2D simulations of inductive RF heating in the drivers of the SPIDER device

This paper presents the basic physical and numerical principles of a fluid model of the negative ions 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 paper focuses on details of the RF model and on the initial code developments to simulate the currents in the source induced by the RF currents flowing in the feeding coils. In our approach, the RF electrical field is split in a plasma part plus another one in vacuum, E = Ep + EV, which simplifies the boundary conditions for Ep while EV is obtained from a theoretical formulation for the field generated by a current loop, which results in a fast and flexible numerical algorithm providing converged solution for the RF field after a few iterations, even for the cases with high conductivity of the plasma. The numerical method is based on finite volume approximation and 9-point discretization is used to account on 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). The RF model has been successfully coupled to the fluid equations of the source and self-consistent solutions are analyzed in order to see the influence of the driver parameters and RF model assumptions (e.g. stochastic conductivity, induced magnetic field) on the heating efficiency and the plasma dynamics. It has been found that without magnetic field the plasma dynamics in the SPIDER source is almost independent on the details of the RF coupling model.