Ameres, J.

Angioni, C.

Bobkov, V.

Bruhn, C.

Cavedon, M.

Dux, R.

Kappatou, A.

Lebschy, A.

Manas, P.

McDermott, R.

Ochoukov, R.

Pütterich, T.

Viezzer, E.

English

MPG.PuRe

Low-Z impurity transport studies using CXRS at ASDEX UpgradeC. Bruhn1,2, R.M. McDermott1, A. Lebschy1,2, R. Dux1,C. Angioni1, P. Manas1, J. Ameres3,1, A. Kappatou1, V. Bobkov1, R. Ochoukov1,M. Cavedon1, T. Pütterich1, E. Viezzer4,1, and the ASDEX Upgrade Team1 Max-Planck-Institut für Plasmaphysik, Boltzmannstr. 2, D-85748 Garching, Germany2 Physik-Department E28, Technische Universität München, D-85748 Garching, Germany3 Zentrum Mathematik M16, Technische Universität München, Garching, Germany4 Dpt. of Atomic, Molecular and Nuclear Physics, University of Seville, Seville, SpainImpurities in fusion plasmas arise from many different sources including the erosion andsputtering of material from plasma facing components, the intentional injection of impuritiesfor divertor cooling and core radiation control, and the production of helium from the fusionprocess itself. The plasma performance is highly affected by the impurity concentration and,to achieve a stable burning plasma scenario in future reactors, the build up of impurities in theplasma must be controlled. Therefore, a fundamental understanding of impurity transport infusion plasmas is of great importance. Recent studies have shown discrepancies between theoryand experiment [1], which implies that more work on this topic has to be conducted. A simpleway of describing the particle transport of an impurity Z is with a radial transport equation,where radial implies the transport perpendicular to the flux surfaces.∂nZ(r, t)∂ t=1r∂∂ rr(D(r)∂nZ(r, t)∂ r− v(r)nZ(r, t)), nZ(rmax, t) = s(t) (1)In equation (1), nZ(r, t) is the impurity density, D(r) is the diffusion coefficient, v(r) is thedrift velocity, and s(t) is the boron density source term at at the edge rmax. The process ofparticle transport can, thus, be described by diffusion and convection. By studying steady-statedensity profiles only the ratio of D and v can be obtained and previous work using chargeexchange recombination spectroscopy (CXRS) at ASDEX Upgrade (AUG) has focused primar-ily on steady-state profiles [1, 2]. To disentangle v and D, one needs to measure the temporalevolution of the impurity density profiles after a perturbation, e.g. during a modulation of theimpurity source at the plasma edge. At AUG, a modulation of the power of the boron- andtungsten-coated ion cyclotron resonance frequency (ICRF) antennae results in a modulation ofthe boron density in the plasma. This work aims to exploit this result to determine the borontransport coefficient in AUG plasmas. A requirement for the feasibility of this technique is asteady plasma background which means keeping the electron density and the ion and electrontemperatures constant such that D and v do not depend on time during the modulation. Thisplaces a restriction on the level of the ICRF power that can be modulated. The amplitude of theboron density modulation scales with the ICRH power and, therefore, a compromise betweenthe boron signal and maintaining a constant plasma background has to be found. It has beenconcluded that a power level of ∼ 1 MW of ICRF is sufficient to modulate the boron density up44th EPS Conference on Plasma Physics P5.1702.6 2.8 3.0 3.2 3.4 3.6 3.8time [s]0.00.20.40.60.81.01.21.41.61.8ICRF power [MW], nB [0.86·1017m−3] #33027, f=8.33HzICRFnB at ρtor=0.762.6 2.8 3.0 3.2 3.4 3.6 3.8time [s]0.10.20.30.40.50.60.70.80.9ρtornB [1.3·1017m−3], #330270.53080.58950.64810.70680.76540.82410.88270.94141.00002.6 2.8 3.0 3.2 3.4 3.6 3.8time [s]0.10.20.30.40.50.60.70.80.9ρtornS [1.3·1017m−3], #330270.53080.58950.64810.70680.76540.82410.88270.94141.0000(a) (b) (c)Figure 1: a. Time traces of the modulated ICRF power (blue) and the resultant modulated borondensity (red) for one discharge in the database. The frequency f of the modulation is 8.33 Hz. b.Measured boron density nB. c. Simulated boron density nS.to 10% at the edge while keeping the modulation of the ion and electron temperatures to max-imally 2-4%. It has also been observed that the boron modulation signal is strongest when theexperiments are performed in a freshly boronized machine. This suggests that the ICRF powermodulation affects the boron which originates from the boronization and not the boron from theantenna itself. Furthermore, the resultant modulation does not arise from modulated incidentheat fluxes to the SOL, since a modulation of the power of the electron cyclotron resonanceheating (ECRH) does not result in a modulation of the boron density.At AUG three core CXRS systems can measure the boron content in the plasma. In total thesesystems have 72 lines-of-sight (LOS) and a typical integration time of 10 ms [3, 4]. Figure 1 (a)shows a time trace of the modulated ICRF power, with a frequency of 8.33 Hz, in blue and theresultant boron density in red from one channel at ρtor=0.76 from one of these CXRS systems.To assess the transport coefficients the experimental data is modelled by solving an inverseproblem, where nB is the measured boron density and nS is the simulated one.minD,v,s12‖nS−nB‖2L2([rmin,rmax]×[tmin,tmax]) w.r.t equation (1) (2)Problem (2) is solved by a quasi-Newton method yielding the simulated density nS by solvingequation (1) for various D and v profiles as well as the source term s. A robust ansatz for thesimulated density nS is used when this inverse problem is solved:nS(r, t) = n0(r)+a(r)cos(ωt)+b(r)sin(ωt)s(t) = s0 +a0cos(ωt)+b0sin(ωt).(3)In equation (3), n0 is the steady-state density and ω = 2π f , where f is the frequency of themodulation. The boron source term s(t) is assumed to have the same shape as the density nS.This ansatz suits the used method particularly well, since the measured boron signal has asinusoidal shape, which clearly can be seen in figure 1 (a). The model is thus reduced to thesteady-state and the modulation at the frequency ω , which corresponds to a Fourier transform44th EPS Conference on Plasma Physics P5.1700.50.70.9n0 [1017m−3]Imp. density, #33027, t:2.503 3.943s300306090120Phase [◦]0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8ρtor261014Amplitude [%]simulationexp. data0.2 0.3 0.4 0.5 0.6 0.7ρtor0.00.51.01.52.02.53.0D [m2/s]#33027, t:2.503 3.943exp.GKWNEONEO+GKW0.2 0.3 0.4 0.5 0.6 0.7ρtor321012v [m/s]#33027, t:2.503 3.943exp.GKWNEONEO+GKW(a) (b) (c)Figure 2: a. Steady-state density, phase, and amplitude profiles. b (c). Comparison between experi-mental, neoclassical, and turbulent D (v).in time at the modulation frequency. Thus, no time discretization is necessary. The singularityin equation (1) at r = 0 is resolved by natural Neumann boundary conditions at the axis. D and vare represented with arbitrary degree B-splines and second order finite differences are used forsolving the transport equation. The complete problem can readily be set up and solved using theScipy minimization toolbox in Python. Figure 1 (b) and (c) show an example of the measuredand simulated boron densities, respectively. As one already can see by eye, the agreement isvery good but this becomes even clearer if one looks at the phase and amplitude profiles. Theresulting steady-state density as well as the phase and amplitude of the modulation are depictedin figure 2 (a). The red points represent these quantities as obtained from the measured borondensity profiles and the blue lines are B-spline representations of these quantities from thesimulated density. In this particular case, the steady-state boron profile is hollow. The phaseshift indicates how fast the modulation propagates into the core. The amplitude modulation isstrongest at the edge where the source is located. Looking at this plot it becomes more evidentthat the agreement with experiment is very good. The analysis region is between ρtor=0.2-0.7,as sawteeth are present in the center and there are too few data points outside ρtor=0.7 to capturethe edge gradient properly. Several discharges exploiting this technique have been performed atplasma currents of 0.6 and 0.8 MA. The applied heating powers vary between 0.5-2.4 MW ofECRH and 2.5-10 MW of NBI. The ICRF has a modulation frequency of either 8.33 or 10 Hzin all of these discharges. The measured boron density profiles in the database collected so farrange from slightly hollow to peaked ones.For a subset of the database the experimental data is compared to theoretical predictions. Inthis study the code NEO [5, 6] was used for simulating the neoclassical transport coefficients.The modelling of the turbulent transport was performed with the gyrokinetic code GKW [7].The data shown in this paper was achieved through quasi linear GKW simulations. Turbulentand neoclassical transport components are summed under the assumption that the turbulenttransport heat conductivity matches the anomalous part of the power balance heat conductiv-ity, which is computed with TRANSP, see Ref. [8] for more details. An example comparisonbetween experimental and theoretical D and v for one discharge in the database is depicted in44th EPS Conference on Plasma Physics P5.1700 2 4 6 8 10D (theory) [m2/s]0246810D (exp.) [m2/s]ρtor= 0.45-0.558 6 4 2 0 2v (theory) [m/s]864202v (exp.) [m/s]ρtor= 0.45-0.552 1 0 1 2 3 4R/LnZ (theory)2101234R/LnZ (exp.)ρtor = 0.5B, see ref. [1]He, see ref. [1]B, new(a) (b) (c)Figure 3: a (b). Total theoretical D (v) plotted against experimental D (v) averaged over a ρtor intervalof 0.45 to 0.55. The red point represents the data shown in previous figures. c. Experimental andtheoretical values of the normalized gradient at ρtor=0.5.figures 2 (b) and (c). Neoclassical diffusion (black line) is, as expected, much smaller than themeasured values. The turbulence driven transport (green), however, is of the correct order ofmagnitude. In this case the total theoretical D (magenta) agrees quantitatively with the experi-mental one, whereas the total theoretical v is in the opposite direction. It should be noted thatthere are cases in which the D profile shows poorer agreement, see figure 3 (a) overall, however,it trends quite well with the experiment. In all cases the predicted v from GKW is significantlymore negative, which is shown in figure 3 (b), and this suggest much more peaked profiles thanwhat is seen in the experiment. This is consistent with earlier work at AUG looking at the steady-state profiles, see figure 3 (c), in which the normalized gradient R/LnB from the boron modula-tion database collected so far, cyan diamonds, is compared to previously conducted steady-statetransport experiments, red and blue points [1], at ρtor=0.5. It can be concluded that the new datais able to reproduce the prior experiments.In summary, the ICRF modulation technique has been exploited at AUG for obtaining time-dependent boron density signals. A database of transport coefficients at different heating scenar-ios have been collected and compared to theory. The first comparison shows that the diffusionpredicted by GKW is of the correct order of magnitude and tends well with the experimentaldata. The predicted convections, on the other hand, are significantly more negative (inward)than seen in the experiment.References[1] A. Kappatou, Conference proceeding, EPS Conference Lisbon, 39E O4.128 (2015)[2] R. Dux, Impurity Transport in Tokamak Plasmas, IPP Report 10/27 (2004)[3] E. Viezzer et al, Review of Scientific Instruments 83, 10 (2012)[4] R. McDermott et al, Review of Scientific Instruments, accepted (2017)[5] E. Belli and J. Candy, Plasma Phys. Control. Fusion 50, 9 (2008)[6] E. Belli and J. Candy, Plasma Phys. Control. Fusion 54, 1 (2012)[7] A. G. Peeters et al., Comp. Phys. C. 180, 12 (2009)[8] C. Angioni et al, Nuclear Fusion 51, 2 (2011)We thankfully acknowledge the financial support from the Helmholtz Association of German Research Centres through the Helmholtz Young Investigators Group program. This work hasbeen carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 under grant agreement No633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.44th EPS Conference on Plasma Physics P5.170

Low-Z impurity transport studies using CXRS at ASDEX Upgrade

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Low-Z impurity transport studies using CXRS at ASDEX Upgrade

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