Magnetospheric Configuration with Magnetotail Current

Abstract

Magnetospheric configuration with magnetotail current is studied on a two-dimensional formulation. The planar magnetic field is represented by an analytic function of a complex variable that represents points of the noon-mid night plane. In our treatment, which accounts for both the Chapman-Ferraro magnetopause current and the magnetotail current, the function that describes the magnetospheric magnetic field is a rational function. Thus, the magnetic neutral points, which characterize the magnetic topology of the field lines, can be simply ascertained by finding the roots of a polynomial function. The function for the magnetic field is the derivative of a complex potential, the real part of which is a flux function and the imaginary part a magnetic potential of the magnetic field. The inverse function of the complex potential describes the position variable in terms of the complex potential. Field lines are described by a parametric equation obtainable form the afore-mentioned inverse function. Thus, no integration of the differential equation for field lines is needed.

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