带电粒子在中性线磁场中运动的解析轨道

本文我们计算了带电粒子在中性线磁场中运动的解析轨道。其结果是:(1)带电粒子在中性片磁场中的运动是粒子在中性线磁场或在具有北向分量的中性片磁场中的第一级近似形式。(2)带电粒子在中性片磁场中的解析轨道的第三级近似形式与电子计算机计算的数值轨道基本相同。它们仅仅在小扰动区与非小扰动区的交界线上出现一些偏差。(3)带电粒子在整个中性片磁场的运动可以分成三种形式。粒子一方面在垂直于磁场的平面上作闭合的周期性轨道运动, 同时闭合轨道的中心还沿着垂直于磁场平行于中性线方向漂移。另一方面粒子还沿磁力线方向做等速运动。(4)在小扰动区中粒子的闭合轨道是一个圆轨道, 但在非小扰动区中却是一个“8”字形轨道, 其漂移速度与小扰动区漂移方向相反, 其大小也比小扰动区漂移大很多。以上结果本文都给出一个完整的解析形式。 

THE ANALYTICAL TRAJECTORY OF THE CHARGED PARTICLE MOVING IN A NEUTRAL MAGNETIC FIELD

Neutral magnetic field was found wide important applications in space physics and satrophysics1-4].In a rectangular coordinate system x y and z, the neutral magnetic field is, given by Eq.(2-1), where h is a small northward magnetic field5], a and e are the parameters of the field.When ε=0 the field is a neutral sheet.An analytical trajectory of the charged particle moving in this field has been calculated The results are:(1)By means of a perturbation method5], we found that the motion of the charged particle in a neutral sheet field can be defined by the first approximation of motions either in a neutral magnetic field or in a neutral sheet field with a small northward component.The first, second and third approximation of the motion in a neutral magnetic field satify respectively the Eqs.(2-7);(2-8)and(2-9), and in neutral sheet with northward component they satify Eqs.(2-12), (2-13)and(2-14).(2) In the neutral sheet field, the whole region can be devided into a perturba-tion region and non-perturbation region(|x|≤L).Innon-perturbation region, the Alfven’s perturbation method can not be used, the analytical solution of the motion equation(2-7)is given by Eqs.(3-7)and(3-16), where z’ and the drift velocity Vz are given by Eqs.(3-17)and(3-15).In the perturbation region, the anlytical solution of Eq.(2-7)is given by Eqs.(4-8)and(4-22), where z’ and Vz are given by(4-23)and(4-18).The thrid approximation of the analytical trajectory and the trajectory evaluation by computer agree quite well, except for a slight deviation around the boundary of the perturbation region and the non-perturbation region.(3)The trajectory of the particle moving in a neutral sheet field can be devided into two motions, one is along a closed oscillation trajectory in the plane perpendicular with the magnetic field while its center drifts in a direction parallel to the neutral line, and the other along the magnetic line with an uniform velocity.In the non-perturbation region, the closed oscillation trajectory of particles with diference initial conditions are shown in Fig.2 by lines(1), (2), (3), (4)and(5)They are derived from Eqs.(3-7)and(3-17), and take a "8" shape motion.Lines(5), (6), (7)and(8)are derived from Eq.(4-8)and(4-23)in the perturbation region, and take a circular motion.There is a slight deviation between(5)and(5)The drift velocity in non-perturbation region determined by Eq.(3-15)has an opposite direction and a much higher value than that in the perturbation region.The projection of the trajectories on x-y plane corresponds to the particles with different initial conditions are shown in Pigs.1 and 3 by full lines, and the dashed lines denote the founda-mental and higer harmonic of the corresponding trajectories.Acomplete analytical form has been obtained from the above results.