Sheath structure in a magnetized plasma

Abstract

The sheath formed between a magnetized plasma and a particle absorbing wall is examined for the case in which the magnetic field intercepts the wall at a small angle 0°<ε≲9°, where sin ε=B⋅n̂/‖B‖, and n̂ is the unit normal to the wall. The model is time-independent and one-dimensional (1-D) with all functions varying only in the direction normal to the wall. The ions are modeled by a Maxwellian velocity distribution which is modified by the condition that ions, which would have hit the wall, are absent. For the electrons a fluid description is used, including the effects of electron–neutral collisions. The transport of particles due to turbulent electrostatic fluctuations is modeled by a constant electric field perpendicular to both B and n̂. It is found that in the range of angles under consideration, there are two distinct regimes of sheath formation. If ε≲ν̄=ν/Ωe (grazing incidence), where ν is the electron–neutral collision frequency and Ωe is the electron cyclotron frequency, then the properties of the sheath are determined by a parameter λ which is the ratio of the convective (E×B) and diffusive electron flows. If λ≲1, the wall potential is negative and the sheath scale length is on the order of an ion gyroradius. If λ≳1, the wall potential is positive and, for large λ, the sheath is characterized by two scales: a short length, which is a decreasing function of λ, adjacent to the wall, and the ion gyroradius farther from the wall. For ε≫ν̄, (oblique incidence) the potential at the wall is negative with a magnitude close to that of the unmagnetized plasma and is only weakly dependent on ε. In addition, for this case, the sheath scale length is on the order of an ion gyroradius and is weakly dependent on ε, larger values of ε resulting in a slightly shorter scale length.