Euler potentials for two current sheets along ambient uniform magnetic field

Abstract

Euler potentials of two current sheets of finite width parallel or antiparallel to each other and aligned with a uniform ambient magnetic field are constructed analytically. It is shown how analytic treatment can be simplified using complex number analysis. Our approach generalizes results obtained earlier for a system of two line currents (wires). In the present solution the latter system represents a limiting case, and differences between results from configurations with sheets/wires are discussed. 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 to laboratory plasma experiments.