Revisiting the anomalous rf field penetration into a warm plasma

Radio frequency waves do not penetrate into a plasma and are damped within it. The electric field of the wave and plasma current are concentrated near the plasma boundary in a skin layer. Electrons can transport the plasma current away from the skin layer due to their thermal motion. As a result, the width of the skin layer increases when electron temperature effects are taken into account. This phenomenon is called anomalous skin effect. The anomalous penetration of the rf electric field occurs not only for transversely propagating to the plasma boundary wave (inductively coupled plasmas) but also for the wave propagating along the plasma boundary (capacitively coupled plasmas). Such anomalous penetration of the rf field modifies the structure of the capacitive sheath. Recent advances in the nonlinear, nonlocal theory of the capacitive sheath are reported. It is shown that separating the electric field profile into exponential and non-exponential parts yields an efficient qualitative and quantitative description of the anomalous skin effect in both inductively and capacitively coupled plasma.Comment: 44 pages, invited paper at "Nonlocal, Collisionless Phenomena in Plasma" worksho

Accuracy of the Explicit Energy-Conserving Particle-in-Cell Method for Under-resolved Simulations of Capacitively Coupled Plasma Discharges

The traditional explicit electrostatic momentum-conserving Particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical accuracy. The explicit electrostatic energy-conserving Particle-in-Cell algorithm alleviates this constraint with minimal modification to the traditional algorithm, retaining its simplicity and ease of parallelization and acceleration on modern supercomputing architectures. In this article we apply the algorithm to model a one-dimensional radio-frequency capacitively coupled plasma discharge relevant to industrial applications. The energy-conserving approach closely matches the results from the momentum-conserving algorithm and retains accuracy even for cell sizes up to 8x the electron Debye length. For even larger cells the algorithm loses accuracy due to poor resolution of steep gradients in the radio-frequency sheath. This can be amended by introducing a non-uniform grid, which allows for accurate simulations with 9.4x fewer cells than the fully resolved case, an improvement that will be compounded in higher-dimensional simulations. We therefore consider the explicit energy-conserving algorithm as a promising approach to significantly reduce the computational cost of full-scale device simulations and a pathway to delivering kinetic simulation capabilities of use to industry