The typical treatment of time-dependent potentials, such as those used for radio frequency cavities, is to average a potential’s time component through the interval that a reference particle spends in the cavity. Such an approach, using the so-called transit-time factor, uses time as the independent variable in the Hamiltonian. In this paper, we instead propose a fully covariant Hamiltonian to treat a potential’s time component like any other space component. We show how to calculate the dynamics of particles in a pill-box cavity using an explicit symplectic integrator. Finally, we compare the results with the simulator TraceWin.

中文翻译：

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应用于药盒腔的时变势的协变哈密顿方法

对时间相关的电势（例如用于射频空腔的电势）的典型处理方法是，在参考粒子在空腔中停留的时间间隔内，平均电势的时间分量。这种方法使用所谓的过渡时间因子，将时间用作哈密顿量中的自变量。相反，在本文中，我们提出了一个完全协变的哈密顿量，以像其他空间分量一样对待势的时间分量。我们展示了如何使用显式辛格积分器来计算药丸盒型腔中颗粒的动力学。最后，我们将结果与模拟器TraceWin进行比较。