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

Abstract

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.

TALIF at H− ion sources for the determination of the density and EDF of atomic hydrogen

“…This causes in turn an increase of the H 2 dissociation rate. The fact that this rise is less pronounced for 0.3 Pa compared to 0.6 Pa is attributed to neutral depletion which depends strongly on the pressure as is observed at BUG experimentally [45] and results from model calculations [46,47]. Neutral depletion describes a reduction of the density of neutral particles due to an elevated electron pressure in the discharge center, strong heating of neutral particles or the strong ionization of neutral particles in the discharge [48].…”

Ion flux measurements using a Mach-Langmuir probe in the ITER prototype neutral beam injection ion source

“…In absolute numbers, the flux component towards the PG increases from around 10 21 to 5 • 10 21 m −2 s −1 . This increase of the flux results partly from an increased plasma density, since the magnetic filter field tends to push the plasma back into the driver, and from the change in the electron momentum balance, where the Lorentz force leads to an increase in the axial component of the electric field [11,14]. In front of the PG the situation is different, as can be seen from a comparison of the three plots in the lower row.…”

“…However, when the magnetic filter field is switched on, also the ions at the top half of the PG start to flow downwards. Results from fluid models [11,14] indicate that this behavior is indirectly caused by the Lorentz force in the electron momentum balance, which affects the vertical component of the electrostatic field, such that the ions experience an additional downward force. Note that the Lorentz force term in the ion momentum balance adds only a negligibly small downward force, which is consistent with the estimation in section 2, that the ions are not fully magnetized.…”

“…In the conclusion section 4, potential use of the obtained data and insights are highlighted. This mainly concerns input and validation data for fluid and kinetic models [11,[13][14][15], which could then be used for optimizing the positive ion and atomic fluxes towards the PG. In this way it becomes possible to improve the negative ion yield and minimize the asymmetry of the co-extracted electrons.…”

RF efficiency measurements of inductively-coupled plasma H− ion sources at accelerator facilities

“…The measured value is indeed high at 80%, but plasma self-shielding and the small contribution of capacitive coupling limit the perfect inductive coupling expected for an ideal transformer. It is to be noted that there are many more parameters, for example the gas pressure and RF-coil quality factor, that affect the spatial distributions of the RF fields and, hence, the coupling and resulting plasma parameters [17,18]. In summary, independent methods have been used to determine or estimate that the coupling efficiency from an external RF-coil into the plasma is around 50%-60%.…”