Coster, D.

de Pena Hempel, S.

Fahrbach, H.

Fischer, R.

Haas, G.

Herrmann, W.

Kardaun, O.

Khutoretsky, A.

Reiter, D.

Schneider, R.

Stober, J.

Verbeek, H.

English

MPG.PuRe

.‘1.|.I 5,,'1 i..'.'.ir!.-_'L:‘Il‘ f0”0f Ion Temperature and Neutral Density from the Simulation ofSPrflfile nts and Additional Experimental Data.-Charge' Exchange MeasuremeJ, Stober, D. P. Coster, H.-U. Fahrbach, R. Fischer, G. Haas, W. Herrmann,.0. Kardaun, A. Khutoretsky l, S. de Peiia Hempel, D. Reiteri, R. Schneider,H. Verbeek, the ASDEXrUpgrade team, and the N131 teamMaxePlanclt-lnstitut fiir PlasmawPhysik, EURATOM—Association,D-85T48 Garching, GermanyT ERG “Kurchatovvlnstitute", 123182, Moscow, Russia1 WP, Forschungseentrum Jiilich GmbH, EURATOM~Associatiom35242.5 Jiilich, Germany1 Introduction.At ASDEXrUpgrade a method to evaluate the ion temperature profile has been developedby fitting the measured energy spectra of the neutral hydrogen and deuterium fluxes. varying the parameters of the T,- profile. Two detection principles are used to cover theextremely wide energy range [15 eV, 2i] half]. It turned out that a reasonable accuracyat the separatrix can only be obtained when measurements of the total neutral fluxare included in the fit as well [1]. In addition to the T,- prpfile, the neutral densityalong the lines of sight and a spatially constant H /D-ratio are determined. The methodcan also be used during neutral beam injection (NBI) so that comparison with local T;measurements from. charge exchange recombination spectroscopy (CXRS) is possible. Theresults are also compared to classical logarithmic slope evaluation. Finally, the problemof the parameterisation—dependent results is addressed and we present first results of aBayesian approach to determine the necessary degree of regularisation.2 Experimental 'The energy spectra of the neutral fluxes are measured with two methods. One is based onthe reionisation in a gas cell and an energy and mass separation of these ions in parallelelectric and magnetic fields [2]. The lowest detectable energy is normally set to 500 e‘v’.At ASDEXuUpgrade, there are two analysers of this type which both view the plasmafrom the outer midplane. One is fixed and views the plasma center (CXA I), the otheris turnable to vary its poloidal'and toroidal direction (CXA II). The other method is atime+of4flight analysis of the neutrals without isotope separation (LENA) [3]. Its energyrange is between 15 eV and 1 half. The total neutral flux is measured directly with an iongauge at the outer vessel wall [4]. Additionally an Ha Incasuremei'it has been set up witha line of sight close to the one of LENA (horizontal, 28 cm above the magnetic axis). Forthe T; evaluation further experimental data are used: 11,, from interferometry combinedwith lithium beam, T, from Thompson scattering or ECE, and the proton density fromspebtroscopy [ti]. These quantities, as wellas Tr, are assumed to be constant on fluxs11 rtanea.I023{0103 Fitting procedure 'To model the energvdresolved neutral finnes 8(Eu), we assume that the velocity distrib-utign of the ions has Maxwellian form:I :v3(30) : fififl *1: gunfire! 3-?" ($)'flg(1fl )‘n1"(3) 6% Eli-'exl} (“/0 $3) (litThe neutral densityr is 'obtained with the EIRENE Monte—Carlo code [5], using only theexperimental data and the T; parameters of the corresponding iteration step as input forthe plasma background. The positioning of. an assumed source of neutrals at the outerplasma—facing structures (outer source), which is required by the code, turned out tohe of miner importance. For verger lear densities inner—wall sources also playr a role, butonly for the central plasma. Volume recombination as source of neutrals must not beneglected. For the T,- profile a linear spline parameteriaation is used. Parameters to befitted are the T,- values at the knots. Additional parameters are the spatially constantI'I/DLratio and the strength of the outer source. We use a get—type minimization, whichtakes experimental errors into account. The number of time consuming neutral densitj,rcalculations could be reduced to 3 or even less by a two step algorithm, which optimizesthe parameter values for a fixed neutral density which is recalculated only in an outerloop. Parameter errors are estimated from the curvature at the minimum of X2. In thefollowing graphs error bars refer to one standard deviation.4 Comparison with T,- from other diagnosticsIn the case of NEI heated plasmas, local Ti-data are available from CXRS [7] also. Figure 1 shows a comparison of the two methods. The agreement is quite good in this case.so ,§ 10 '% 1 - . 25m ......1 (nae, ' 1D'2; 1olfl-Lnl‘ig: m ————————————i 16' 2‘1”“ for?. , r2" w “1150:: '" ‘ --“ 5 3%5%.: Till Te 5., E31““rriue i pit: 12' . 2:.g 10 ~ 53.} 2n§1dw_ fl l.a-exns %h‘e' an assisted ea lives ii iii? ‘d.i"‘d.s" Ell-Hid]energy {at} rho poloidalFigural: Analysis ofa WEI-heated plasma (l : 1.0 Md, B; : ~25 T, 5 .41l N30.Left: data with errors, fit {solid lines) and iii-rile regions oftlie neutrals. Since deuteriumis injected, this isotope deviates from the fit at higher energies. Only the 3‘ lowest pointsare used for X2. Note that LENA data are given as uncalibrated count rates lflnii or see)since isotopes cannot be separated. Right: temperature and density profiles. The thinsolid line refers to a fit of the flames alone. The thick solid line is the result when thedeviation from the C'XRS values is included in X2 (pm; = “W:Int—i? ll! 2 poll. Flue}.1924inclusion 0f the CKRSdata improves the fit in the central plasma.W'th the movable SKA II analyser, a series of similar shots was used to obtain the_ lmaximum T,- on difi‘erentFor the analysed scenario_CXRS the fit could be improved including the fiddltional data,5 Ohmic densityr scanIAs an application, an ohmic density scan is Shown infigure 2:lines of sight from the logarithmic slope at high energies [8].(ohmic, at. m 3~1019m'"3) the agreement was good and, as with._ ..... 55.. 1500 :4 E jg. 55' a . §' E "m i; es 2 r r5W ”3 :3s ' Itat rr'“tl“'té“'rr“‘rt' as so as as as 1s_rho poloidsl _ . rho pololdsl 'fit *r1 ._a, a;E e*3 1{E.. E . ._.$1gi:$10“ . n-- ----- n”0.0 0.2 0.4 0.0 0.3 1.0 . . _ .rho poloidsl rho colonialFigure 2: Comparison of ohmic discharges with. difierent plasma densities.The increased coupling between the primarily heated electrons and the ions with increaseddensity leads to a decrease of the relative difference between T, and Tr. In the analyseddensityr range, the dominant source of neutrals in the center changes: In the low density'case (a), onlyr wall neutrals are important. As a,2 increases (reduction of neutral meanfree path), on decreases Us). Here, wall and volume sources are of equal importancefor the center. With further increasing a, (and nearly-the same T6), the volume source- dominates (c) and leads to a rather constant nu over a wide radial range.6 Bayesian RegulariaationA problem of the procedure discussed so far, is the choice of the knot configuration of thelinear spline for T,-. In practice, a trial configuration is accepted, if the resulting Ti-profile1025foraMMhas no oscillations and if X2 is reasonably low. ICl'l'ten several trials are necessary. Sinceseveral configurations are acceptable, the choice is somewhat arbitrary. Alternatively, usecan choose “many“ knots and use a regularization, for example by adding A f olp f(Tlhl(,,))to the minimization functional. The choice of the weight A, or even several weights forseparate radial intervals, is often made manually (as is the choice of the intervals) and isto some extent arbitrary also.Here, we present the results of a procedure that automatically determines its local degreeof regularisation combining an adaptive kernel method with Bayesian statistics [9]. Theparameterization is T,-(,o) = fik‘f -exp'(~££:,1§3{fl)f\/2—nhj with N “large enough” (here .N = 37) and 5,; fixed and spjaced “narrowly enough". The regularisation enters via .3,-Bayesian prior distribution for ii: 31(3) : I‘(N,,/2)/(2ir £31 biptfl, Ni: 2 i ,1, 13,,n Calledthe generalized dimension of the parameterisation. Then-posterior distrihih‘tion is analysed1and its maximum (MAP), its mean, and its variance are determined. As a first step, themethod has been implemented with fixed neutral densities, that were obtained from themanual linear spline method. Figure 3 shows a comparison of both methods.use} Adaptive kernel methoué1WD: _ FFFFF mean : Figure 3: Comparison of the optimized tin-Z ' ear sptine {3rd triat, same as fig. 2c) with51 300 the result of the Bayesian adaptive hornet:3: 500 method. The error bars of the dashed curverepresent the corresponding standard riooia-tions of the posterior distribution. The T,-.............. “near spline oatuesunct their errors agree roof! over a large_ _ , , -. _ , , ,' realist range. The intuitive positioning of the[1.0 0.2 ill-4 {II—i} 3-3 ”3 hnots seems to he sensihte.' rho paroles!References[l] Stoher J. et al., Proc. of the 92nd EPS Conference on Controlled Fusion and .PtasmcPhysics, Bournemouth, 1995, 19G,III,249 (1995), EPS[2] Bart-ironic et al., Rev. Sci. Instrum, 58, 7’88 (1987’)[3] Verbeelr H., J. Phys, E19, 954 (1986),Verbeek H., Schiavi 5L, {PP-Report, iii/1&3, (1994)[4] Haas G. et al., J'. Nuct. Mater.,121, 151 (1984),Klepper C. C. et al., J. Vac. Sci. Technol., A 11, 445 (1993)[5] Box R. et al., IPP-Heport, 10/1, (1996){6] Reiter 1)., mos Josie reports, stinger, (1984), misses, (1992)[7’] Boileau A“, Pissing Phys. Controlled Fusion, 31, 779, (1989)[8] Wagner F., J. Vac. Sci. Technoi, 20, 1211 (1982)_ [9] Fischer H. et al., to he published1026

Profiles of Ion Temperature and Neutral Density from the Simulation of Charge Exchange Measurements and Additional Experimental Data

http://hdl.handle.net/21.11116/0000-000A-970B-0

Profiles of Ion Temperature and Neutral Density from the Simulation of Charge Exchange Measurements and Additional Experimental Data

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