ASDEX Upgrade Team

Coster, D. P.

Krieger, K.

Laux, M.

Pugno, R.

Yoon, S. W.

English

Coster, D.

Yoon, S.

MPG.PuRe

Modelling of Impurities in the ASDEX Upgrade Divertor II with DIVIMP and B2-Eirene

MODELING OF IMPURITIES IN THE ASDEX UPGRADEDIVERTOR II WITH DIVIMP AND B2-EIRENER. Pugno, K. Krieger, D.P. Coster,M. Laux, S.W. Yoon and the ASDEX Upgrade TeamMax-Planck-Institut für Plasmaphysik, EURATOM Association,Boltzmannstr. 2 D-85748 Garching, GermanyIntroduction In this study the spectroscopic measurements of C  emission in the DivertorII configuration of ASDEX Upgrade are compared with modeling results of carbon erosionand transport. The plasma is simulated using the multifluid-Monte Carlo ‘B2-EIRENE’ codepackage [1]. The computed hydrogenic plasma is also used as input for the two dimensionalMonte Carlo impurity transport code ‘DIVIMP’ [2]. Line of sight integrated C  emissivitiesobtained from both codes are compared with measurements.                                                inboarddivertor outboarddivertor1.0 1.2 1.4 1.6 1.8 2.0-0.6-0.8-1.0-1.2-1.4R [m]z [m] s = 1.24 ms = 0.30 ms = 0.47 ms = 1.07 ms = 0.00 mFigure 1: Simulated 465 nm C  emissiv-ity [ph m s sr ] obtained from ‘DI-VIMP’ and geometry of the measuringlines of sight in the divertor .Experiment In the ASDEX Upgrade divertor arraysof lines of sight viewing radially across the strikepoints are available for spectroscopic measurementsin the visible spectral range (Fig.1). The lines of sightare coupled via optical fibers to two photomultipliersystems equipped with interference filters. The C  line at 465 nm was measured with a time resolutionof 150  s. The discussed results refer to the station-ary phase of a hydrogen fuelled L-mode discharge(#11275). The main plasma parameters are as follows:plasma current I = 1 MA, average electron densityn  = 4 	   m , toroidal magnetic field B  = -2.5 T,neutral beam power P    = 3.4 MW. The plasma wasradially shifted during the discharge to provide im-proved spatial resolution of edge temperature and den-sity measurements. The presented measured data arethe time average between 2.1 and 2.7 s.Plasma modeling The plasma is modeled by usingthe ‘B2-EIRENE’ code package. Bulk species Hand C -C are considered and describedin the fluid approximation by the ‘B2’ multi-fluid code. This description is self-consistentlycoupled to the ‘EIRENE’ Monte Carlo code, which calculates the spatial distribution of neutralhydrogen and the source term for the impurities. The numerical grid for the simulation isobtained from magnetic equilibrium data of the analyzed shot.For parallel transport, classical coefficients are used. With respect to the cross-field diffusion,anomalous heat and particle diffusion are assumed. The heat diffusivity and the particle diffu-sion coefficients are assumed constant with values obtained from the interpretive version of thetwo dimensional edge plasma fluid code ‘B2.5-SOLPS5.0’ [3]. The diffusion coefficients forthe discharge (         1 m /s, D "  1 m /s) are obtained by minimizing the differencebetween code prediction and measurements. This interpretive vesion of the code is faster andwell suited to model the main plasma, but not very accurate in divertor plasma modelling. Nopinch velocity is considered.Power  density    [10  W/m  ]52Flux  density  [10  1/s m  ]222531S_coordinate - S_separatrix [m]0.00 0.10 0.200.00 0.10 0.200.00 0.10 0.200.05 0.15480S_coordinate - S_separatrix [m] S_coordinate - S_separatrix [m]Electron temperature [eV]0102030CODEThermographyBolometry (deconvolved)CODELangmuir probesCODELangmuir probesb)a)c)Figure 2: a) Power density and radiation power den-sity, b) ion flux density c) electron temperature and thecorresponding calculated quantities as function of thecoordinate S-S $ % & along the target.B2-EIRENE 1%B2-EIRENE 3%DIVIMP 3%DIVIMP 1%       [10   ph m s sr  ]19-2-1-12.01.51.00.50.0S  coordinate [m]1.151.10 1.20 1.25Intensity Figure 3: Line of sight integrated C ' ( intensity(465 nm) for 1% and 3% chemical erosion yield for DI-VIMP and B2-EIRENE.The diffusion coefficients, the tempera-ture and density profiles and other mainchamber measurements are used as inputparameters for the full version of the code.Since divertor measurements are not usedas code input, it is important to validatethe computed plasma in the divertor.The integrated flux and power in both di-vertor legs and the total radiated power arereasonably well reproduced by the code(Tab.1). The inboard divertor is how-ever partially detached. In this condi-tions the measurements are more difficultto interpret and the code has difficulties tomodel the observed asymmetries betweenthe two divertor legs. In the following thediscussion is therefore restricted to the re-sults for the outboard divertor.In Fig.2 are plotted a) power density mea-sured from thermography and radiationpower density onto the target plate frombolometry deconvolution, b) flux den-sity and c) electron temperatures mea-sured from Langmuir probes and the cor-responding values predicted from the codeas function of the distance S along the tar-get in the outboard divertor. The com-puted plasma in the outboard divertor re-produces nicely the measurements andtherefore will be used to study impurityproduction from the target plate.Impurity modeling Both ‘DIVIMP’ and ‘B2-EIRENE’ codes can treat impurities, howeverwith different underlying physical models. ‘DIVIMP’ follows trajectories of impurity neutralsand ions in a given background plasma. ‘EIRENE’ calculates the particle sources with theresulting ion source rate transferred to B2, which treats the ion species as a fluid. In ‘DIVIMP’the impurity source is calculated similarly to ‘EIRENE’, however without taking into accountneutral hydrogen impact.Integral values DIVIMP B2-EIRENE MeasurementsParticle Flux In [s ) * ] 6.6e22 5.3e22 1e22Particle Flux Out [s ) * ] 6.4e22 6.2e22 3e22Power In [W] 5.1e5 3.1e5 2e5(Probes)/2.5e5(Therm.)Power Out [W] 7.2e5 8.6e5 6e5(Probes)/2.8e5(Therm.)Total radiation [W] 1.1e5 (Only C) 6.3e5 7.5e5Table 1: Comparison of global plasma measurements and code predictionsDIVIMP 2% 1 eVDIVIMP Garcia R.-Roth 0.4 eV       [10   ph m s sr  ]19-2-1-12.01.51.00.50.0S  coordinate [m]1.151.10 1.20 1.25Intensity DIVIMP Garcia R.-Roth 1.0 eVDIVIMP 3%  1 eVMEASUREMENTa)b)B2EIRENE 2% 1eV       [10   ph m s sr  ]19-2-1-12.01.51.00.50.0S  coordinate [m]1.151.10 1.20 1.25Intensity B2-EIRENE 3% 1.0 eVMEASUREMENTB2-EIRENE 5% 1.0 eVFigure 4: Measured and calculated line of sight in-tegrated C , - intensity (line at 465 nm) for differentchemical erosion models with a) ‘DIVIMP’and b)‘B2-EIRENE’.‘DIVIMP’ needs as input the plasma geome-try mesh, as also used by ‘B2-EIRENE’, theplasma background parameters and the crossfield diffusion coefficient D . (here assumedradially constant). The background plasma isobtained from ‘B2-EIRENE’ and the diffu-sion coefficient set to D . = 1 m , /s accordingto the ‘B2-EIRENE’ value. For the calcula-tion of the carbon source term, both physi-cal sputtering and chemical erosion are takeninto account. The self-sputtering contribu-tion are negligible. Atomic data used for cal-culation of line emissivities are taken fromthe ADAS database [4] for both codes.Fig.3 shows the line integrated intensitiesalong the line of sight in the outboard di-vertor as function of the cross-section coor-dinate S (see Fig.1) of the line of sight withthe target plate, assuming physical sputteringand 1% and 3% constant chemical erosionyield for both ‘B2-EIRENE’ and ‘DIVIMP’,using the corresponding ‘B2-EIRENE’ back-ground plasma. The two models agree for S/1.17 m, but differ towards the separatrix.Here and in the following physical sputteringis always considered, in addition to chemical erosion, with yields obtained from Eckstein/93[5].Results and discussion Fig.4(a) shows line integrated C , - intensities from ‘DIVIMP’ as-suming chemical erosion yields according to Roth-GarciaRosales/96 [6], with 0.4 eV and 1 eVinput (Franck-Condon) energy, and for constant chemical erosion yield (2% and 3%, 1 eVFranck-Condon energy). The best agreement with the experiment is obtained with 3% constantchemical yield. Still this sputtering option fails to reproduce the emission maximum near theseparatrix at the strike point.C1+ C2+ C3+C4+C1+ C2+ C3+C4+Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #Radial cell #Poloidal  cell #DIVIMPB2-EIRENE13 6.5 1.8 10 0 0 0C  ion density    [10  m  ]C   ion density   [10  m  ]    C    ion  density       [10  m  ]C   ion   density      [10  m ]1718-3 -317 17 -3 17 -34+3+2+1+SeparatrixSeparatrixSeparatrixSeparatrixSeparatrixSeparatrixSeparatrixSeparatrixSOLSOLSOLSOLSOLSOLSOLSOL To plasma coreTo plasma coreTARGET PLATETARGET PLATEFigure 5: Carbon densities for different ionization states calcu-lated from ‘DIVIMP’and ‘B2-EIRENE’.Fig.4(b) shows the line inte-grated emission obtained from‘B2-EIRENE’ for 2%, 3% and5% constant chemical erosionyields, with 1 eV input energy.The best matching is obtained fora erosion yield between 3% and5%.To illustrate the influence of thetransport models on the calcu-lated spatial distribution of car-bon, Fig.5 shows the two dimen-sional density distribution fordifferent carbon ionization statesfor both codes. In each image inthe Figure the vertical coordinaterepresents the magnetic field linedirection from the target (bot-tom) towards the plasma core (top) and the horizontal coordinate represents the perpendiculardirection to the field, from private flux region (PFR,left) into the scrape off layer (SOL, right).The C 0 1 density in the SOL is similar in both the codes, but differs in the PFR. Moreover thedifferent evolution in the ion density distribution among the different ionization states for thetwo codes, indicates an effect of the different transport models.Conclusion Similar results are obtained with ‘B2-EIRENE’ and ‘DIVIMP’ using the samebackground plasma and analog sputtering models, but significant discrepancies arise approach-ing the separatrix position. A fairly good agreement is shown between divertor measurementsand model predictions, both for the profile shape and the absolute value in the outboard divertor.‘B2-EIRENE’ is able to reproduce the emission maximum near the separatrix better than ‘DI-VIMP’. This is explained with an important contibution to the carbon influx from neutral par-ticles sputtering, accounted for in ‘B2-EIRENE’ but not in ‘DIVIMP’. Another difference, butapparently less important in this first analysis, is the different underlying transport approach:fluid in the first case, kinetic in the second. More measurements and analysis are underway forcomparing other emission lines (CII, H 2 ) in both L-mode and H-mode discharges.References[1] D.P. Coster et al., J.Nucl.Mater. 241-243 (1997) 690.[2] P.C. Stangeby and J.D. Elder., J.Nucl.Mater. 196-198 (1992) 258.[3] J.W. Kim et al., J.Nucl.Mater. 290-293 (2001) 644.[4] H.P. Summers, in: Atomic Data and Analysis Structure User Manuals Users Manual, Rep. JETIR(94) 06, JET Joint Undertaking, Abingdon (1994)[5] W. Eckstein et al., Sputtering Data Rep. IPP 9/82, Max-Planck-Institut fur Plasmaphysik, Garching(1993).[6] J. Roth, C.Garcia-Rosales, Nucl.Fus. 36 (1996) 1647.

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Modelling of Impurities in the ASDEX Upgrade Divertor II with DIVIMP and B2-Eirene

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