
THE ANALYTICAL TRAJECTORY OF THE CHARGED PARTICLE MOVING IN A NEUTRAL MAGNETIC FIELD
Xu Honglan
1981, 1 (1):
214.
doi: 10.11728/cjss1981.01.002
Neutral magnetic field was found wide important applications in space physics and satrophysics[14].In a rectangular coordinate system x y and z, the neutral magnetic field is, given by Eq.(21), where h is a small northward magnetic field[5], 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 method[5], 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.(27);(28)and(29), and in neutral sheet with northward component they satify Eqs.(212), (213)and(214).(2) In the neutral sheet field, the whole region can be devided into a perturbation region and nonperturbation region(x≤L).Innonperturbation region, the Alfven’s perturbation method can not be used, the analytical solution of the motion equation(27)is given by Eqs.(37)and(316), where z’ and the drift velocity Vz are given by Eqs.(317)and(315).In the perturbation region, the anlytical solution of Eq.(27)is given by Eqs.(48)and(422), where z’ and Vz are given by(423)and(418).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 nonperturbation 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 nonperturbation 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.(37)and(317), and take a "8" shape motion.Lines(5), (6), (7)and(8)are derived from Eq.(48)and(423)in the perturbation region, and take a circular motion.There is a slight deviation between(5)and(5)The drift velocity in nonperturbation region determined by Eq.(315)has an opposite direction and a much higher value than that in the perturbation region.The projection of the trajectories on xy 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 foundamental and higer harmonic of the corresponding trajectories.Acomplete analytical form has been obtained from the above results.
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