Modeling inductive radio frequency coupling in powerful negative hydrogen ion sources: validating a self-consistent fluid model

Radio frequency (RF) negative hydrogen ion sources utilized in fusion and for accelerators use inductively coupled plasmas, which are operated at a low driving frequency, high power densities and gas pressures in the order of 1 MHz, 10 W cm(-3) and 1 Pa, respectively. In this work a numerical fluid model is developed for a self-consistent description of the RF power coupling in these discharges. After validating the RF power coupling mechanism, such a model is a valuable tool for the optimization of RF power coupling and hence can help to increase the efficiency and reliability of RF ion sources. The model validation is achieved using measurements from the ITER RF prototype ion source. Steady state numerical solutions are obtained for the first time, where all modeled trends fit well. Remaining systematic quantitative differences could be caused by 3D effects such as highly non-uniform magnetic fields that cannot be captured in the current model formulation, which is 2D cylindrically symmetric. The coupling between the RF fields and the electrons is realized in the electron momentum transport equation, where approximations consistent with the operating regime of RF ion sources are applied. Here large magnetic RF fields lead to a plasma compression by the nonlinear RF Lorentz force. Using a local approximation for the electron viscosity, it is found that increased diffusion of the RF current density mitigates the compression. Navier-Stokes equations for the neutral atoms and molecules are used to capture neutral depletion. In this way it is shown that at high powers neutral depletion has a large impact on the power coupling via the viscosity of the electrons. The application of the self-consistent model for optimization of the RF power coupling will be described in a forthcoming paper.