Neutral gas physics and neutral interactions with the plasma are key aspects of edge plasma and divertor physics in a fusion reactor including the detachment phenomenon often seen as key to dealing with the power exhaust challenges. A full physics description of the neutral gas dynamics requires a 6D kinetic approach, potentially time dependent, where the details of the wall geometry play a substantial role, to the extent that, e.g., the subdivertor region has to be included. The Monte Carlo (MC) approach used for about 30 years in EIRENE (Reiter et al 2005 Fusion Sci. Technol. 47 172–86), is well suited to solve these types of complex problems. Indeed, the MC approach allows simulating the 6D kinetic equation without having to store the velocity distribution on a 6D grid, at the cost of introducing statistical noise. MC also provides very good flexibility in terms of geometry and atomic and molecular (A&M) processes. However, it becomes computationally extremely demanding in high-collisional regions (HCRs) as anticipated in ITER and DEMO. Parallelization on particles helps reducing the simulation wall clock time, but to provide speed-up in situations where single trajectories potentially involve a very large number of A&M events, it is important to derive a hierarchy of models in terms of accuracy and to clearly identify for what type of physics issues they provide reliable answers. It was demonstrated that advanced fluid neutral models are very accurate in HCRs, and at least an order of magnitude faster than fully kinetic simulations. Based on these fluid models, three hybrid fluid–kinetic approaches are introduced: a spatially hybrid technique, a micro–macro hybrid method, and an asymptotic-preserving MC scheme, to combine the efficiency of a fluid model with the accuracy of a kinetic description. In addition, A&M ions involved in the edge plasma chemistry can also be treated kinetically within the MC solver, opening the way for further hybridisation by enabling kinetic impurity ion transport calculations. This paper aims to give an overview of methods mentioned and suggests the most prospective combinations to be developed.

A method of analysis of experimental spectra for obtaining the plasma parameters is presented and discussed. Based on the coupling of the spectral line-shape code PPP with the genetic algorithm PIKAIA, the proposed method is inspired by natural selection mechanisms resulting in the development of basic genetic operators. The spectra analysis is performed by fitting experimental spectra with synthetic spectral line profiles obtained by using theoretical models and a set of plasma parameters, such as its temperature and electron density. In the present paper, the diagnostic procedure based on a genetic algorithm coupled with the PPP code has been used for the analysis of both hydrogen Balmer-β and He I 492.2 nm lines in the helium plasma created by corona discharge. The broadening of these spectral lines due to the Stark effect has been considered, together with the van der Waals and instrumental broadening.

We look at the effect of wave collapse turbulence on a hydrogen line shape in plasma. An atom immersed in plasma affected by strong Langmuir turbulence may be perturbed by a sequence of wave packets with a maximum electric field magnitude that is larger than the Holtsmark field. For such conditions, we propose to calculate the shape of the hydrogen Lyman α Lyman β and Balmer α lines with a numerical integration of the Schrödinger equation coupled to a simulation of a sequence of electric fields modeling the effects of the Langmuir wave. We present and discuss several line profiles of Lyman and Balmer lines.

The development of the fourth generation light sources based on the X-ray free electron laser (XFEL) opens new perspectives in the investigation of high-energy-density plasmas. The properties of these tunable X-ray laser sources permit to consider an active spectroscopy experiments to improve the understanding of hot and dense plasmas. In this work, we present prospective calculations of spectral line shapes and redistribution functions of the neon-like aluminum 1s2s(2)2p(6)nl - 1s(2)2s(2)2p(5)nl, (n = 3, 4, 5, ..) and 1s2s(2)2p(6)3l - 1s(2)2s(2)2p(6) lines at 1490 eV and 1572 eV, respectively, for typical laser-plasma conditions. These calculations are based on a theoretical model for calculating the redistribution function in hot and dense plasmas. It relies on an extension of the Frequency Fluctuation of Model. This model takes into account the complexity of the atomic structure of ionic emitters and the various line broadening mechanisms including effects of the emitter environment fluctuations.

Power exhaust of fusion devices is determined by the interaction between the plasma and the wall of tokamaks. The way how fuel ions are reflected has a strong influence on the plasma temperature close to the surface. We investigate with the Soledge2D-EIRENE code different elements like sheath physics and surface roughness that have an effect on those interactions. We show that including realistic ion incidence angles based on 1D PIC sheath simulations provides a less efficient power exhaust than the original model where the ion cyclotron motion was not taken into account. The importance of the reflection database is also investigated considering two values of the Surface Binding Energy (SBE). This leads to consequent differences in the regions where the impact energy of deuterium ions is the smallest. Finally surface roughness is shown to have a positive effect on power exhaust.

Power exhaust is one of the major challenges that future devices such as ITER and DEMO will face. Because of the lack of identified scaling parameters, predictions for divertor plasma conditions in these devices have to rely on detailed modelling. Most plasma edge simulations carried out so far rely on transport codes, which most of the times consist of a fluid code for the plasma coupled to a kinetic Monte Carlo (MC) code for neutral particles. One of the main difficulties in interpreting code results is the statistical noise from the MC procedure, which makes it difficult to define a convergence criterion for the simulations. In this work, we elaborate on similarities between noisy transport code simulations and turbulence simulations, and argue that the time averaged solution is a well defined stationary solution for the system. We illustrate these ideas with a simple slab test case with fluid neutrals, to which we add synthetic noise. In this case, the effects of noise are found to be significant only at high noise levels and for large enough correlations times.

Power exhaust is a key challenge for future magnetic fusion devices. The modeling tools currently available to predict steady-state heat loads are transport codes, which solve mean field fluid equations for the plasma and often a kinetic Boltzmann equation for neutral particles. In several of the main transport codes available in the community, the latter is solved by a Monte Carlo procedure (implemented in the EIRENE code [4]). This has the adverse effect of introducing statistical noise in the system, whose effect on convergence and on code results have been poorly understood until recently. In this contribution, we highlight the analogy between turbulent fluctuations and statistical noise, from which a theoretical formulation of the problem can be extracted. We then illustrate the practical application of these results on a simple slab case, using a fluid model for neutrals, to which statistical noise is added.

Plasma material interactions on the first wall of future tokamaks such as ITER and DEMO are likely to play an important role, because of turbulent radial transport. The latter results to a large extent from the radial propagation of plasma filaments through a tenuous background. In such a situation, mean field descriptions (on which transport codes rely) become questionable. First wall sputtering is of particular interest, especially in a full W machine, since it has been shown experimentally that first wall sources control core contamination. In ITER, beryllium sources will be one of the important actors in determining the fuel retention level through codeposition. In this work, we study the effect of turbulent fluctuations on mean sputtering yields and fluxes, relying on a new version of the TOKAM-2D code which includes ion temperature fluctuations. We show that fluctuations enhance sputtering at sub-threshold impact energies, by more than an order of magnitude when fluctuation levels are of order unity.

The influence of the plasma facing components material on the scrape-off layer plasma is investigated. In particular, the energy recycling is found to be more pronounced for tungsten wall compared with carbon wall. Edge plasma simulations performed with the transport code SOLEDGE2D-EIRENE show that this enhanced energy recycling in the tungsten case leads to an increase of the scrape-off layer temperature. Moreover, the energy recycling depends on the ion angle of incidence with the wall. A PIC code has been used to model the ion acceleration in the magnetic pre-sheath and determine the later angle of incidence. These simulations show that ions mostly impact the wall with rather shallow incident angles leading to a further increase of the energy recycling.

In order to model plasma interaction with full complexity of the geometry of PFCs, an immersed method to impose boundary conditions has been implemented in the transport code SolEdge2D. This penalization technique has proven to properly recover Bohm boundary conditions, including supersonic solutions at the sheath entrance. The role of the ionization source has been taken into account by coupling SolEdge2D with the 3D kinetic neutral code Eirene. Density regimes are properly recovered and major differences between core located and divertor located ionization source regimes are emphasized. One also presents main chamber wall recycling regime simulations that can now be addressed with simulations of the entire edge plasma up to the wall.

The role of neutral particles (atoms, molecules) on scrape-off layer turbulence is investigated using a 2D interchange model. This work is a first step towards a synthetic diagnostic for Gas Puff Imaging experiments, where gas is injected to visualize turbulent structures. A simple neutral model is used to identify various limiting cases of interest. Too strong puffing leads to a reduction of the turbulence fluctuation level. In the strong interaction regime, where the neutral density fluctuates, the relationship between plasma density maps and synthetic camera pictures is discussed. The EIRENE Monte Carlo code has been coupled to TOKAM2D, and a first study of the effect of the Monte Carlo noise on statistical properties of turbulence is presented.

The transport of neutral particles in turbulent plasmas is addressed from the prospect of developing coarse-grained transport models which can be implemented in code suites like B2-EIRENE, currently used for designing the ITER divertor. The statistical properties of turbulent fluctuations are described by a multivariate Gamma distribution able to retain space and time correlations through a proper choice of covariance function. We show that in the scattering free case, relevant for molecules and impurity atoms, the average neutral particle density obeys a Boltzmann equation with an ionization rate renormalized by fluctuations. This result lends itself to a straightforward implementation in the EIRENE Monte Carlo solver for neutral particles. Special emphasis is put on the inclusion of time correlations, and in particular on the ballistic motion of coherent turbulent structures. The role of these time dependent effects is discussed for D2 molecules and beryllium atoms. The sensitivity of our results to the assumptions on the statistical properties of fluctuations is investigated.

A coarse-grained kinetic equation for neutral particles (atoms, molecules) in magnetized fusion plasmas, valid on time scales large compared to the turbulence correlation time, is presented. This equation includes the effects of plasma density fluctuations, described by gamma statistics, on the transport of neutral particles. These effects have so far been neglected in plasma edge modeling, in spite of the fact that the amplitude of fluctuations can be of order unity. Density fluctuations are shown to have a marked effect on the screening of neutrals and on the spatial localization of the ionization source, in particular at high density. The coarse-grained equations obtained in this work are readily implemented in edge code suites currently used for fusion plasma analysis and future divertor design (ITER, DEMO).

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.

This work addresses the transport of neutral particles (atoms, molecules) in magnetized fusion plasmas, in the presence of density fluctuations with given statistics. The latter are described by a multivariate gamma distribution. The geometry is a 2D slab and turbulence is assumed to be statistically homogeneous. The average neutral density and ionization source, which are the quantities relevant for integrated simulations and diagnostic applications, are calculated analytically in the scattering free case. The boundary conditions and the ratio of the turbulence correlation length to the neutral mean free path are identified as the main control parameters in the problem. The non-trivial relationship between the average neutral density and the ionization source is investigated. Monte Carlo calculations including scattering are then presented, and the main trends obtained in the scattering free case are shown to be conserved.

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.

In this work we present a statistical model aimed at retaining edge turbulence fluctuations in the EIRENE neutral transport code. The model relies on sampling a large number of plasma backgrounds, using a given 1 point PDF and a 2 points correlation function, and computing the corresponding average quantities (neutral density profile, ...). Its implementation is validated using a simplified case for which the calculations can be carried out analytically. An intuitive picture of neutral transport in turbulent plasmas is presented. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

This work addresses linear transport in turbulent media, with emphasis on neutral particle (atoms, molecules) transport in magnetized fusion plasmas. A stochastic model for turbulent plasmas, based upon a multivariate Gamma distribution, is presented. The geometry is a 2D slab and turbulence is assumed to be statistically homogeneous. The average neutral density and ionization source, which are the quantities relevant for integrated simulations and diagnostic applications, are calculated analytically in the scattering free case. The boundary conditions and the ratio of the turbulence correlation length to the neutral mean free path are identified as the main control parameters in the problem. The non trivial relationship between the average neutral density and the ionization source is investigated. Monte Carlo calculations including scattering are then presented, and the main trends obtained in the scattering free case are shown to be conserved.

A spatially resolved calculation of the charge exchange particle and energy fluxes on the Toroidal Pumped Limiter (TPL) of Tore Supra is presented, as a first step towards a better understanding and modelling of carbon erosion, migration, as well as deuterium codeposition and bulk diffusion of deuterium in Tore Supra. The results are obtained with the EIRENE code run in a 3D geometry. Physical and chemical erosion maps on the TPL are calculated, and the contribution of neutrals to erosion, especially in the self-shadowed area, is calculated.