Dux, R.

Janzer, A.

Pütterich, T.

English

MPG.PuRe

Flushing and Erosion of Tungsten during Edge Localised ModesR. Dux, T. Pütterich, A. Janzer, and the ASDEX Upgrade TeamMax-Planck-Institut für Plasmaphysik, EURATOM Association, Garching, GermanyIntroductionIn ASDEX Upgrade, the transition from carbon based plasma facing components towardsa full tungsten machine offers the opportunity to study the erosion and transport of a high-Zelement. In H-mode discharges with type-I ELMs, the tungsten production at the plasma fac-ing components is dominated by the erosion during ELMs. Nevertheless, discharges with lowerELM frequency have higher tungsten concentration in the confined plasma and a minimumELM frequency of about 80 Hz is required to perform long steady discharges with constanttungsten concentration. The ELM frequency is usually increased by increasing the deuteriumpuff level. The flushing of tungsten from the confined plasma during the ELM seems to be thedominant effect compared to the expected increase of tungsten production. In order to disentan-gle the effects of production and flushing of tungsten during an ELM cycle, the experimentalsituation of a series of discharges #22895-#22901 with varying ELM frequency was modelledwith the impurity transport code STRAHL. The experimental results were presented in [1].The Impurity Transport ModelThe STRAHL code [2] solves the radial continuity equation for each ionised stage of an im-purity. For the radial transport turbulent diffusion coefficients and drift velocities are set ad hoc,while a full treatment of the neo-classical transport parameters is included. The backgroundplasma parameters likene, Te andTi are taken from the experiment. The calculation domainextends into the scrape-off layer. Here, the parallel transport towards the divertor or to the lim-iting elements in the main chamber is described by volumetric losses with a loss frequency, thatis given by the parallel connection length between the surface elementsLk and the mean flowvelocity of the deuterium ions:νk = (2M==Lk)pkB(3Ti +Te)=mD, where the Mach numberMwas set to 0.1 for the presented results. At a certain radius in the SOL, the main chamber limitersare introduced into the code by switching the connection length from 50 m to 1 m. The neutralimpurities start with a prescribed rate at this limiter position. They have a constant radial ve-locity v0 and their density decays radially according to the rateνion = nehσionvei for ionisation:n0(r) = n0(r lim)(r lim=r)exp[ R(νion=v0)dr].For this work, the code was enhanced to model light impurities and tungsten during one runin order get a more realistic description of the tungsten behaviour during the ELM cycle. For theshown results carbon and oxygen were included. The tungsten erosion is mainly due to physicalsputtering by light impurities and the new version allows to calculate the influx rate of neutraltungsten from the loss of light impurity ions onto the limiter and the sputtering yield [3]. Here,the yield for normal incidence is used, which is a function of impurity mass and energy. Theenergy at the surface is approximated byE = kB(2Ti +3ZTe), where the second term describesthe acceleration in the sheath, that depends on the ion charge. The ion stage distribution variesduring an ELM cycle, when higher charged ions are swept out from the ETB and hit the limiter.An example for the temporal evolution of the W influx is given in the upper left graph of Fig.1,36th EPS Conference on Plasma Phys. Sofia, June 29 - July 3, 2009 ECA Vol.33E, O-5.056  (2009)which gives results for the modelling of a phase with 100 Hz ELM frequency of discharge#22895.The blue curve shows the influx change due to the increased losses of C, O, and Wwithout considering the changes in the sputtering yield. For the red curve, only the temperature12300 1 2 3 4 5∆t [ms]010203040TiTe〈Z〉=const.〈Z〉 and T=const.all effects01 1-fprompt0 1 2 3 4 5∆t [ms]01 ne,lim [1019m-3]Tlim [eV]Φ [1019s-1 ] #22895Fig.1: Temporal evolution of the tungsten influx andthe fraction of not promptly redeposited W during anELM cycle. The used values forTe, Ti andne at thelimiters are shown in the lower graphs.change at constant charge distribution is con-sidered, while the black curve is calculatedtaking all effects into account. The ELM con-tributes 73% to the time integrated influx dur-ing one ELM cycle of 10 ms duration.From the energy of the sputtering impu-rity a mean neutral velocity for the sputteredW is calculated assuming a Thompson dis-tribution. The ionisation length of W is inthe range of the Larmor radius of the ionisedtungsten and a fractionfprompt of ionised Wreturns to the surface on the first travel alongthe Larmor radius. This prompt redepositioneffect is included for the sputtering by eachion species. To this end, we use the resultfor a cosθ angular velocity distribution in a homogeneous plasma, wherefprompt = 1=(1+(∆tionωc)2), and integrate it over the whole distribution of times∆tion to reach the ionisationradius. This simplified treatment yields nearly the same values forfprompt as the correct integra-tion over the angular distribution in a plasma with radial gradients and is justified consideringthe uncertainty about the angular distribution. In Fig.1, the upper right graph shows the part ofthe ionised tungsten that is not promptly redeposited, where the toroidal field wasBt = 2:5 T.During the ELM, the rise ofne and Te lead to shorter ionisation lengths and thus enhancedprompt redeposition. From the influx during on ELM cycle, 29% is not promptly redeposited.The simultaneous treatment of light impurities and tungsten is also needed for the calculationof the collisional transport parameters in the ETB. For carbon and other light impurities, the#228950.9 0.95 1 1.05ρpol-300-200-1000100C O W v/D [      ]m-10.11.010.0 an. ELMan.no ELM+neo C O W D [        ]m2/s0.9 0.95 1 1.05ρpolFig.2: Profiles of diffusion coefficient and driftparameter for the modelling of #22895.transport in the ETB between ELMs has beenfound to be in accordance with neo-classical trans-port coefficients [4, 5]. Since it is characterised bya strong inwardly directed Pfirsch-Schlüter (PS)pinch, it is assumed that tungsten transport in theETB is also dominated by PS transport leadingto even higher pinch velocities due to the highercharge. The collisional transport of tungsten isdominated by collisions with low-Z impurities andit is necessary to include impurity-impurity colli-sions in the calculation of the PS transport coefficients of W. With increasing low-Z impurityconcentration the diffusion coefficientDPS increases. Furthermore, the low-Z impurities lead toa dilution of the deuterium ions. Thus, thenD profile has a decreasing gradient with increasinglow-Z concentration in the ETB and the PS inward pinch of tungsten decreases. The elements36th EPS 2009; R.Dux et al. : Flushing and Erosion of Tungsten during Edge Localised Modes 2 of 4of the radial transport model are depicted in Fig.2, which is again for #22895. In the phase be-tweenELMs, the anomalous diffusion coefficient (blue curve) was reduced in the ETB to a lowvalue of 0.1 m2/s. The collisional values from classical and PS transport are much larger withhighest values for W. The red curves show the sum of both contributions for each element. Thetotal value of the drift parameterv=D in this phase are shown in the right box, where W has thestrongest inwardly directed drift. It is just calculated from the collisional pinch which dependson the impurity charge. The mean charge at poloidal flux labelρpol=0.99 is 5.6 for C, 7.4 for Oand 16 for W. An ELM is induced by a sudden switch-on of a large diffusion coefficient in theedge (black curve), which decays linearly within 1 ms.The resulting evolution of the total W density during an ELM cycle of #22895 is shown innW [10   m   ]-314∆t (ms) 0.9 0.95 1 1.05ρpol02468100.20.40.60.81.01.21.4 #22895Fig.3: Modelled evolution ofthe total W density during oneELM cycle.Fig.3. The cycle has been repeated up to quasi-equilibrium, i.e.the density profile at the end and at the beginning of the cycleare equal. The density gradient around the separatrix is stronglydegraded during the ELM and the increasing source from thelimiter, which is atρpol=1.063, leads to a density rise in the outerSOL. After the ELM, the source decreases and a strong densitygradient forms in the ETB. The ratio of the tungsten density atρpol=0.9 to the value atρpol=1 is 22 at the end of the cycle and7.2, when taking the temporal average during an ELM cycle. ora similar discharge #22901, which had 10 times less deuteriumpuff and an ELM frequency of about 50 Hz, the respective den-sity ratios are 51 and 17.Modelling Procedure and ResultsThree discharge phases with different deuterium puff levelsΦD and ELM frequencies weremodelled #22898:ΦD=1.51022 s 1, fELM200 Hz, #22895:ΦD=1022 s 1, fELM100 Hz, and#22901:ΦD=1021 s 1, fELM50 Hz. Average profiles ofne, Te andTi were fitted for equal timedelays to the ELM start using a 500 ms long discharge period. For each quantity a profile withtime delays in the range 0-2 ms after the ELM and 4-2 ms before the ELM was fitted. A simpli-fied time evolution of the profiles during an ELM cycle was generated using a temporal shapef (∆t) = (∆t=τc)exp[ ∆t=τc] to switch on and off the ELM profile, where the characteristictime τc=0.4 ms was used. The carbon influx level was set ad hoc and complete recycling ofthe carbon loss to the wall was used. The influx level was chosen to get a fit of the measuredC concentration atρpol = 0:95 which was 0.9% for #22898, 1.2% for #22895, and 2.1% for#22901. The oxygen influx was set to 1/4 of the carbon influx. Thei profiles from edge CXRSdo not extend into the far SOL and theTe profiles from Thompson scattering are too uncertainin the far SOL in order to decide whether the temperature at the limiter is 10 or 15 eV, whichhas a dramatic effect on the sputtering yield. Thus, the ELM and inter-ELM value ofTe andTiat the limiters were prescribed in order to get the measured tungsten influx from the outboardlimiters, which were shown to be the dominant source for the tungsten concentration in theconfined plasma [1]. Here,Ti = 2Te was taken and the adjustments were done until the tempo-rally averaged influx as well as the ELM contribution to the influx, which is about 70% for allELM frequencies, was fitted. The used inter-ELM and ELM values forTe at the limiter were36th EPS 2009; R.Dux et al. : Flushing and Erosion of Tungsten during Edge Localised Modes 3 of 48.4 eV/12 eV for #22898, 10 eV/20 eV for #22895, and 12 eV/35 eV for #22901. Only 1/3 ofthelow-Z impurity losses were considered for the W production at the outboard limiters. Thischoice reflects the difference in the poloidal profile of the impurity penetration for W and low-Zimpurities, where the latter are assumed to pentrate equally well from low- and high-field sideplasma facing components.The transport model for each input parameter set was solved until temporal equilibrium wasreached. This was done for an artificial scan of the ELM frequency withfELM=0, 50, 100,and 200 Hz using all three settings for the background profiles, limiter temperatures and low-Zfluxes. Fig.4 shows a number of key quantities for these scans. Black curves are for the settings0246810[1018s-1]Φ0 50 100 150 200fELM [s-1]110100τp [ms]110100nnsepρ=0.90 50 100 150 200fELM [s-1]10-510-4cW(ρpol=0.8)Fig.4: Calculated edge density ratio, sourcerate, particle confinement time and W con-centration for a scan of the ELM frequency.All quantites are temporal averages of oneELM cycle.of #22898, blue for #22895, and red for #22901.The black circles surround the points, for which thelimiter temperatures, ELM sizes, and influx valueswere adjusted to the measurement. The upper left boxshows the strong decrease of the W density peak-ing with increasing ELM frequency, which can reachvalues on the order of 100 for the artificial zeroELM case. The plasma with the lowest puff level hasthe highest peaking factors. The particle confinementtime τp of W (lower left box) is calculated with thetotal number of W ions in the confined regionNWand the total sourceΦ. It decreases strongly with theELM frequency. The higher parallel losses for the lowpuff plasma with higher SOL temperatures leads toslightly lower τp than for the high puff case. In theupper right box, the increase of the erosion source withfELM is due to the linear picture withouttaking the change of the ELM size and the lower inter-ELM temperatures into account. The en-circled points reflect the measured behaviour. Nevertheless, the rise of the source is not strongenough to beat the change inτp andcW at ρpol=0.8 decreases on each of thelinear curves,as shown in the lower right box. Going along the encircled points the values are 3.5x10 5,1.6x10 5, and 8.7x10 6 from low to high ELM frequency. The drop from 50 to 100 Hz is dueto the decay inτp and from 100 to 200 Hz due to the drop inΦ. The calculatedcw values areactually within 10% of the measured values 3.6x10 5, 1.8x10 5, and 8.4x10 6. Even thoughthis is an encouraging result, we consider the model only to be a consistent description basedon many ad hoc assumptions, which need further detailed experimental investigations. How-ever, it seems, that we captured the dominant mechanisms to understand the tungsten particleconfinement.References[1] R. Dux, et al., J. Nucl. Mater.390-391, 858 (2009).[2] R. Dux, Rep. IPP 10/30, Max-Planck-Institut für Plasmaphysik, Garching (2006).[3] W. Eckstein, et al., Rep. IPP 9/82, Max-Planck Institut für Plasmaphysik, Garching (1993).[4] T. Pütterich, et al.,Proc. of the 35rd EPS Conf., vol. 32F, P–2.083, Geneva (2008).[5] T. Pütterich, et al.,this conference(2009).36th EPS 2009; R.Dux et al. : Flushing and Erosion of Tungsten during Edge Localised Modes 4 of 4

Flushing and Erosion of Tungsten during Edge Localised Modes

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Flushing and Erosion of Tungsten during Edge Localised Modes

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