非零磁场作用下带电粒子在黎曼曲面上的运动
The Motion of a Charged Particle on a Riemannian Surface Under a Non-Zero Magnetic Field
摘要：
本文研究了正磁场B作用下带电粒子在黎曼曲面上的运动。利用Moser的扭曲定理和经典微扰理论的思想，我们找到了在磁场的水平集附近永久捕获具有足够大电荷的粒子运动的充分条件。在磁场水平集上保证俘获的条件是局部的，并且在B的所有非简并临界局部极小值或极大值附近保持。利用辛约化，我们将我们的工作结果应用于R^3上的某些S^1不变的磁场。
英文摘要：
In this paper we study the motion of a charged particle on a Riemannian surface under the influence of a positive magnetic field B. Using Moser's Twist Theorem and ideas from classical pertubation theory we find sufficient conditions to perpetually trap the motion of a particle with a sufficiently large charge in a neighborhood of a level set of the magnetic field. The conditions on the level set of the magnetic field that guarantee the trapping are local and hold near all non-degenerate critical local minima or maxima of B. Using symplectic reduction we apply the results of our work to certain S^1 - invariant magnetic fields on R^3.
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