Review of particle-in-cell modeling for the extraction region of large negative hydrogen ion sources for fusion

Abstract

Particle-in-cell (PIC) codes are used since the early 1960s for calculating self-consistently the motion of charged particles in plasmas, taking into account external electric and magnetic fields as well as the fields created by the particles itself. Due to the used very small time steps (in the order of the inverse plasma frequency) and mesh size, the computational requirements can be very high and they drastically increase with increasing plasma density and size of the calculation domain. Thus, usually small computational domains and/or reduced dimensionality are used. In the last years, the available central processing unit (CPU) power strongly increased. Together with a massive parallelization of the codes, it is now possible to describe in 3D the extraction of charged particles from a plasma, using calculation domains with an edge length of several centimeters, consisting of one extraction aperture, the plasma in direct vicinity of the aperture, and a part of the extraction system. Large negative hydrogen or deuterium ion sources are essential parts of the neutral beam injection (NBI) system in future fusion devices like the international fusion experiment ITER and the demonstration reactor (DEMO). For ITER NBI RF driven sources with a source area of 0.9 × 1.9 m and 1280 extraction apertures will be used. The extraction of negative ions is accompanied by the co-extraction of electrons which are deflected onto an electron dump. Typically, the maximum negative extracted ion current is limited by the amount and the temporal instability of the co-extracted electrons, especially for operation in deuterium. Different PIC codes are available for the extraction region of large driven negative ion sources for fusion. Additionally, some effort is ongoing in developing codes that describe in a simplified manner (coarser mesh or reduced dimensionality) the plasma of the whole ion source. The presentation first gives a brief overview of the current status of the ion source development for ITER NBI and of the PIC method. Different PIC codes for the extraction region are introduced as well as the coupling to codes describing the whole source (PIC codes or fluid codes). Presented and discussed are different physical and numerical aspects of applying PIC codes to negative hydrogen ion sources for fusion as well as selected code results. The main focus of future calculations will be the meniscus formation and identifying measures for reducing the co-extracted electrons, in particular for deuterium operation. The recent results of the 3D PIC code ONIX (calculation domain: one extraction aperture and its vicinity) for the ITER prototype source (1/8 size of the ITER NBI source) are presented.

Kinetic sheath in presence of multiple positive ions, negative ions, and particle wall emission

“…For the simplest case of an electropositive hydrogen plasma with one positive ion specie (protons), potential sheath drops and sheath sizes of the presented analytical model were successfully benchmarked in 51 against two particle-in-cell codes ONIX 52,53 and BACON 21 and one analytical model 28 . Both ONIX and BACON enforce the Bohm criterion and the presheath voltage drop within 20 % when compared to fluid sheath results.…”

“…The one-dimentional PIC code BACON 21 is used to benchmark the present analytical results. Only the main properties of this code will be recalled here as it was already presented 21 and benchmarked 51 . This code permitted to model the sheath using typical plasma parameters for a hydrogen plasma in a negative hydrogen ion source 21 .…”

Negative Hydrogen Ion Sources for Fusion: From Plasma Generation to Beam Properties

“…A result of an ONIX simulation for the former BATMAN test facility is shown in Figure 8 [50]. Plotted is the negative hydrogen ion density for a vertical cross-section through one extraction aperture, axially starting 15 mm upstream of the PG surface until the EG surface.…”

Characterisation of negative ion beam focusing based on phase space structure

“…One candidate is a three-dimensional meniscus shape. Recently, a three-dimensional meniscus shape is reported with particle-in-cell simulations [21,22]. Three-dimensional magnetic fields and the inhomogeneity of the negative ion flux may cause the threedimensionality of the meniscus.…”

“…One of the most important factors that determines the beam focusing is the formation of a plasma meniscus, which is the boundary between the source plasma and the beam [21,22]. The meniscus is physically defined as the equipotential surface, where the quasi-neutrality is broken [23,24].…”