带电粒子在成任意夹角的电场和磁场中的闭合轨道及其分叉现象研究

从哈密顿正则方程出发,推导出了带电粒子在电场和磁场成任意夹角时的运动方程.根据运动方程讨论了带电粒子的运动轨迹形成闭合轨道所满足的条件,借助于计算机编程对带电粒子的闭合轨道进行了模拟.计算结果表明：在交叉的电场和磁场中,带电粒子的闭合轨道是三维的.随着带电粒子能量的不断增大,闭合轨道的条数不断增多.当能量增加到某一边界能量时,一条新的闭合轨道出现,当能量大于此边界能量时,这条新的闭合轨道发生分叉,由一条分为两条.对应第j个边界能量,共有2j条闭合轨道出现,当能量在第j个和第j＋1个边界能量之间变化时,共有2j＋1条闭合轨道存在.

Exploration of the Closed Orbits and Its Bifurcation of the Electric Particle in the Electric and Magnetic Fields with any Orientation

Starting from the Hamiltonian motion equations,the movement equations of the electron in electric and magnetic fields with any orientation have been deduced.The initial conditions of the closed orbits of the electron＇s trajectory have been discussed according to the movement equations.With the help of the computer program,the closed orbits of the electrical particle have been simulated.The results suggest that the closed orbit is three-dimensional in crossed electric and magnetic fields.With the increase of the electron＇s energy,the number of the closed orbits is increased.As the energy is increased to some boundary energy,a new closed orbit appears;when the energy is greater than this boundary energy,this closed orbit bifurcates into two new closed orbits.Corresponding to the jth boundary energy,2j closed orbits appear.As the energy varies between the jth and the（j＋1）th boundary energy,there are altogether 2j＋1 closed orbits.