【摘要】 Ioffe阱因能对中性粒子实现稳定囚禁而成为一种倍受关注的磁阱。若只讨论阱中的近原点区域时,阱中的磁场可以呈现出一种简明的形式。磁矩μ反平行于磁场的中性粒子在阱中与磁场发生相互作用,借助相互作用势,可以获得粒子在阱中的经典运动方程。本文着重探究这种方程的近似求解方法。在一定的条件下,我们可以采用逐次近似的方法,使方程演化为我们熟悉的马丢方程的形式。若阱的参数设置使得马丢方程中λ>>q>0成立时,我们可以利用传统的WKBJ方法近似求解马丢方程。作为一种新的尝试,本文还采用傅立叶级数展开的办法来对马丢方程进行求解,从而得到中性粒子在阱中的经典运动规律。更多还原

【Abstract】 The study of the magnetostatic traps for neutral particles is one of the most interesting topics at present. Among those, the Ioffe trap is one of the most important traps. We consider a neutral particle with magnetic moment μ antiparallel to the field of the Ioffe trap. With the interaction potential energy between the magnetic moment of the particle and the magnetic field, we obtain the classical motion equation of the neutral particles in the Ioffe trap. In some limit conditions, by using the perturbative method, the equations may take on concise forms, i.e Mathieu equations. If we properly set the parameters, we can solve the Mathieu equation with the traditional WKBJ method. As a new attempt, with Fourier series expansion we solve the Mathieu equation and obtain the classical motion law of the neutral particles.更多还原