Optimum Cross-Section of the Current Flowing Through Magnetic Field Lines

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Scientific paper

Electric current flowing along magnetic fields occurs commonly in both the ionosphere-magnetosphere coupling system and the solar photosphere-corona loop system. In the former case, the current flows from one area of the ionosphere to one area of the magnetosphere or vice versa; in the latter case, the current flows from one foot of the coronal loop to its other foot. In either case, we assume that the total current flowing along the magnetic field lines is determined by the electrodynamics at the end areas of the loop but that the cross-section of the current and, hence, the current density, may vary. The parallel current produces a magnetic field perpendicular to the background magnetic field and causes field lines to twist. The magnetic flux also changes because a current perpendicular to the original field lines appears. For a uniform background magnetic field, analysis based on the magnetic energy shows that the cross-section of the current tends toward that value that produces a magnetic field comparable to the original magnetic field. When the cross-section changes, there is a transformation of magnetic field energy into particle energy.

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