Radio frequency sheaths in an oblique magnetic field

Abstract

The physics of radio-frequency (rf) sheaths near a conducting surface is studied for plasmas immersed in a magnetic field that makes an oblique angle θ with the surface. A set of one-dimensional equations is developed that describes the dynamics of the time-dependent magnetic presheath and non-neutral Debye sheath. The model employs Maxwell-Boltzmann electrons, and the magnetization and mobility of the ions is determined by the magnetic field strength, and wave frequency, respectively. The angle θ, assumed to be large enough to insure an electron-poor sheath, is otherwise arbitrary. Concentrating on the ion-cyclotron range of frequencies, the equations are solved numerically to obtain the rectified (dc) voltage, the rf voltage across the sheath, and the rf current flowing through the sheath. As an application of this model, the sheath voltage-current relation is used to obtain the rf sheath impedance, which in turn gives an rf sheath boundary condition for the electric field at the sheath-plasma interface that can be used in rf wave codes. In general, the impedance has both resistive and capacitive contributions, and generalizes previous sheath boundary condition models. The resistive part contributes to parasitic power dissipation at the wall.