EIRENE Code Research Articles

Integration of kinetic ions in a three‐dimensional Monte‐Carlo neutral transport code

AbstractCharged particles of species different from the major constituents of a plasma might not reach local thermodynamic equilibrium during their lifespan. Such low collisional ions render the often‐used fluid description, assuming Maxwellian velocity distribution, as insufficient. Hence, kinetic treatment of such minorities becomes inevitable. The three‐dimensional kinetic neutral particle Monte‐Carlo code EIRENE [D. Reiter et al., Fusion Science and Technology, 47 (2), 172 (2005)] possesses a model for ion transport reduced in physics, consisting of field‐line tracing and energy relaxation of particles. The trajectory integration is now extended to account for first‐order particle drifts, anomalous cross‐field diffusion denoting for turbulence effects, and the consideration of the magnetic mirror force. The technical implementation, as well as the verification of the enhanced kinetic ion transport is being reported.

Investigations of the first-wall erosion of DEMO with the CELLSOR code

Fusion reactor systems codes (SCs) are 0.5d codes used for optimization studies towards the design of a tokamak demonstration power plant (DEMO). These codes usually comprise a description of the core plasma physics, technology aspects and reactor economy, while only a coarse description of plasma-wall interaction (PWI) aspects is included. Therefore, the new systems code extension CELLSOR (Code to Estimate the Lifetime Limited by Sputtering Of a Reactor wall) was developed in order to allow inclusion of PWI effects into reactor optimization studies. CELLSOR is foreseen to be used as a secondary tool for PWI evaluations, taking design point parameters from the European PROCESS systems code as input. CELLSOR consists of an analytical treatment of the plasma in the scrape-off layer (SOL) for fuel ions (D, T), solving the 1.5d continuity equation in fluid approximation to obtain perpendicular flux and ion density in the SOL, and a fast Monte-Carlo description of the neutral particle (D, T) behavior. The Monte Carlo (MC) implementation of the new code extension was successfully benchmarked with results from the EIRENE code. The trajectories of eroded neutral W were computed within CELLSOR ERO, an add-on code used for calculations of prompt re-deposition and self-sputtering. The damage by ions was calculated analytically for fuel (D, T), ash (He), seeding gas (N) and wall material (W), including the acceleration by a sheath in front of the wall, assuming radially constant impurity concentrations.Six exemplary DEMO SOL test-cases were defined, covering the range of predicted diffusive and convective transport strength within the SOL, and of upstream separatrix density levels sufficient for detached diverter conditions. The damage by ions (D, T, He, N, W) and by hot neutrals (D, T), being born by charge-exchange within the hot pedestal region (ΔT=−300eV/cm), was compared for the six cases. The results indicated, that in the investigated low density and weak transport cases, the recharged neutrals caused the major threat to the FW due to bad SOL screening ability, i.e. deeper plasma penetration for neutrals. In the other cases, N ions were the dominant driver for erosion due to their high concentration levels and strong sheath acceleration.Furthermore, the net erosion, incl. prompt re-deposition and self-sputtering, was investigated for variations of the wall clearance ΔSOL, which was identified as the main control parameter to keep the FW erosion in the main chamber below acceptable levels. Within the intermediate reference case, i.e. medium transport (D⊥=0.5m2s−1, v⊥=5ms−1), the net erosion rate was acceptable, if the wall clearance was at least ΔSOL ≥ 14 cm, whereas a clearance of ΔSOL ≈ 25cm was sufficient within all 6 investigated test-cases.

Asymmetry of the Balmer-alpha line shape and recovery of the effective hydrogen temperature in the tokamak scrape-off layer

An algorithm for recovering the effective temperature of atoms of hydrogen (and its isotopes) in the tokamak scrape-off layer from the asymmetry of the Balmer-alpha line shape is proposed. The algorithm is based on the parametrization of the asymmetry of the line shape caused by the nonlocal character of neutral hydrogen flux from the wall into the tokamak plasma. The accuracy of the algorithm is tested against the results of simulations of the velocity distribution function of deuterium neutrals in the scrape-off layer by the EIRENE code with the use of the source data on the main plasma component in the quasi-stationary stage of the inductive mode of ITER operation calculated by the SOLPS4.3 (B2-EIRENE) code.

Two-dimensional imaging of edge plasma electron density and temperature by the passive helium emission ratio technique in TJ-II

An intensified visible camera looks tangentially at a poloidal limiter where helium recycles, acting as a wide neutral source, and the atomic line emission due to plasma excitation becomes strongly localized there. It includes a bifurcated coherent bundle, each end with a different interference filter to select helium atomic lines, so that two simultaneous filtered images are captured in one single frame. The object of the proposed technique is to apply the well-known helium-beam line-ratio technique to obtain from selected filtered images the two-dimensional (2D) edge plasma ne and Te. The code EIRENE was used to demonstrate that the helium emission from recycling neutrals dominates the emission for the lines of view passing close above the limiter. Since these chords are nearly parallel to magnetic field lines in the emission region, the images can be approximated to poloidal cuts of the plasma emission within the tolerances discussed in the paper. The absolute radial profiles of Te and ne obtained with the method presented here were checked in the TJ-II stellarator to be in relatively good agreement with other diagnostics within a wide range of plasma parameters for both ECRH and NBI plasmas. The method is finally used to get 2D images of edge plasma Te and ne.

Numerical estimates of the ITER first mirrors degradation due to atomic fluxes

A systematic numerical study of the deposition of Be and C atoms on the ITER main chamber first mirrors and their erosion due to fast D(T) atoms has been carried out. The calculations are based on Monte-Carlo neutral transport modelling (with the EIRENE code) on a simulated steady-state plasma background. A generic reduced model of cylindrical and conical diagnostic ducts is considered. The results indicate that the sputtering of the mirrors can be made acceptably small if they are installed in sufficiently long ducts. At the same time the deposition of impurities can be a serious issue even for mirrors protected in long channels. However, the calculations of deposition are not very reliable at the current stage and a need to seriously improve them is indicated.

Scaling of carbon erosion in Tore Supra

The scaling law for carbon erosion in Tore Supra previously established by Hogan et al. [1] (ΦC(C/s)=5×1020 Pcond (MW), where Pcond is the conducted power) is revisited both from the experimental and the modelling point of view. New developments with the EIRENE code, that allow relating measured CII emission intensities to the total amount of carbon sputtered from the Toroidal Pumped Limiter, are presented. Recent measurements carried out at high input power show a good agreement with the database used to establish the scaling law.

Design and installation of the closed helical divertor in LHD

Neutral particle behavior in the Large Helical Device heliotron has been investigated to conduct the effective particle control using the intrinsic helical divertor. It was revealed that the torus in–out asymmetry observed in the neutral pressure distribution depended on the divertor particle flux distribution, and thus, on the operational magnetic configuration. It was also revealed that the neutral pressure in the vacuum vessel in LHD was below 0.1 Pa. Degradation of the plasma confinement with increasing of the neutral pressure was observed, and that suggested the effective particle control is necessary for the sustaining of long discharge with high performance plasma and the further improvement of the confinement. The modification of the open helical divertor to the closed one was investigated for the particle control using helical divertor by using EIRENE code. Results of the calculation showed that proper rearrangement of divertor plates and additional components, such as dome structure make the neutral particles to be compressed well in the divertor region, and effective divertor pumping to be possible. Based on the simulation and experimental results, design of the closed helical divertor was completed and it will be partially installed in the Large Helical Device before the experimental campaign in 2010.

2D edge plasma modeling extended up to the main chamber

Far SOL plasma flow, and hence main chamber recycling and plasma surface interaction, are today still only very poorly described by current 2D fluid edge codes, such as B2, UEDGE or EDGE2D, due to a common technical limitation. We have extended the B2 plasma fluid solver in the current ITER version of B2-EIRENE (SOLPS4.3) to allow plasma solutions to be obtained up to the “real vessel wall”, at least on the basis of ad hoc far SOL transport models. We apply here the kinetic Monte Carlo Code EIRENE on such plasma solutions to study effects of this model refinement on main chamber fluxes and sputtering, for an ITER configuration. We show that main chamber sputtering may be significantly modified both due to thermalization of CX neutrals in the far SOL and poloidally highly asymmetric plasma wall contact, as compared to hitherto applied teleportation of particle fluxes across this domain.

Transport Characteristics in the Stochastic Magnetic Boundary of LHD: Magnetic Field Topology and Its Impact on Divertor Physics and Impurity Transport

Transport characteristics of the stochastic magnetic boundary of the Large Helical Device (LHD) are investigated, based on three-dimensional Monte-Carlo Braginskii-type fluid model code, EMC3, coupled with the kinetic neutral transport code EIRENE, in direct comparison with experimental observations for aspects of the relation between the magnetic topology and the resulting transport in terms of counter acting flux tube flows and impurity screening/transport. Divertor probe measurements show a rather weak divertor parameter dependence on upstream density in contrast to those of tokamaks at high-recycling regime. This is found to be due to the loss of parallel momentum via cross-field interaction between the stochastic flux tubes, where strong flow shear exists. The three-dimensional modeling predicts an impurity screening potential of the stochastic scrape-off layer (SOL) at high densities. The remnant island geometry affects the energy transport, which leads to suppression of the thermal forces by increasing cross-field energy flux across islands at high collisionality. The screening effect is most pronounced at the edge surface layers with a strong friction force exerted by the background plasma flow, where the flow toward divertor is enhanced due to the rich ionization source. Modeling results are compared to the edge carbon emission obtained in experiments, where a reasonable agreement on the density dependence is found, indicating the existence of the impurity screening mechanism in the stochastic SOL of LHD.

Progress on Radiative Transfer Modelling in Optically Thick Divertor Plasmas

AbstractThe physical model used in the photon transport module of the Monte‐Carlo code EIRENE (www.eirene.de) is presented. A critical assessment of the spectral line broadening mechanisms (which give the shape of the photon‐atom reaction rates) and of their relevance in a transport simulation is carried out (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Line shape modeling for radiation transport investigations in magnetic fusion plasmas

Hydrogen line radiation can be trapped in some spatial regions within magnetic fusion experiments at high density, typically when N H(∼ N e) ∼ 10 15 cm −3. The corresponding photoexcitation yields a significant additional source of ionization that must be properly characterized by numerical simulations. Kinetic Monte-Carlo codes provide a capability to study this subject; however, these codes require accurate physical models for the reaction rates, including spectral line shapes. In this paper we deal with the Zeeman–Stark model used for the Ly α transition in the EIRENE code [D. Reiter, M. Baelmans, P. Börner, Fusion Sci. Technol. 47 (2005) 172; www.eirene.de] and we address the influence of ion dynamics, which can affect these line profiles. The impact theory for ions, that we first consider, is shown to be suited for description of the lateral components of the Lorentz triplet. By contrast, comparisons to numerical simulations show that this theory is not well suited for description of the central component, which is significantly affected by incomplete and non-binary collisions. A refinement of the model in the framework of the unified theory is proposed and discussed.

Spatially resolved Hα-emission simulation with EIRENE in TJ-II to study hydrogen atomic and molecular physics in low density, high temperature fusion edge plasmas

This paper is a continuation of previous studies (de la Cal et al 2007 J. Nucl. Mater. 363–365 764, de la Cal et al 2007 Proc. 34th EPS Conf. (Poland, Warsaw) P 2.029), where hydrogen recycling under ionizing plasma conditions was analysed by spatially resolved Hα-emission spectroscopy with a tangentially viewing camera looking at a poloidal limiter of the TJ-II stellarator operated with a low density, high temperature plasma edge (ne = (1–10) × 1012 cm−3 and Te = 40–400 eV). In this study, the first objective is to validate for hydrogen the recently implemented EIRENE codea www.eirene.de by comparing simulated Hα-emission chords with that obtained experimentally. The second objective is to analyse the atom and molecular neutral distributions in front of the limiter and at other plasma and chamber locations. The third one is to study the atomic and molecular reactions involved in the dissociation, ionization and excitation reactions, as calculated from the EIRENE code, in order to study hydrogen atomic and molecular physics in a low density, high temperature fusion plasma edge, with special focus on interpretation of Hα-emission. The contribution of the different reactions to the emission is analysed as a function of plasma radius. A relevant result obtained from EIRENE under this item is that the main precursor of the molecular Hα-emission is not H2 as proposed in many previous studies, but .

Towards radiation transport modelling in divertors with the EIRENE code

Opacity effects, in particular of Lyman lines, in divertors are believed to be relevant for plasma spectroscopy and for the overall divertor dynamics through possible redistribution of excited hydrogen atoms and radiation losses. Quite elaborate computational radiation transport tools have been developed, specialized for numerous applications. The task in fusion research has been adaptation to fusion edge plasma conditions. In this paper, we start from an existing kinetic neutral particle code already well adapted to divertor applications, and extend this from the `particle' simulation to an analogue `photon gas' simulation. It is shown how this can be achieved and that a quite flexible and detailed divertor radiation transport code can conveniently be obtained. We apply this to study Lyman opacity effects on population kinetics and hydrogen divertor radiation losses.This article was scheduled to appear in issue 7 of Plasma Phys. Control. Fusion. To access this Special issue on advanced Tokamak research in EFDA-JET please follow this link: http://stacks.iop.org/0741-3335/44/7

Modelling of plasma momentum transference to side-walls by neutral particles

Monte Carlo modelling of plasma extinction by neutral particles requires energy and momentum sinks to be determined with sufficient statistical significance. We focus on this aspect using calculations of an idealized 1D plasma-gas interface with the Eirene code. A novel non-linear version including self-collisions amongst neutral particles is also applied to admit gas viscosity. It emerges that statistically significant momentum losses often cannot practicably be determined, even at modest plasma temperatures (∼ 10 eV), using conventional collision-estimator techniques. Gas viscosity effects also tend to inhibit extraction of plasma momentum and hinder extinction. Certain possibilities to improve numerical methods are mentioned.

Boundary layer study on the WENDELSTEIN 7-AS stellarator

At low ι (∼ 0.34), W7-AS is operated with limiter; smooth flux surfaces extend into the limiter shadow. At higher ι, the plasma surface is separatrix dominated. The resonant 5/ m island chain gives rise to corrugated surfaces. This paper deals with two difficulties on the way to a complete edge transport modelling in this complex 3D geometry. (1) At low ι, strong deviations from exponential edge density decay (shoulders) are observed. Measurements with reversed B-field indicate that they are caused by superimposed, stationary E θ × B particle drifts. (2) The open edge topology of the corrugated high ι case cannot be represented by standard magnetic coordinates. As a first step towards 3D modelling, the open structures were parametrized on the basis of the flux conserving, open magnetic surface concept. As a first application, wall recycling fluxes for a low density ECRH discharge have been derived by mapping Langmuir probe data onto the wall along the open surfaces and used to simulate the 3D neutral gas distribution with the EIRENE code.

Measurement and monte carlo computations of H α profiles in front of a TEXTOR limiter

In order to assess the existing data for hydrogen reflection and penetration into boundary plasmas, the spectral profile of Hα emitted in front of a TEXTOR limiter has been measured with a high resolution spectrometer and calculated with the EIRENE code. The emission has been investigated for standard recycling conditions of hydrogen, but also for the case that this recycling is superimposed by a strong puff of hydrogenic molecules injected through a hole at the limiter tip. This latter case was used to calibrate the molecular transport model. The Hα profiles during recycling have been observed and calculated for both a graphite and a stainless steel limiter. As expected, the number of reflected particles strongly increases in going from the C to the Fe limiter and seems to be slightly overestimated by present surface reflection databases.

Assessment of critical physical assumptions in consistent 2D plasma edge modelling

Two dimensional multifluid plasma edge transport codes, combined with complete Monte Carlo models for the neutral particles, have become a standard tool to investigate tokamak boundary layer physics. In this paper one of the most widely applied plasma edge codes, i.e. the BRAAMS (B2) code, is evaluated firstly by testing the influence of different neutral particle source term models of various degrees of sophistication, ranging from the original “minimal” analytic description in B2 to the fully three-dimensional Monte Carlo code EIRENE. Secondly, by comparison with another plasma edge transport code, the assumption of ambipolarity and the absence of diamagnetic fluxes, resulting in the omission of contributions to ion-electron energy transfer, is investigated. It is demonstrated that already in a low recycling open limiter tokamak, plasma conditions are very sensitive to details of the neutral particle transport. Therefore, it is expected to be even more sensitive in higher recycling divertor configurations. Furthermore, it is shown that the assumption of ambipolarity may lead in some circumstances to spurious features in radial profiles, in particular for the ion temperature.

Particle exhaust above the ohmic density limit in TEXTOR

Experiments have been carried out in the TEXTOR tokamak to investigate the performance of the pump limiter ALT-II at the highest achievable core densities. Neutral beam heating allows the density to be extended beyond the ohmic limit. The use of one beam raises the line-averaged density limit by approximately 50%. Results from discharges with co- and balanced injection are shown. Plasma fluxes to the pump limiter increase with density. Up to 4.5×10 21 ions/s (720 A) are collected in the eight segment belt, with pumped particle fluxes of up to 3×10 21 atoms/s (60 mbar l/s). Exhaust efficiency determination requires knowledge of the efflux of plasma from the core, which can be estimated from SOL profiles and from D α emission. Both exhaust efficiency estimates increase with density. Experimental results are discussed in terms of predictions from the neutral transport code EIRENE.