Equilibrium properties of the plasma sheath with a magnetic field parallel to the wall

Abstract

Motivated by the magnetized target fusion (MTF) experiment [R. E. Siemon et al., Comments Plasma Phys. Controlled Fusion 18, 363 (1999)], a systematic investigation of the force balance and equilibrium plasma flows was carried out using analytical theory and the particle-in-cell code VPIC [K. J. Bowers et al., Phys. Plasmas 15, 055703 (2008)] for a one-dimensional plasma sheath with a magnetic field parallel to the wall. Initially uniform full Maxwellian plasma consisting of equal temperature collisionless electrons and ions is allowed to interact with a perfectly absorbing wall. The analysis of the steady-state force balance of the entire plasma as well as its individual components illuminates the roles that the hydrodynamic, magnetic, and electric forces play. In particular, when ρthi<λD, the magnetic force balances the divergence of the pressure tensor. As the magnetic field is decreased, the electric force becomes prominent in areas where quasineutrality breaks, which can be a substantial part of the sheath. Its importance depends on the relation between three parameters, namely, electron and ion thermal Larmor radii and plasma Debye length: ρthe, ρthi, and λD. The relative importance of the electron and ion current in the magnetic or Lorentz force term can be understood through the analysis of the two-fluid force balance. It reveals that the current is carried primarily by the electrons. This is due to the direction of the electric field that helps confine the ions, but not the electrons, which are forced to carry a large current to confine themselves magnetically. In the regimes where the electric field is negligible, the ions also need the current for confinement, but in these cases the divergence of ion pressure tensor is much smaller than that of the electrons. Consequently the ion current is also smaller. The study of the electron and ion flow parallel to the wall clarifies this picture even further. In the regime of strong magnetic field, the particle average velocity parallel to the wall uy is purely diamagnetic. However, since the ion number density is very low near the wall, they do not produce considerable contribution to the current. In the ρthi<λD regime, uy consists of two parts: diamagnetic and E⃗×B⃗ drifts. Since the direction of the former depends on the particle charge while the latter does not (at least to lowest order), the drifts for the electrons add, while for the ions they mostly cancel each other. Although the primary motivation for this research is MTF, the analytical and computational results presented in this paper can also be applicable to the plasma sheath in the conventional magnetic confinement devices, in particular, near the first wall of tokamaks.