带电粒子在电场和磁场中的运动及电磁力的求解_硕士学位论文 精品

硕士学位论文

带电粒子在电场和磁场中的运动及电磁力的求解

摘要

带电粒子在电场和磁场中的运动对于物理学和科学技术的许多重要领域都有重大意义。例如，质谱仪，示波器，电视显像管，粒子加速器等仪器应用都与之有密切关系。此外，研究带电粒子在电场和磁场中的运动已经成为等离子体物理理论研究的一个重要组成部分。关于带电粒子在电场和磁场中的运动，许多人进行了大量的工作。在前人的工作中，基本上是从经典电磁场理论和经典力学出发研究带电粒子的经典轨道，也很少有人对存在弹性界面的情况进行分析。本文将考虑存在弹性界面的情况，同时考虑带电粒子的经典运动和相对运动，并通过求解带电粒子的哈密顿正则方程及Mathematica科学计算软件程序包来描绘带电粒子的运动轨迹。

本文还求解了磁标量满足的拉普拉斯方程，电磁矢量满足的亥姆霍兹方程，利用边值问题求解电磁场，并且应用麦克斯韦应力张量来计算某些电磁作用力。本项目的研究成果对开拓和扩展电磁场理论应用的新领域具有一定的参考作用。

本文主要阐述了五个方面的内容。一，带电粒子在电场和磁场中的经典运动；二，带电粒子在电场和磁场中的相对论运动；三，带电粒子在平行电场和磁场及弹性界面附近的运动；四，求解某些磁标量满足的拉普拉斯方程，电磁矢量满足的亥姆霍兹方程；五，应用麦克斯韦应力张量计算某些电磁作用力。

关键词：带电粒子，电磁场，洛伦兹力，弹性界面，电势，边值关系

The Movements of C harged Particles in Electric and Magnetic Fields and the Solutions of Electromagnetic Force

ABSTRACT

Study the movements of charged particles in the electric and magnetic fields with a great significance in many important areas of physics and scientific technology. For example, the applications of mass spectrometers, oscilloscopes, TV picture tubes, particle accelerators and other equipments are closely related to this study. In addition, study the movements of charged particles in the electric and magnetic fields have become an important component of the theory research in plasma physics. Many people carried out a lot of work about the movements of charged particles in the electric and magnetic fields. Most previous work basically started from the theory of classical electromagnetic field and classical mechanics to study the classical track of charged particles, but few people analyzed the situation of flexible interface when it existed. This article will both consider the condition of the existence of a flexible interface and the classical and relative motion of charged particles, and then use the quantum theory to solve the particles’ Schr?dinger eigen equation .

This article will introduce the solutions of the Laplace equation when the magnetic scalar meet it and the Helmholtz equation when the electromagnetic vector satisfy it. This paper also solves the electromagnetic field through the use of boundary value problem and calculates certain electromagnetic force through the application of Maxwell stress tensor. Research results of this project have a great reference significance to explore and expanse new areas of the application of electromagnetic theory.

This article focuses on five aspects, it is arranged as follows:

1. The classical movement of Charged particles in electric and magnetic fields.

2. The relative movement of Charged particles in electric and magnetic fields.

3. The movement of Charged particles in parallel electric and magnetic fields and

near the flexible interface.

4. Solutions of the Laplace equation when certain magnetic scalar meet it and the

Helmholtz equation when the electromagnetic vector satisfy it.

5. Calculate certain electromagnetic force by the application of Maxwell stress

tensor.

key words: Charged particles, Electromagnetic Field, Lorentz force, Flexible interface, electric potential , The relationship between boundary value

目 录

摘 要 .......................................................................................................................................... II ABSTRACT ................................................................................................................................ II 1引言 . (1)

1.1 课题研究的背景及意义 (1)

1.2 本论文的主要工作及主要成果 ........................................................................................... 1 2带电粒子在电场和磁场中的经典运动 (2)

2.1 问题的提出 (2)

2.2 带电粒子在电磁场中运动方程的分析 (2)

2.3 普遍情况 (2)

2.3.1 空间仅存在电场 (3)

2.3.2 空间仅存在磁场 ........................................................................................................ 4 2.3.3 电场E 与磁场B 同方向 ........................................................................................... 4 2.3.4 电场E 与磁场B 垂直 .. (4)

2.4 讨论 ..................................................................................................................................... 5 3带电粒子在电场和磁场中的相对论运动 .. (6)

3.1 问题的提出 (6)

3.2电磁场相对论变换的一种推导 ............................................................................................ 6 3.2.1 E 和B 的变换式的推导 ........................................................................................... 6 3.2.2 D 和H 的变换式的推导 (8)

3.3带电粒子在电磁场中的相对论运动的求解 (10)

3.4 讨论 ................................................................................................................................... 14 4带电粒子在平行电场和磁场及弹性界面附近的运动 . (15)

4.1 问题的提出 (15)

4.2 理论模型和公式推导 (15)

4.2.1 带电粒子在平行电场和磁场中的运动方程 (15)

4.2.2 带电粒子在平行电场和磁场及存在两个弹性界面时闭合轨道形成的条件 (16)

4.3带电粒子在平行电场和磁场及存在两个弹性界面时闭合轨道的模拟 (19)

4.3.1 粒子没有碰到任何界面时的闭合轨道 (19)

4.3.2 粒子只碰到上界面时的闭合轨道 (20)

4.3.3 粒子只碰到下界面时的闭合轨道 (21)

4.4 讨论 (21)