Numerical simulations of the plasma parameters in the SPIDER device

The experimental fusion reactor ITER will be heated by injection of fast neutral beams generated by acceleration and neutralization of negative ions. The prototype negative ion source used for this purpose (SPIDER), constructed at the Consorzio RFX (Italy), consists of driver volumes where radio-frequency (RF) power is inductively coupled to the plasma electrons, and an expansion chamber containing a magnetic filter (MF). This paper presents the basic physical and numerical principles of a fluid model of this source. The model gives self-consistent two-dimensional description of the source, including the neutral gas flow, plasma chemistry, RF coupling in the source driver and plasma transport through the magnetic filter. The different particle species (electrons, the three types of the positive ions: H+ , H2+ , H3+, negative ions H- and the neutral species: hydrogen atoms H and molecules H2) are described by separate continuity equations and the electron temperature is governed by the electron energy balance equation. The particle fluxes are found from momentum equations neglecting the inertia terms (drift-diffusion approximation). The electrostatic coupling between electrons and ions is described by the Poisson equation. The numerical method is based on finite volume approximation and 9-point discretization is used to account for the anisotropy due to magnetic field. The semi-implicit numerical solver allows for large time steps (> 1000 x explicit time step) producing steady-state solution in a reasonable time (few hours for a typical mesh). An important element in the development of the numerical framework is the benchmarking of the code results with the experimental data. For this aim, a series of numerical simulations have been performed and compared to the experimental data form the SPIDER experimental campaigns including the cesium operation (S21). The paper presents critical assessment of the benchmarking results and outlines the necessary code/model enhancements necessary to improve the predictive capability of the FSFS2D code.