Particle trajectories in model current sheets: 1. Analytical solutions

Abstract

Approximate analytical solutions are found for two model current sheets. In the first the magnetic field is linear and reverses across a neutral sheet, and the electric field is everywhere uniform, perpendicular to the magnetic field and parallel to the neutral sheet. Charged particles of either sign never come out of the neutral sheet, and their energies increase without bound. In the second model a small component of the magnetic field perpendicular to the neutral sheet is added. This component not only serves to bring particles out of the sheet, but turns protons and electrons toward the same direction, 90° away from the accelerating electric field. The particles are accelerated and then ejected when they have been turned 90°, and the emergent pitch angles to a magnetic line of force will be small if the perpendicular magnetic field component is small.