Euler potentials for two line currents aligned with an ambient uniform magnetic field

Abstract

Euler potentials of two line currents parallel or antiparallel to each other and aligned with a uniform ambient magnetic field are constructed. Explicit expressions for magnetic field lines are found. The solution is applied for study of bouncing motion of particles trapped between mirror points of this field structure. The result can be applied to Birkeland currents and also to laboratory plasma experiments. Copyright 2011 by the American Geophysical Union.