带电粒子在非稳态电流感应电磁场中的运动
Motions of a charged particle in the electromagnetic field induced by a non-stationary current
摘要：
本文研究了带电粒子在沿无限长、无限细的直线流动的周期性时变电流J所产生的电磁场中的非相对论动力学。运动由洛伦兹-牛顿方程描述，其中电磁场通过以电流分布J作为数据求解麦克斯韦方程来获得。我们证明了许多功能的可积时间无关的情况下被保存。更确切地说，引入柱坐标，我们证明了存在（非共振）的径向周期运动，也是扭曲型。特别是，这些解决方案是李雅普诺夫稳定和积累的次谐波和准周期运动。
英文摘要：
In this paper we study the non-relativistic dynamic of a charged particle in the electromagnetic field induced by a periodically time dependent current J along an infinitely long and infinitely thin straight wire. The motions are described by the Lorentz-Newton equation, in which the electromagnetic field is obtained by solving the Maxwell's equations with the current distribution J as data. We prove that many features of the integrable time independent case are preserved. More precisely, introducing cylindrical coordinates, we prove the existence of (non-resonant) radially periodic motions that are also of twist type. In particular, these solutions are Lyapunov stable and accumulated by subharmonic and quasiperiodic motions.
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