带电粒子在常梯度磁场中横向运动稳定性研究.doc

-  PAGE 17 - 带电粒子在常梯度磁场中横向运动稳定性研究 摘 要 在导出常梯度磁场中带电粒子运动的微分方程的基础上，求出了微分方程的解。研究了带电粒子在常梯度磁场中运动的稳定性，确定了粒子作回旋运动的稳定条件。结果表明，粒子在作回旋运动的同时，在轴向和径向均作简谐振荡，可以保持粒子绕回转轨道运动。粒子的横向运动轨迹的形状取决于磁场的对数梯度,而与粒子的初始状态无关。粒子的初始状态确定其横向运动的振幅。 【关键词】常梯度磁场；回旋运动；横向运动；稳定性条件 Study on the lateral stability of charged particles in a constant gradient magnetic field Abstract In constant gradient magnetic field is derived the basic differential equations for the motion of charged particles in the upper, the solution of the differential equation. The stability of charged particles in constant gradient magnetic field research, determine the particle stability conditions of cyclotron motion. The results show that, particles in the cyclotron motion at the same time, in the axial and radial directions were simple harmonic oscillation, can keep the particles around the rotary motion. Logarithmic gradient magnetic field n in lateral motion trajectory of particle shape depending, regardless of the initial state and the particle. The initial state of the amplitude of the transverse motion of particle is determined. [Key words] constant gradient magnetic field;  HYPERLINK /s?wd=lateral%20motion \t _blank lateral motion;  HYPERLINK /s?wd=stability%20condition \t _blank stability condition 目 录  TOC \o 1-3 \h \z \u  HYPERLINK \l _Toc357111837 引 言 4  HYPERLINK \l _Toc357111838 1 带电粒子在恒定均匀磁场中的运动 4  HYPERLINK \l _Toc357111839 1.1带电粒子在恒定电磁场中的运动方程 4  HYPERLINK \l _Toc357111840 1.2带电粒子在均匀磁场中的运动 5  HYPERLINK \l _Toc357111841 2 带电粒子在常梯度磁场中的运动方程 6  HYPERLINK \l _Toc357111844 2.1理想常梯度磁场分布的特点 6  HYPERLINK \l _Toc357111845 2.2带电粒子在常梯度磁场中的运动方程 7  HYPERLINK \l _Toc357111846 2.3 轴向运动方程 8  HYPERLINK \l _Toc357111846 2.4 径向运动方程 9  HYPERLINK \l _Toc357111849 2.5非相对论情况下带电粒子横向运动的稳定性 10  HYPERLINK \l _Toc357111850 3.带点粒子运动规律的数值分析 11  HYPERLINK \l _Toc357111851 3.1非相对论情况下横向振荡方程的通解 11  HYPERLINK \l _Toc357111851 3.2初始条件确定时横向振荡方程的定解 12  HYPERLINK \l _Toc357111890 3.3粒子运动轨道的分析 13  HYPERLI