foils, the proton energy can be inferred without relying on direct current or charge measurements, making the method suitable even for low-vacuum environments or air-exposed setups. This technique is further extended to configurations where the beam energy is degraded to levels around 8 MeV. A Bayesian fit of the measured activity profile allows not only for a robust energy estimation but also for a consistent treatment of uncertainties and nuisance parameters. Monte Carlo simulations are employed to validate the underlying assumptions, including the impact of energy dispersion or cross-section uncertainties. Our results demonstrate that this method provides accurate beam energy measurements across several typical experimental setups used at the Bern Medical Cyclotron. Additionally, we evaluate the sensitivity of the method to the choice of nuclear cross-section data and assess how the number of foils in the stack affects the uncertainty in the inferred beam energy. Show Chinese abstract

Abstract: 我们提出了一种实用的方法，使用叠加箔技术结合贝叶斯推断方法，在医疗回旋加速器上测量质子束的能量。 通过测量在辐照钛箔堆中产生的$^{48}$V 活性，可以在不依赖直接电流或电荷测量的情况下推断质子能量，使该方法即使在低真空环境或暴露于空气的设置中也适用。 该技术进一步扩展到束流能量降低到约 8 MeV 的配置。 对测量的活性分布进行贝叶斯拟合不仅允许稳健的能量估计，还可以一致地处理不确定性和干扰参数。 蒙特卡罗模拟用于验证基本假设，包括能量分散或截面不确定性的的影响。 我们的结果表明，这种方法在伯尔尼医疗回旋加速器使用的几种典型实验设置中都能提供准确的束流能量测量。 此外，我们评估了该方法对核截面数据选择的敏感性，并评估了堆叠中的箔片数量如何影响推断的束流能量的不确定性。