We present recent progress with our algorithm and its implementation called simpa described in a previous paper. The algorithm has a new and unique approach to long-term 4D tracking of charged particles in arbitrary static electromagnetic fields. Using the improvements described in this paper, we made frequency analysis and dynamic aperture studies in ELENA. The effect of the end fields and the perturbation introduced by the magnetic system of the electron cooler on dynamic aperture is shown. A special feature of this study is that we have not introduced any multipole errors into the model. The dynamic aperture calculated in this paper is the direct consequence of the geometry of the magnetic elements. Based on the results, we make a few suggestions to reduce the losses during the deceleration of the beam.

中文翻译：

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具有真实3D磁场的低能反质子环的频率分析和动态孔径研究

我们介绍了我们在先前论文中描述的算法及其实现（称为simpa）的最新进展。该算法具有一种新颖独特的方法，可以在任意静态电磁场中对带电粒子进行4D长期跟踪。使用本文中描述的改进，我们在ELENA中进行了频率分析和动态孔径研究。显示了电子冷却器的磁系统引入的端场和扰动对动态孔径的影响。这项研究的一个特色是我们没有在模型中引入任何多极误差。本文计算的动态孔径是磁性元件几何形状的直接结果。根据结果​​，我们提出了一些减少光束减速过程中的损耗的建议。