Self-consistent fluid model for simulating power coupling in hydrogen ICPs at 1 MHz including the nonlinear RF Lorentz force

Radio frequency (RF) power coupling in inductively coupled plasmas is investigated numerically using a self-consistent fluid model. Hydrogen discharges are simulated at pressures from 0.3-10 Pa and at RF powers of around 1 kW. At the low excitation frequency of 1 MHz a high magnetic RF field of around 30 G is generated by the RF coil, meaning that discharges at low pressures are in the nonlinear skin effect regime. Therefore, a description of the RF power coupling by simple collisional Joule heating is not appropriate. Moreover, models that account for collisionless heating by means of a stochastic collision frequency or as diffusion of the RF current density (as is state of the art for discharges operated in the anomalous skin effect regime at higher frequencies of e.g. 13.56 MHz) are incapable of describing the RF power coupling in the nonlinear skin effect regime properly. This is due to their total neglect or simplified treatment of the RF Lorentz force. Instead, this work demonstrates that the RF power coupling mechanism for discharges operating at low RF in the nonlinear skin effect regime can be described by an electron momentum balance retaining the nonlinear RF Lorentz force as well as electron inertia and advection. The crucial role of the RF Lorentz force in generating the RF plasma current density and thus in shaping the plasma parameter profiles is validated successfully with experimentally obtained electrical and spatially resolved plasma parameters for pressures as low as 0.5 Pa. Below this pressure the results obtained from the model and the ones from the experiment diverge. Most likely this is caused by a sudden change in the electron distribution function at the lowest pressures.