帶電粒子在變化電場中有重力作用時的運動規律
摘要：本文研究了入射速度為任意方向的情況下，帶電粒子在相互正交的恆定磁場 和振盪電場 中並考慮重力情況下的運動規律，並且針對拉莫頻率 和振盪頻率 展開1系列的討論，從1般到具體，求得某些特殊情況下粒子的運動狀態。在求解過程中首先選擇了合適的座標系，令 沿 軸正方向， 沿 軸正方向， 沿 軸負方向，然後根據帶電粒子在 軸3方向上的受力情況列出粒子的運動微分方程，用直接求解微分方程法求解出帶電粒子的運動方程。而後則針對拉莫頻率 和振盪頻率 取具體值（
）進行討論，得出帶電粒子在這些情況下的運動狀態和在某些實際情況下的適用條件，並用MATLAB畫出帶電粒子在1些具體條件下的`運動軌跡圖。
關鍵詞：帶電粒子；恆定磁場；振盪電場；重力場；運動規律
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 錄
中文摘要……………………………………………………………………………………………………1
前言…………………………………………………………………………………………………………1
1 帶電粒子運動方程的推導 ……………………………………………………………………………3
1.1 運動微分方程……………………………………………………………………………………3
1.2 運動方程的推導 ……………………………………………………………………………… 4
1.3 粒子的運動軌跡圖………………………………………………………………………………6
2 對運動方程的討論 ……………………………………………………………………………………8
2.1 對 取特殊值的討論……………………………………………………………………………8
2.2 對a取特殊值的討論……………………………………………………………………………10
2.3 取 或 時帶電粒子的運動情況 ………………………………………………11
2.4 對 取具體值的討論 ………………………………………………………………………11
2.5 對 取具體值的討論…………………………………………………………………………12
結論…………………………………………………………………………………………………………13
參考文獻……………………………………………………………………………………………………14
英文摘要……………………………………………………………………………………………………14
致謝…………………………………………………………………………………………………………15
