Bruesehaber, B.

Gehre, O.

Peeters, A.

Ryter, F.

Salzmann, H.

Suttrop, W.

English

MPG.PuRe

1469Particle transport determined from modulated gas puffA.G. Peeters, Hi Salzmann, 0. Gehre, F. Ryter, W. Suttrop, B. Briisehaber,and the ASDEX Upgrade teamMax Planck Institut fiir Plasmaphysik, Euratom-IPP AssociationBoltzmannstrasse 2, 85748 Catching, GermanyThe paper discusses the particle transport which is detennined through modulatedgas puff experiments in ASDEX Upgrade, The Thomson scattering data is used for theanalysis, and a so called forward method is used to determine the transport coefficients.Because the modulated ECRH experiments do not show any density modulationsthe equation that describes the density evolution is assumed independent of the tem—perature. The density (n) evolution is assumed to be given by the linear equationgt?" 3 ‘25:“ TD”)? + T‘V(r)n + S(r,t) flip) 2% £2), (1)Where S = 5(7‘, 15) is the particle source, and 130'} (V(r)) is the diffusion (convection)coeiiicient. The transport operator is written in cylindrical coordinates with r beingthe effective radius of the flux surface labeled by the poloidal flux 7,1), Rm is the majorradius of the magnetic axis, and l) is the volume enclosed by the surfaces on which thepoloidal flux is 1/)Method of analysisA so called forward method is used to determine the transport coefficients. In thismethod the transport equation is solved for certain values of the transport coefficients.Using a non-linear fitting algorithm the transport coefficients are adapted until thesolution of the transport equation (1) fits best to the measurements. If radial profilesof the coefficients are to be found, this procedure is an under—determined problem.Therefore, one has to limit the number of possible solutions. It is preferable to findthe smoothest profile of the coefficients that is allowed by the measurements. Such asolution can be found by regularizationThe code that performs the analysis solves the transport equations in the regionWhere S (at) m 0, for a given set of frequencies, mostly the modulation frequency only.The diffusion (D) and pinch (V) coefficient are given on a grid of the radial coordinate,ri i = 1 —> N. The transport equation is then solved and the solution 1% is determined atthe radial points {1"} j = 1 ~+ M") where the density is measured by Thomson scattering.The nonlinear fit procedure then minimizes the following functionwe), WM) = R + a2, (2)1470where2?; (BDs/é‘ 2 i: BIG/6r)”R=a 15:11)???) +azzlEN=1Vig (3)and M2_ smog—rem”) 2 smog—ens,» 2“EX 0,- i+( 03. )~ (4)Here, n is the measured density profile, 0' is the standard deviation of the measurement,and .‘R (9:) denotes the real (imaginary) part of the Fourier amplitude. Minimizing thelast term in equation (2) yields the normal least square fit to the data. Minimizing thefirst term yields a, solution for which the gradients of the coefiicients are minimized,Le. a smooth function. The coeflicient o: is chosen such that the obtained fit lies withinthe error bars of the measurements. In this way a. fit to the data is found which is bothacceptable and has the most smooth radial profiles of the difi'usion and pinch coefficients.ResultsAs an example two shots will be discussed, one (#8005) in which the working gasis Deuterium and one (#8618) in which the working gas is Hydrogen. The gas pufl"is modulated with a frequency of 5 Hz. The plasma, parameters of the two shots aresimilar, and are given in table 1.Table 1. Plasma parameters of the analyzed shotsshot gas IP H; n 1019 m"3 T; keV8005 D2 1 MA -2.5 T 4.6 1.48618 H2 1 MA —2.5 T ‘ 5.1 1.1The diffusion coeficient and pinch velocity for the Deuterium case obtained fromthe 5 Hz component is shown in Fig. 1 together with the obtained fits to the data.The results for the Hydrogen case are shown in Fig. 2. The error bars on the difi‘usionand pinch are estimated using difi'erent sets of data. points. These error bars only showhow the uncertainty in the measurement influences the determination of the transportcoefficients within this method. Of course non-smooth profiles of the coeficients can beconstructed for which the solution fits just as well to the data. In this sense the errorbars are arbitrarily large.The diffusion coefficient increases towards the plasma edge. A large inward pinchis found at the edge. The transport coefiicients for the case with Hydrogen are highercompared with the Deuterium case. These results agree with those previously found onASDEX [1].The question whether the obtained transport coefficients from the modulation alsoexplain the steady state profiles is investigated by simultaneously fitting the FourierWWW—7‘1471amplitude of the modulation frequency and the steady state profile. The agreement forthe Deuterium case is reasonable {it must be noted that V in this case is not accuratelydetermined from the 5H2 component, see Fig. 1), whereas no good fit is obtained in theHydrogen case.lfusion Dnn [mPJs] Pinch Vnn [m/s]0.0 — — 4 _ _W 05 - v '5‘a.6. E 2 - ~c 0.4 ‘ l:3 :50.2 - - 0 ' 10.0 . . . . . .0.0 0.2 0.4 0.0 0.0 1.0 0.0 0.2 0.4 0.6 0.0 1.0rla maHeal part of density amp/1919 imaginary part of density amp/1 e19005 - - 012° ' ‘ x ‘0.15 - 4_ 0.00 — HE g 0.10 — -6:" E.005 - . ;a: 0.05 » :1X ‘ I0.10 — M - 0-00 ‘ 0 . 1 *0.0 0.2 0.4 0.5 0.0 1.0 0.0 02 0.4 0.6 0.0 1.0r/a r/aF1'3. 1. Obtained results for the Deuterium caseDiflusion Dnn [m2/s] Pinch Vnn [m/s]2.0 . ' ‘ ' - .8 . .Eu" 1.5 v - ._. 6 - -Ill _ .E E 4_,_. l 0 “ ' I: 2 7 .‘5 I:5 > o 4 .0.5 - - .2 - -0.0 . . 4 . -0.0 0.2 0.4 0.6 0.0 1.0 0.0 0 2 0 4 0.0 0 a 1 0r10 r10Real part of density amp/13190.10 1025 - - .0.05 . ‘7,;- 3 0.20 . 1E- E 15:, 9-00 g 0.15 - » ll0.05 . 0.10 - - 10.0 0.2 0.4' 0.6 0.8 1.0 0.0 0.2 0.4 0.0 0.0 1.0We: rlaFig. 2. Obtained results for the Hydrogen case1472Temperature perturbation during modulated gas puffDuring the modulated gas puff experiments a large temperature perturbation isobServed, which increases in amplitude towards the plasma centre. This in contrast tothe density perturbation which decreases in amplitude. This temperature perturbationnevertheless can be explained largely from the convective terms in the linearized energ)rbalance c27%“ = VnDTTVT — gfvro — To‘ — Eros + ohm, (5)where the tilde denotes the perturbation and the index zero the unperturbed quan-tity. In Eq. (5) T is the temperature, I‘ the particle flux, and Qhem is the externalheating (in this caso Ohmic heating). With the particle transport determined themeasured temperature can be fitted with Eq. (5), in which one new unknown ap~peers, the heat diffusion coefficient DTT. A reasonable fit can be obtained as shownin Fig. 3. The heat diffusion coefficient, however, is larger that the ones obtainedin modulated ECRH experiments, which indicates that other terms in the transportequation might play a. role. In future experiments modulated gas puff and modu-lated ECRH experiments will be combined to determine the coupling more accurately.Diffusion Dtt [ma/s] Flea! pan 0! temp. ampl. (eV) Imaginary part. (eV)20 - 404. .15- 42- ‘§ 3 1o “4g -16-a: 20 5- 45.1 0 .200 l l . I I n I '22 w. w . i -0.0 0.2 0.4 0.0 0.0 1.6 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.3 1.0r/a “a rlaFig 3. Results of the fit to the temperature perturbation (Deuterium case).ConclusionThe transport coefficients can be deter-mined accurately from Thomson scatteringusing the forward method, This method has the advantage that no processing of the datais necessary, which would lead to additional sources of errors. The most smooth profileof the coefiicients obtained by the method allows for a study of the radial dependence.References[1] KW. Gentle, O. Gehre, K. Krieger, Nucl. Fusion 32, 217 (1992).

Particle Transport Determined from Modulated Gas Puff

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Particle Transport Determined from Modulated Gas Puff

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