P. Börner

The EIRENE and B2-EIRENE Codes

Abstract The EIRENE neutral gas transport Monte Carlo code has been developed initially for TEXTOR since the early 1980s. It is currently applied worldwide in most fusion laboratories for a large variety of different purposes. The main goal of code development was to provide a tool to investigate neutral gas transport in magnetically confined plasmas. But, due to its flexibility, it also can be used to solve more general linear kinetic transport equations by applying a stochastic rather than a numerical or analytical method of solution. Major applications of EIRENE are in connection with plasma fluid codes, in particular with the various versions of the B2 two-dimensional plasma edge fluid code. The combined code package B2-EIRENE was developed, again initially for TEXTOR applications, in the late 1980s. It too has become a standard tool in plasma edge science. It is currently mainly used for divertor configurations, such as by the ITER central team, to assist the design of the ITER divertor. Both the EIRENE and B2-EIRENE concepts are introduced and illustrated with sample applications.

Transport of neutral particles in turbulent scrape-off layer plasmas

The effect of turbulence on the transport of neutral species (atom, molecules) in plasmas is investigated. A stochastic model relying on a multivariate gamma distribution is introduced to describe turbulent fluctuations, and implemented in EIRENE. The effects of fluctuations on the neutral density and ionization source radial profiles are investigated. The role of temperature fluctuations is discussed in detail. Calculations with ITER scrape-off layer parameters are presented, and two distinct regimes with respect to the effects of temperature fluctuations are identified, depending on the far SOL mean temperature. Finally, the influence of fluctuations on impurity contamination is discussed.

Non-linear effects on neutral gas transport in divertors

Abstract The effects of neutral particles on the condition of the plasma edge play a key role in divertor and limiter physics. In computational models they are usually treated in the linear test particle approximation. However, in some divertor concepts a large neutral gas pressure is required in the divertor chamber to provide sufficient neutral-plasma interaction in the plasma fan (momentum removal and energy dissipation) and to permit adequate pumping performance. In such regimes viscous effects in the neutral gas may become relevant. We have extended the EIRENE code to solve the Boltzmann equation with a non-linear BGK-model collision term added to its standard linear collision integrals. The linear in-elastic collision integrals are reconsidered with respect to volume recombination and momentum removal efficiency from the plasma. The numerical procedure in the EIRENE Monte Carlo code is outlined. A simple test application (Couette flow) shows that the procedure works properly. First numerical studies have been carried out and the results are discussed.

Tokamak plasma edge modelling including the main chamber wall

Quantifying main chamber wall recycling, erosion and resulting material migration, at least on the basis of known or empirical far scrape-off layer (SOL) processes, is still highly uncertain, despite its relevance for ITER and fusion reactor design studies. This affects, for example, the design problem of first mirror performance of many optical diagnostics in the harsh ITER environment. Poor computational access is not least due to a fundamental technical limitation in apparently all current tokamak edge plasma fluid codes, which implicates a wide computationally unresolved gap between the outermost plasma layer treated in codes and the real vessel wall. We show how the current ITER version of the B2-EIRENE code (SOLPS-4.3) can be extended to cover also this far SOL, on the same footing as the rest of the plasma transport model. We discuss consequences of this new model for estimating plasma power and particle sink terms caused by a fairly realistic wall in ITER based on the conventional Bohm criterion along all plasma–wall interfaces.Corrections were made to this article on 14 July 2011. The authors have been assigned to the correct affiliations.

Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracy by making use of averaging in the Random Noise coupling technique.

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.

Studies of protection and recovery techniques of diagnostic mirrors for ITER

In optical diagnostic systems of ITER, mirrors will be used to guide the light from plasma towards detectors and cameras. The mirrors will be subjected to erosion due to fast particles and to deposition of impurities from the plasma which will affect adversely the mirror reflectivity and therefore must be suppressed or mitigated at the maximum possible extent. Predictive modeling envisages the successful suppression of deposition in the diagnostic ducts with fins trapping the impurities on their way towards mirrors located in the end of these ducts. To validate modeling predictions, cylindrical and cone-shaped diagnostic ducts were exposed in TEXTOR for 3960 s of plasma operation. After exposure, no drastic suppression of deposition was observed in the cylindrical ducts with fins. At the same time, no detectable deposition was found on the mirrors located at the end of cone-shaped ducts outlining the advantages of the cone geometry. Analyses of exposure provide evidence that the contamination of exposed mirrors was due to wall conditioning discharges and not due to working plasma exposure. Cleaning by plasma sputtering was performed on molybdenum mirrors pre-coated with a 100 nm thick aluminum film. Aluminum was used as a proxy of beryllium. During exposure in electron cyclotron resonance-generated helium plasma, the entire coating was sputtered within nine hours, leaving no trace of aluminum and leading to the full recovery of the specular reflectivity without detrimental effects on the mirror surface.