Collisionless dissipation at the boundary sheath of magnetized low temperature plasmas

Abstract

Abstract In partially magnetized technological plasmas like magnetron discharges or Hall-effect thrusters, the interaction of gyrating electrons with the plasma boundary sheath plays an important role. This study shows that the interaction can be described as a dissipative process. It is assumed that the Debye length λ D is much smaller than the electron gyroradius r L , and r L in turn much smaller than the mean free path λ and the field gradient length l. Focusing on the scale of the gyroradius, the sheath is assumed as thin ( λ D → 0 ), collisions are neglected ( λ → ∞ ), the magnetic field is taken as homogeneous, and electric fields (= potential gradients) in the bulk are neglected ( l → ∞ ). The interaction of an electron with the electric field of the plasma boundary sheath is represented by specular reflection, v → v − 2 v ⋅ n n , where v is the electron velocity and n is the sheath normal. A previous study showed that this set-up leads to a scattering process where gyrophase invariant incoming velocity distributions are scattered into outgoing distributions with fractal dependence on the gyrophase (Krüger and Brinkmann 2017 Plasma Sources Sci. Technol. 26 115009). The present research focuses on the subsequent evolution. It is shown that the gyromotion results in fast phase mixing with respect to the gyrophase which quickly restores the gyrophase invariance. In combination, the two phases of the sheath interaction constitute a mapping within the space of gyrophase invariant distributions. This combined process is dissipative and leads to isotropization. As an explicit comparison shows, it acts similarly to elastic electron-neutral collisions and can even dominate the latter in low pressure plasmas. A simplified version of the operator that applies for weakly anisotropic distributions is suited for practical simulation work.