The tasks described above require a complex modelling effort which was carried out with ASTRA coupled to STRAHL.The boundary conditions in ASTRA are set at the separatrix by experimental values while in STRAHL they are set at the plasma "limiter".
The following input parameters are given in ASTRA:
• Shape of the separatrix,IpandBT.
• Geometric quantities of vessel and plasma.
• Experimental electron density ne, electron and ion temperatures Te and Ti which were used to set the boundary conditions at the separatrix.
• Power deposition profiles of NBI to electrons and ionsPNBI,eandPNBI,iand depo-sition profiles of the driven current by NBI jNBI are calculated using NUBEAM.
• Power deposition profiles of the ICRH to electrons and ions PICRH,e and PICRH,i obtained with the wave deposition model TORIC4 [85] inside TRANSP.
7.2. ENERGY AND PARTICLE TRANSPORT MODEL
• Power depositions profiles of the ECRH to electronsPECRH and the driven current (jECRH) calculated with TORBEAM.
The current profile is evolved assuming neoclassical resistivity and setting the experimen-tal toexperimen-tal plasma current as boundary condition. The bootstrap current is also taken into account using the Sauter-Angioni formula [86]. The particle source takes into account the ionisation from neutrals, the contribution of the NBI and of the recycling flux through the separatrix. The radial distribution of the neutrals is calculated in the subroutine NEUT, implemented in ASTRA, which solves the kinetic equation for a neutral distribution in slab geometry [41]. To summarise, every STRAHL run needs:
• Plasma geometry provided by SPIDER.
• Plasma background profiles which in this work are provided by ASTRA.
• Atomic data for ionisation, recombination and emission of impurities taken from the ADAS database.
• Transport coefficients as presented below.
7.2.1 Core and pedestal modelling
The electron and ion temperatures, as well as the electron density, are modelled in AS-TRA. The impurity density transport and radiation are simulated in STRAHL which takes the non-coronal effects due to transport into account. For the modelling the following facts are important: in H-mode plasmas, the very steep gradients in the ETB collapse dur-ing an ELM and recover durdur-ing the inter-ELM phase. It was found experimentally that the impurity transport between ELMs is well described by neoclassical theory including both diffusion and pinch [30]. This implies that impurities in the ETB are subject to a neoclassical pinch leading to steep density gradients which are flattened during ELMs.
Therefore, it is possible to identify two main temporal phases: the short phase during the ELM, characterised by a strongly increased transport and the phase between ELMs described by neoclassical theory. According to neoclassical theory, the inward pinch be-comes stronger as Z increases. Consequently, each impurity has a different gradient in the H-mode ETB.
The presence of heat and particle sources needed to rebuild the pedestal after an ELM crash and the transport effects which determine the heat and particle profiles are essen-tial factors in the simulations. Taking into account all these elements, a semi-empirical transport model was built as follows.
• CoreTe,Ti modelling: In the core, Te andTi are modelled assuming turbulent and neoclassical transport. For the turbulent transport the critical gradient model has
CHAPTER 7. MODELLING OF THE RADIATION AND IMPURITY EVOLUTION IN PRESENCE OF ELMS
been employed (see section2.5). For the neoclassical contribution, the neoclassical electron heat conductivity has been used for the electrons, while the neoclassical ion heat conductivity has been used for the ions, withχeNEO<<χiNEO.
• Pedestal (ETB)Te,Ti modelling: In the pedestal bothTe,Ti are modelled assuming neoclassical ion heat conductivity [86]. The neoclassical conductivity for the elec-trons is in fact two orders of magnitude too low to explain the experimental data.
Therefore, the empirical choiceχe=χihas been used. The pedestal is 2.5 cm wide from the separatrix inwards. The diffusivities are prescribed such that they match the ELM-averaged pedestal top temperature profiles. The boundary conditions are set at the separatrix by experimental values.
• Corenemodelling: The evolution ofneis obtained assuming purely turbulent trans-port in the core. The turbulent part of the particle diffusivityDnis chosen as a frac-tion ofχe,turb. Since the particle source in the core is rather small in steady-state the convection velocity V is chosen such that the drift parameter fulfills− V
Dn = ∇ne
ne . With this choice the normalised experimental density gradients are well reproduced.
• Pedestalne modelling: In the pedestal, the evolution ofne is obtained settingD= 0.7·χiNEO. In the following section, whenever the density peaking is mentioned, the following definition is used:npeak= n0
<n>Vol withn0being the density on axis and
<n>Volthe volume-averaged density. Since frequent ELMs erode the pedestal, the source is varied to maintain the pedestal top electron density at the target value.
• Corenz modelling: In the core, the turbulent particle diffusivity of the impurities is chosen as a fraction ofχi. The turbulent convection velocity is set to zero.
• Pedestalnz modelling: The impurity pedestal transport is at neoclassical level. The neoclassical contribution is computed in STRAHL using NEOART [47]. NEOART produces the diffusion coefficient Dneo and the convective velocities Vneo for all impurity species for a given magnetic equilibrium, electron and ion temperature profiles and density profile. The impurity turbulent convection is set to zero. The impurities considered in this work are nitrogen (from impurity seeding) and tung-sten (from the wall). Their source is set 2.0 cm outside the separatrix in STRAHL.
Its magnitude is chosen such that the experimentalPradand impurity concentrations are reproduced once the equilibrium is reached. The SOL is not modelled in AS-TRA, but it is used in STRAHL for the impurity evolution to the separatrix and to the limiter. The SOL parameters are adjusted in order to get the required impurity concentrations in the pedestal. More details about the SOL can be found in [45].
Example profiles of the electron heat diffusivity χe and the electron particle diffusivity D and electron particle convection V are shown in figure 7.1 a) and b). Profiles of the neoclassical impurity diffusion coefficientDneo and the neoclassical impurity convection velocityVneo are shown in figure7.1c).
7.2. ENERGY AND PARTICLE TRANSPORT MODEL
0.0 0.2 0.4 0.6 0.8 1.0 ρtor
6 4
0
[m2/s]
2 8 10 12
14
D
χe -20
-40
-60
-80
0.0 0.2 0.4ρtor0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 ρtor
-0.8 - 0.2 - 0.4 - 0.6
-1.0 0.0 0.2 0.4
Dneo
Vneo V
V[m/s]
[m/s]
[m2/s]
a) b) c)
Figure 7.1:a) Electron heat diffusivityχe and electron particle diffusivityD, b) electron particle convection V, c) impurity diffusion Dneo and impurity convection coefficients Vneo from NEOART.
7.2.2 ELM modelling
The ELMs can be modelled based on two different assumptions. Both consider the fact that ELMs induce a high transport during their short crash.
• Diffusive ELM model: ELMs are simulated as an instantaneous increase in heat and particle diffusivities in the "ELM affected area" which is 2.5 cm wide (ρtor= 0.92−1.0). The diffusive transport during the ELM flattens the profiles. They steepen again during the inter-ELM phase due to sources and the presence of the neoclassical inward pinch.
• Convective ELM: An outward convective velocity causes a loss of the impurity content. The instantaneous increase of the convective transport coefficients in the ELM affected area is applied to both particle and impurity convection velocities.
In both cases, the ELM frequency is set according to the experiments. In the following simulations an ELM lasts for 2 ms. In this time interval the increase of the diffusivities (diffusive case) or of the convection velocity (convective case) in the ELM affected area is adjusted to reproduce the experimental variation of the line integrated density measured by the H-5 channel from interferometer measurements and the stored energy obtained from the equilibrium reconstruction.
CHAPTER 7. MODELLING OF THE RADIATION AND IMPURITY EVOLUTION IN PRESENCE OF ELMS