Coaxial discharge with axial magnetic field: Demonstration that the Boltzmann relation for electrons generally does not hold in magnetized plasmas

Abstract

A one-dimensional two-fluid model is used to describe the quasineutral plasma of a discharge formed between coaxial cylinders under the influence of an axial magnetic field. The geometry treated in this paper is symmetric about the z-axis and is radially varying. The nested cylinders are necessarily different in size, leading to a potential difference between the sheath edges of the discharge plasma. This can be removed by applying a strong enough magnetic field, which also has the effect of flattening the potential profile, i.e., reducing the electric field in the plasma volume. In a previous publication [T. M. G. Zimmermann et al., Phys. Plasmas 16, 043501 (2009)], the authors examined the validity of the Boltzmann relation for electrons when applied to a similar geometry. When the magnetic field becomes strong enough to affect the electron flow in the radial direction, this expression breaks down. It was further discovered that certain situations require a self-consistent treatment of magnetic fields, since significant azimuthal currents can arise in such geometries. This work is applied and extended to offer a complete description of the electron density.