带电粒子在变化电场中有重力作用时的运动规律

带电粒子在变化电场中有重力作用时的运动规律

摘要：本文研究了入射速度为任意方向的情况下，带电粒子在相互正交的恒定磁场 和振荡电场 中并考虑重力情况下的运动规律，并且针对拉莫频率 和振荡频率 展开1系列的讨论，从1般到具体，求得某些特殊情况下粒子的运动状态。在求解过程中首先选择了合适的坐标系，令 沿 轴正方向， 沿 轴正方向， 沿 轴负方向，然后根据带电粒子在 轴3方向上的受力情况列出粒子的运动微分方程，用直接求解微分方程法求解出带电粒子的运动方程。而后则针对拉莫频率 和振荡频率 取具体值（

）进行讨论，得出带电粒子在这些情况下的运动状态和在某些实际情况下的适用条件，并用MATLAB画出带电粒子在1些具体条件下的运动轨迹图。

关键词：带电粒子；恒定磁场；振荡电场；重力场；运动规律

The motive law of charged particle in changing electric field and gravity field

Abstract：In this article we have examined the law of motion of a charged particle when it is put into a constant magnetic field and a vibration electric field , and a gravity field at a uniform speed along arbitrary orientation, we also calculate some particle’s motion states in some certain circumstances via the discussion aiming for the Larmor frequency a and the vibration frequency w from general to concrete. In the solution process, we choose an appropriate coordinate system first, that is to say we make along x axis direction, along y axis direction, along y axis negative direction. Then we list the particle’s differential equation according to its stress situation upwards axis, and solve the motion equation of charged particle by means of solving differential equation directly. Finally we take the concrete value of the a and the w to discussion, and obtain the charged particle’s state of motion in these situation, as well as the suitable condition in certain actual situation, and also draw some pictures of motive track by using MATLAB.

Key words: charged particle; constant magnetic field; vibration electric field; gravity field; motive law

目 录

中文摘要……………………………………………………………………………………………………1

前言…………………………………………………………………………………………………………1

1 带电粒子运动方程的推导 ……………………………………………………………………………3

1.1 运动微分方程……………………………………………………………………………………3

1.2 运动方程的推导 ……………………………………………………………………………… 4

1.3 粒子的运动轨迹图………………………………………………………………………………6

2 对运动方程的讨论 ……………………………………………………………………………………8

2.1 对 取特殊值的讨论……………………………………………………………………………8

2.2 对a取特殊值的讨论……………………………………………………………………………10

2.3 取 或 时带电粒子的运动情况 ………………………………………………11

2.4 对 取具体值的讨论 ………………………………………………………………………11

2.5 对 取具体值的讨论…………………………………………………………………………12

结论…………………………………………………………………………………………………………13

参考文献……………………………………………………………………………………………………14

英文摘要……………………………………………………………………………………………………14

致谢…………………………………………………………………………………………………………15