an international pellet ablation database

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AN INTERNATIONAL PELLET ABLATION DATABASEL.R. BAYLOR, A. GERAUD", W.A. HOULBERG, D. F R I G I O N E b , M . G A D E B E R G " ,T . C . J E R N I G A N , J. D E K L O E d , P. KUPSCHUS", B.V. KUTEEVe, P. L A N G f ,A.A.M. OOM ENSd, A.L. QUALLS, K.N. SATOg, G.L. SCHM IDThOak Ridge N ational Laboratory,Oa k Ridge, Tennessee, United S tate s of Am ericaa Association Euratom-CEA, Centre d'Qtu desnucleaires de Ca darac he,St-Paul-Lez-Durance, France

Associazione Euratom-ENEA , C.R.E . Frascati, Rome, Italy" J E T Joint Undertaking, Abingdon, Oxfordshire, United K ingdom

Association Euratom-FOM , FO M Instituu t voor Plasmafysica,Rijnhuizen, Nieuwegein, Net herlands

Max-Planck-Institut fur Plasmaphysik, Eurato m Association, Garching, GermanyPrince ton Plasm a Physics Laboratory, Princeton University,Princeton, New Jersey, United States of America

e State Technical University, St. Petersburg, Russian Federationg National Institute for Fusion Science, Nagoya, Japan

ABSTRACT. The contents are described of an international pellet ablation database (IPADBASE)that has been assembled to enable studies of pellet ablation theories that are used to describe thephysics of an ablating fuel pellet in a tokamak plasma. The database represents an international effortto assemble data from several tokamaks of different magnetic configurations and auxiliary heatingmethods. In the initial configuration, data from JET, Tore Supra, DIII-D, FTU, TFTR, ASDEXUpgrade, JIPP T-IIU, RTP and T-10 have been included. The database contains details of measure-ments of deuterium and hydrogen pellet ablation, including pellet mass and speed, plasma electrondensity and temperature profiles, and pellet ablation light emission. A summary of th e databasecontents and a scaling analysis of the data are presented.

1. INTRODUCTION

In order to p redict the effect of fuelling the plasm awith pellets in a next generation tokamak such asthe Intern ationa l Thermonuclear Experimental Reac-to r ( IT ER ) , i t is essential to have a pellet ablationmodel that adequately describes the experimentaldata in the current generation of devices. To date,most s tud ies of experim ental pellet ablation have con-centrated on da ta f rom a single device [l-31 and there -fore may not accurately reflect the general applicabil-ity of a particular theoretical model. An earlier effortto benchm ark pellet ablation models with dat a fromseveral different tokamaks w as performed by Gougeet al. (41, ut was limited by the quantity and qual-ity of the ablation data. Another recent analysis byKuteev [5] lso examined a limited set of data fromseveral devices. A more controlled set of experimen-tal pellet ab lation da ta is needed in which the pelletspeed and size are known accurately and the back-ground plasma parameters (temperature and densityprofiles) are well measured. It is the purpose of this

effort, originating from discussions during the IAEATechnical Meeting on Pellet Injection held in Naka inMay 1993, to provide such a database of controlledpellet ablation experiments that can be used to val-idate an improved pellet ablation model and to pro-vide the necessary confidence for extrap ola tion of themodel to the next generation of fusion devices, suchas I T E R .

Th e pr imary purpose of this paper is to present th edatabase to the community, together with a statisti-cal description of the d ata . T he a uth ors fully expectand encourage other researchers to perform detailedanalysis of th e da ta w ith codes tha t use sophisticatedablation physics models. The authors look forwardto the use of this database in the determination ofthe best ablation models to use for future large scalefusion devices.

2. DATA SELECTIONIdeally one would like to constru ct a pellet abla-

t ion databa se with da ta tha t cover a wide region ofNUCLEAR FUSION, Vol. 37,No.4 (1997) 445


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FIG. . Plasma central electron densityand emperature at the time ofpellet injection for the recordain the IPADBASE, identified by tokamakdevice.

Table I. Range of Experimental Parameters for Ohmic, NBI and ICRH Plasmas

pellet and plasma parameter space. For a given toka-mak device, the plasma parameter space is limitedowing to the capability of the plasma to withstanda pellet perturbation and also limited because ofcollineairties in the plasma density and temperature.Therefore, it is desirable to use data from varioustokamak devices with different ranges of parametersto obtain a more extensive selection of data.

The data selected for inclusion in the databaseare the logical pellet parameters of interest, such as

the pellet speed and mass. Additional pellet data,such as pellet shape and temperature, are includedin the database for completeness. Plasma parametersthat are likely to be involved in the ablation physicsare also included and consist of plasma electron den-sity and temperature profiles, magnetic configuration,and auxiliary heating details. All auxiliary heatingmethods have been considered, even ones that pro-duce suprathermal electron populations, in particu-lar, electron cyclotron resonance heating (ECRH)and

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FIG. . Pellet masa and speed for the pellet events in the IPADBASE,identified by tokamak device.

lower hybrid (LH) current drive or heating scenarios.In these cases, the ablation process is dominated bythe fast electron contribution and the data given inthe database must be supplemented by data on theelectron distribution functions in order to model theablation process. The corresponding shots are givenas a reference and interested persons are encouragedto contact the responsible physicist.

density perturbation in the ohmic plasma assuminga fuelling efficiency of 80%.

3. DESCRIPTION OF PARAMETERSThe ablation process in the plasma is ordinarily

monitored with a photodiode that observes the lightemitted by the ablating pellet (assumed to be p mdominately D, or Ha ight). The penetration depthof the pellets is usually determined from time offlight measurements of the pellet speed and fromduration of the D, emission intensity, assuming thepellets have a constant radial velocity through theplasma, which was verified on JET by soft X ray cam-era measurements [2].Pellets that penetrate beyondthe magnetic axis are not included because of thelarger uncertainty in the penetration depth caused bystrongly reduced D, emission. For the high speed pel-let injection experiments carried out in Tore Supra,the penetration depth and the Da emission evolutionare directly measured using a high dynamic rangecharged coupled device (CCD) camera. A standardCCD camera was used to measure the penetrationdepth when the centrifugal pellet injector was usedand the Da emission was measured, as on the otherdevim, by photodiodes that view the ablation lightemission with a suitable D, filter. The mass of thepellets is in general measured by a microwave cavity

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The range of pellet injection experimental parame-ters in the database for the different tokamak devicesis tabulated in Table I. The ranges of plasma cen-tral electron density and temperature of the plasmaduring the pellet injection events in the database areshown in Fig. 1.There is a significant spread amongthe different devices but the spread in data for eachindividual device is somewhat leas. The ranges of pel-let mass and speed are shown in Fig. 2 for all thepellets in the database from each device. The ToreSupra data have the largest variation in pellet speeddue to having both a centrifuge and two-stage lightgas gun injector. The mass variation seen in the JETand DIII-D tokamak data is due to having multi-ple size barrels in the injectors on those devices. Thepellet mass is not currently measured in the AxiallySymmetric Divertor Experiment Upgrade (ASDEX-U) and Frascati Tokamak Upgrade (FTU) devices,and therefore nominal pellet massea are used. n theFTU data, the pellet mass is estimated from theNUCLEAR FUSION, Vol. 97,No. 4 (1997)


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Table 11. Results of Regression Analysis of the IPADBASE and Comparisonwith NGS Scaling

Device~~

C T, ne mP UP Corr.(const.) exponent exponent exponent exponent coeff., RJE T 0.031 -0.89 -0.30 0.24 0.41 0.91DIII-D 0.150 -0.60 0.23 0.10 0.27 0.76Tore Supra 0.146 -0.84 0.07 0.18 0.27 0.70ASDEX-U' 0.208 -0.41 0.07 0.06 0.18 0.69All databases 0.079 -0.51 -0.03 0.12 0.32 0.67All ohmic 0.076 -0.45 0.08 0.11 0.35 0.82NGS model 0.079 -0.56 -0.11 0.19 0.33* Note: The ASDEX-U da ta do not include a measured pellet mass.

in the injection line. The Q of the cavity changes inproportion to th e dielectric change introduced by thepellet and thus with proper calibration can yield anaccurate measure of the mass [6]. The plasma elec-tron density and temperature profiles are measuredby Thom son sc attering diagnostics or interferometersand e lectron cyclotron emission ( E CE ) diagnostics onthe different devices. T he pellet velocity is commonlydetermined by measuring the time of flight betweensignals from two light b arriers or between signals froma light barrier a nd a microwave cavity in the injectionline. For centrifugal injec tors, the velocity is given bythe rotation frequency of the centrifuge arb or.

4. SCALING OF P E N E T R A T I O N D E P T HT he IPADBASE covers a wide range of pellet and

plasma p aram eters, and thu s is well suited t o a scalinganalysis of the pellet penetra tion dep th. For our scal-ing stud y we choose to examine the penetration d ep thdependence on pellet mass, pellet speed, plasma elec-tron temperature and electron density, s ince theseare the d ataba se parameters that are most l ikely todirectly affect the ablation of the pellet. We assumethe p ene tration de pth scaling to have a form given byX/a = T,(keV)" n,(102' m-3)b

x m,(102' atom slc wp(m/s)dwhere X i s the penetrat ion depth, a is the plasmaminor radius, T, is the central electron temperature,ne is the central electron density, mp is the pel-let mass, wp is the pellet velocity, C is a constantand the exponents are the scaling law dependencesthat will be derived. I t should be noted that in this

scaling study, the sensitivity of the pellet ablationto the profile shapes is not taken into considerationand could lead to discrepancies between cases withdifferent plasma conditions and different devices.

It is possible to linearize the above equation bytaking the natura l logarithm of b oth sides, thus yield-ing an equ ation w hose coefficients can be d etermin edthrough a linear regression technique [7].An analysisof this type has been carried o ut on th e datab ase forthe d at a from each device by itself an d for th e entiredatabase. Database entries that include auxiliaryheating that yields significant numbers of suprather-mal electrons (EC RH and LH) are excluded from thisscaling stu dy for reasons discussed earlier. Only th osedevices whose data have a significant variation inthe penetration d ept h scaling parameters ( JE T, ToreSup ra, DIII-D and A SDEX-U) are analysed using theregression technique on their data alone. The pelletsinjected into ohmic plasmas with no auxiliary heat-ing are also analysed separately. The results of theregression analysis for the ind ividual devices and theentire datab ase are shown in Table 11.

A number of models have been proposed for thephysics of pellet ablation in a fusion plasma overthe past 20 years (Ref. [8]and references therein).Among these different models, the neu tral gas shield-ing (NGS) model of pellet ablation [9] has becomethe most widely adopted model. Despite the fact tha tit only considers the shielding of the neutral cloudexpanding from the pellet surface, uses a simple 1-Dablation geometry and assumes monoenergetic inci-dent electrons, i t has predicted pellet penetrationdep ths tha t are in good agreement with a numberof experiments. W ith t he NG S model it is possible toderive a simplified relationship between the erosion

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FIG. 3. Comparison of penetration depth with scaling using regressionanalysis for the IPADBASE database.

rate of the pellet and the pellet size and backgroundplasma parameters [lo]. If one assumes pellet injec-tion normal to the plasma from the outside midplaneand linear profiles for the electron temperature anddensity,a scaling of the penetration depth isobtainedthat has the relationshipX/a= Te'5/9 nL-1/9 i/9 vi/3C sa constant that includes the atomic mass numberof the ablatant and the plasma.

In the NGS model the pellet equivalent sphericalradius is used as a parameter' whi1e in Our databasethe pellet mass in units of number of atoms is used

shows remarkably good agreement with the penetra-tion depth scaling for all the parameters of the NGSmodel except the plasma central electron density,which varies somewhat among the different devices.This may be because of the fact that the actual den-sity profiles are quite different from the assumed lin-ear shape in the NGS model and that there is sub-stantial variation of the plasma profile shapes in thepenetration depth data on density is rather weak asit is in the NGS model. The regression analysis fromthe individual machines and overdl database showsa distinct dependence of penetration depth on pelletvelocity. Thisdoes not agree with the originalneutral

where r p is the equivalent sPherid pellet radius and different devices. In any -, the dependence of the

since the shape Of the pellet is not in general 'Pher-ical*Since the number Of Particles is Proportional to gas and plasma shielding (NGPS) model [lo],wherethere is no dependence of pe]let penetration depththe equivalent spherical radius cubed' the penetra-like to make the comparison with isgiven byX/a = T'-5/9 nL-1/9 $13wherem, is the pellet mass, and central electron tem-peratures and densities are used.

The multiple correlation coefficient R in Table I1measures the strength of the dependence of X/a onthe four variables. R2 is the proportion of the mi -ance in the data that is explained by the re-sion [7]. The regression analysis for the database

on the pellet velocity and electron density, but doesetration depth scalings from the more recent NGPSmodel [3] and from the cloud charging model [5]areVery similar to that from the NGS "iel Shown. InFig. 3,we plot the penetration depth from the re-SiOn scaling against the actual Penetration depth forthe data from the different devices. This shows thescatter in the scaling data from the different devi-and shows that d l the devices follow the regressionscaling about equally well.

tion depth d i n g Of the NGS model that We would agree with a more recent NGPS model [31.The pen-

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The J E T d a ta in the da tabase show the l a rgestcorrelation coefficient and the regression analysis ofthese data agrees well with the scaling from theNGS model. This is not surprising since an earlierdetailed a nalysis of these da ta [2] yielded good agree-ment with the NGS model. The DIII-D data yieldthe most unusual regression scaling of penetrationdepth and th i s may be due to the type of plasmasth at are encountered, which are H mode plasmas withsignificant neutral beam injection power.

5. DATA FORM AT AND ACCESSThe presently released database is identified as

IPADBASE 1.0 to d istinguish it from futu re releases.It is desirable for the present d atab ase to be extendedwith m ore da ta , in part icul ar from devices which werenot considered in this first version. In order t o achievethis, the experimentalists concerned are invited tocontact the authors .

The d a ta in the IPADBASE 1.0 are stored in anEXCEL spreadsheet file for each tokamak device.These data are then easily transferable to personalcomputers via floppy disk or internet electronic mail.Th e da ta f iles that make up th e database are in factavailable to interested parties over the internet viathe World Wide Web from the following address:http://www.ornl.gov/fed/pellet/Ornlpell.html.

6. SUMMARYA database has been established for hydrogenic

pellet ablatio n da ta from a num ber of ope ratin g toka-mak devices that covers a wide range of plasma oper-atin g space and pellet p aram eters. A statistical anal-ysis of th e da ta h as been presented and shows somefeatures that are consistent with the NGS model ofpellet ablation; however, much additional detailedcomparison with ablation physics models is needed

to determine the best physics models to use in cur-rent and future devices. The data in this databaseare made available to the fusion research commu-nity for detailed analysis and extrapolation to nextgeneration fusion devices, such as ITER.

ACKNOWLEDGEMENTSTh e aut hor s gratefully acknowledge useful discus-

sions and assistance in obtaining the pellet ablationda ta used in this study from the experimental teamson each device. Support and encouragement fromDrs. M. Chatelier (C EA ) and S.L. Milora (O RN L) aregreatly appreciated. This research was sponsored inpar t by th e Office of Fusion Energy Science, USD OE,under Contract No. DEAC05-960R22464 withLockheed Martin Energy Research Corporation.

REFERENCESBUCHL, K., et al., Nucl. Fusion 27 1987) 1939.HOULBERG, W.A., et al., Nucl. Fusion 32 (1992)1951.PEGOUFUE, B., et al., Nucl. Fusion 33 (1993) 591.GOU GE, M .J., et al., Fusion Technol. 19 (1991) 95.KUTEEV, B.V., Nucl. Fusion 35 (1995) 431.JENSE N, P.B., ANDERSEN, V., J. Phys. , D , Appl.Phys. 15 (1982) 785.BEVINGTON, P.R., \ Data Reduction and ErrorAnalysis, McGraw-Hill, New York (1969).MILORA, S.L., et al., Nucl. Fusion 35 (1995) 657.PARKS, P.B., TURNBULL, R.J., Phys. Fluids 21(1978) 1735.HOULBERG, W.A., et al., Nucl. Fusion 28 1988)595.

(Manuscript received 5 March 1996Final m anuscript accepted 6 December 1996)(E-mail address of L. R. Baylor: [email protected])

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an international pellet ablation database

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