Analytic Modeling of Magnetic Field in the Magnetosheath and Outer Magnetosphere

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Abstract
Magnetosheath is a region surrounded by the bow shock and the magnetopause. According to statistical analysis, the boundaries can be treated as nonconfocal paraboloids of rotations. It is not easy to meet boundary conditions simultaneously on both sides. This problem is treated here and its solution is presented. A linear combination of harmonics that satisfy the condition on the magnetopause are selected in order to meet the condition on the bow shock. The method allows to calculate surface currents on the magnetopause. It is applied for typical conditions in solar wind. A modified magnetic dipole is used as a model of the magnetospheric field. Its modification is found by the method of potentials using cylindrical harmonics. Magnetopause currents are compared with results from a model with confocal paraboloids, which is commonly used in literature.

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