【摘要】 基于单粒子轨道模型和地磁场偶极子模型，考虑相对论效应，对近地球区域磁场中运动的带电粒子轨迹使用Mathematica软件中六阶龙格—库塔算法进行数值计算和模拟，并对极光现象的产生进行了解释，同时讨论了带电粒子在地磁场中运动的引导中心近似.结果表明：1)从地球北极方向观察，被地球磁场捕获的质子沿顺时针方向漂移，电子沿逆时针方向漂移；2)粒子各个分运动的运动周期数值模拟结果与文献中理论值非常吻合；3)从(4R_e,0,0)入射的粒子投掷角小于7.38°时，带电粒子将会与地球表面大气层碰撞而沉降，存在产生极光现象的可能.大于7.38°时，粒子将会被束缚在地磁场中，形成辐射带；4)其他条件相同时，带电粒子投掷点距离地球越远，其漂移速度越大；投掷角越大，其漂移速度也越大；5)对于能量较低的粒子，一阶近似下引导中心轨迹能很好地代表粒子实际运动轨迹.更多还原

【Abstract】 Based on the single particle orbit model and the geomagnetic field dipole model, and considering the relativistic effect, the sixth-order Runge-Kutta algorithm in the Mathematica software is used to numerically calculate and simulate the trajectories of charged particles moving in the magnetic field in the near-Earth region. The generation of auroras is explained, and the approximation of the guiding center of the charged particles moving in the geomagnetic field is discussed. The results show that:(ⅰ) Observed from the earth’s north pole, the protons captured by the earth’s magnetic field drift in the clockwise direction, and the electrons in the anti-clockwise direction;(ⅱ) The numerical simulation results of the motion period of each particle motion are in good agreement with the theoretical values in the literature;(ⅲ) When the throwing angle of the incident particle from(4R_e,0,0) is less than 7.38°, the charged particle will collide with the atmosphere on the earth’s surface and sink, and there is the possibility of producing auroras. When it is greater than 7.38°, the particles will be bound in the geomagnetic field, forming a radiation belt;(ⅳ) When other conditions are the same, the farther the charged particle throwing point is from the earth, the greater the drift velocity; the greater the throwing angle, the greater the Its drift speed is also greater;(ⅴ) For particles with low energy, the guided center trajectory can well represent the actual trajectory of particles in the first-order approximation.更多还原