【作者】 刘小良；

【导师】 曾高坚；

【作者基本信息】 湖南师范大学 ， 理论物理， 2003， 硕士

【摘要】 中性粒子的磁囚禁是近年来研究的一个重要课题，具有磁矩的中性粒子由于受到场的作用力，在特定的条件下可以实现对它的囚禁。我们首先讨论了几种基本的静磁阱的结构，对其中的场进行了精确计算，并在近轴条件下，利用级数展开等方法导出了场的近似表达式，这种近似有利于经典和量子轨道及对称性的研究。对Ioffe阱来说，因其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洁的形式，人们把它称为理想Ioffe阱。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。在一定的近似条件下，我们可以采用逐次近似的方法，使方程简化，其中三个分量式中关于z的方程比较容易求解，而关于x、y的方程则演化为我们熟悉的马丢方程的形式。若阱的参数设置使得条件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。在研究Ioffe阱对中性粒子的囚禁问题时，实际上我们更感兴趣的是马丢方程的周期解，而要想获得这种周期解，λ和q必须满足一定的关系，亦即必须选择阱的特定的参数和粒子的特定初始条件，对这一问题我们进行了尝试性的研究。更多还原

【Abstract】 The study of the magnetostatic traps for neutral particles is one of the most interesting studies at present . In this paper we study some basic and simple magnetostatic traps. In cylindrical coordinates frame, by using Biot-Savart law and other techniques, the general formulas of these fields are gi\en. From the exact expression of the field, we obtain a multipole polynomial expansion, and under the paraxial condition we furthermore obtain the approximate expression.The loffe trap, consisting of two coils with parallel currents and four straight conductors with currents in alternating directions, is one of the most important traps.We specially study the field structure of it by using both the exact expression and a multipole polynomial expansion that facilitates studies of classical or quantum orbits.If the region near the origin is of interest,we may obtain a simple expression of the field and this configuration may be called idealized loffe trap. We consider a neutral particle with magnetic moment antiparallel to the field.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 loffe trap.In some limit conditions,by using the perturbative method, the equations may take on concise forms.of which the two equations about x and y are Mathieu equations.If we properly set the parameters and have the condition A >> q > 0,we can solve the Mathieu equation with the traditional WKBJ method.As a new attemptation,with Fourier series expansion we solve the Mathieu equation and obtain the classical motion law of the neutral particles.更多还原