Neutral magnetic field was found wide important applications in space physics and satrophysics[1-4].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 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.(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.
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