Hatae, T.

Horton, L.

Hubbard, A.

Igitkhanov, Y.

Janeschitz, G.

Kamada, Y.

Lingertat, J.

Osborne, T.

Sugihara, M.

Suttrop, W.

English

MPG.PuRe

26th EPS Conf. on Contr. Fusion and Plasma Physics, Maastricht, 14 - 18 June 1999      ECA Vol.23J (1999) 1449 - 14521449STUDIES ON THE SCALING OF H-MODE PEDESTAL WIDTH IN THEITER MULTI-MACHINE PEDESTAL DATABASEM. Sugihara1, Yu. Igitkhanov1, G. Janeschitz1, T. Hatae2, L. Horton3,A. Hubbard4, Y. Kamada2, J. Lingertat3, T. Osborne5, W. Suttrop6and ITER H-mode Edge Pedestal Expert Group1ITER Joint Central Team, Joint Work Site, D-85748 Garching, Germany2 JAERI, Naka Fusion Research Establishment, Ibaraki-ken, 311-01 Japan3 JET Joint Undertaking, Abingdon Oxon., OX14 3EA, UK4 Plasma Fusion Centre, MIT, Cambridge, MA 01239, USA5 General Atomics, P.O. Box 85608, San Diego, CA 92186-5608 USA6 Max-Planck-Institut für Plasmaphysik, EURATOM Assoc., D-85748 Garching, Germany1. IntroductionEnergy confinement during H-mode in Tokamaks strongly depends on the temperature atthe top of the H-mode pedestal [1]. This pedestal temperature is determined by the gradient andthe width of the pedestal edge.  In the case of the Type-I ELMy regime, which is assumed forpulsed operation in ITER, it is widely observed that the pressure gradient is close to the idealballooning stability limit.  Thus, the discharge parameter and machine size dependence of thepedestal width is of primary importance for predicting the pedestal temperature in ITER.  The ITER multi-machine pedestal database activity has been started to identify the overallfeatures of the pedestal region for the various discharge modes including the LH transition, TypeI and Type III ELMs, the ELM-free and EDA (Enhanced Dα) phases. For these regimes, thepedestal data (mainly scalar data and limited data for profiles from some machines) from majordivertor Tokamaks, ASDEX-U(AUG), C-MOD, DIII-D, JET and JT-60U, are archived in thedatabase.  Although the data archive is still on-going, this paper presents an initial study on thepedestal width/height during the ELM-free, EDA and Type I ELMy phases based on thepresently available data.So far, the width studies have been limited to one machine [2-6] or at most to a comparisonbetween two machines (C-MOD and DIII-D [7]).  Studies show, however, that the parameterdependence of the pedestal width is rather different from machine to machine, e.g., somemachines observe ion poloidal Larmor radius dependence when considering thermal or fast ions[8, 9], while such dependence is not observed in some machines [6].  Universal scaling is stilldifficult to derive.  Another limitation of the database is that direct comparison of the width is notpossible in many machines due to diagnostic limitations.  Thus, in this paper, we mainly examinethe pedestal pressure in terms of several candidate width scalings such as poloidal Larmor radiusand other theoretical models assuming that the pressure gradient is determined by the idealballooning stability limit.We will also propose one possible interpretation of the divergent observations of the widthbased on turbulence suppression by a combination of the electric and magnetic field shear.Some examinations on this interpretation on the database are also presented.2. Examination on pedestal heightSeveral machines observe the ion poloidal Larmor radius dependence for the pedestalwidth and a majority of the machines observe the critical pressure gradient which is close to theideal ballooning limit.  Thus, as an initial choice of the scaling parameters for the pedestal height,we will employ ( / )dp dr c polρ  , where ( / ) ( )dp dr RRaBc p= +1221022µ κ is the critical pressuregradient for the ideal ballooning mode, ρpol  is the ion poloidal Larmor radius measured at thepedestal temperature and Bp  is the average poloidal field in cylinder approximation with ellipticcross section.  Total pressure is evaluated by twice the electron pressure, except for JT-60U, inwhich ion pedestal temperature is routinely measured by CXR.  In C-MOD and JT-60U, densityand temperature at 95 % flux surface are used for the pedestal values assuming that they are very26th EPS CCFPP 1999 ; M.Sugihara et al.: Studies on the Scaling of H-mode Pedestal width in the ITER ...1450close to the pedestal quantities.  This may underestimate the pedestal temperature ( Tped ) in C-MOD, which can have wider pedestals.  In C-MOD, the pedestal density is assumed to be 2/3 ofthe line average density [2].  In DIII-D and AUG, pedestal values are evaluated by tanh fitting,whereas, in JET, they are evaluated by linear fitting. Several fitting exercises show that thepedestal top values by both fitting methods are very similar. Each machine has generally goodcorrelation with this scaling parameter and the summary results are  shown in Fig. 1, where datafrom all machines for various operationregimes are plotted together : Type-IELMy (AUG, DIII-D, JET), ELM-free (C-MOD, JT-60U) and EDA (C-MOD).Generally good correlation can be seen foreach machine, though each machine has avery different proportional coefficient andthere are some scatter and some systematicdeviations.  It is also seen that the ELM-free data (assuming that EDA are similar toELM-free) have lower pedestal pressuredue mainly to narrower width. Possibleunderestimates of Tped  in C-MOD maypartly explain why C-MOD points tend tolie below the others. DIII-D data have asimilar tendency, though they are in adifferent operation regime with fairly steepgradient and narrow width, which aresupposed to be in the second stabilityregime. Other important dependences to be  Fig. 1 Experimental pedestal pressure for all machines assummarised by a chosen scaling of critical pressure gradienttimes poloidal Larmor radius.examined are (i) the effect of plasma shaping (triangularity δ ), (ii) difference by differentoperation regime (ELM-free vs. ELMy or second stability), (iii) size dependence.  We firstexamine the effect of δ  using the results from series of discharges with changing δ  in JT-60U[10].  From these experiments, enhancement factor for the critical pressure gradient by δ  at 95% flux surface, g( )δ  can be expressed as g( ) . .δ δ= +1 9 3 3 4 .  This is consistent with DIII-Dexperimental results, in which the pedestal pressure with two different separatrix δ  arecompared. With the enhancement factor g( )δ , the pedestal pressure data are re-summarised by ( / ) ( )dp dr gc polρ δ , which is shown in Fig.2  Although the correlation still remainsgenerally good by introducing thetriangularity effect, no significantimprovement for the scatter of data in eachmachine can be seen.  In this figure, JETand JT-60U have similar size and plasmashape effect is already included, so that theremaining difference between twomachines could be that of operation regime(ELM-free for JT-60U and ELMy forJET).  In fact, if we make proper correctionbased on the comparison between ELM-free and ELMy in JT-60U [5], i.e., pedestalwidth increases by a factor 2-3 in ELMyphase, JT-60U data become fairly close tothe JET data.  DIII-D data are nowsomewhat deviating from JET line and C-MOD data are clearly shifting to the rightFig. 2 Experimental pedestal pressure for all machines withinclusion of triangularity effect.due to its high δ . The figure also indicates that the pedestal top values in DIII-D may scale notso much differently regardless of the operation regime (1st and 2nd stability regime), since DIII-D has almost the same size as AUG and shaping difference is already included in the figure.26th EPS CCFPP 1999 ; M.Sugihara et al.: Studies on the Scaling of H-mode Pedestal width in the ITER ...1451Another indication for size effect could be seen from the comparison between C-MOD vs. JT-60U, and JET vs. AUG, since they are in the same discharge regime, respectively.  However,further detailed investigations on these effects and derivation of the scaling need more systematicexperiments in each machine and comparisons of these data, which is to be performed in future.3. Examinations of various theoretical models for pedestal width/heightIn this section, we will briefly examine several theoretical models proposed so far by usingthe ITER pedestal database.  It is proposed that ρpol  (or banana width; ρban ) scaling with fast ionenergy can explain the JET experimental observation that the Tped  dependence of the width isweaker than that of the Larmor radius (square root of Tped ) for fixed plasma current and toroidalfield discharges [9].  Although, in JET, the experimentally inferred width of 5-7 cm are exactly inthe range of ρban  evaluated with the injected beam energy Eb  of 120 keV, data from othermachines in the database show clear contradiction, especially for small machines, i.e., (0.5-1) Ebfor JT-60U, (0.2-0.3) Eb  for AUG, (0.03-0.07) Eb  for DIII-D are expected to reproduce theexperimental width by ρban .  In addition, no fast ions are expected for the ICRF heating in C-MOD.  Moreover, this approach cannot explain the experimental fact that the pedestal widthduring the ELM-free phase is much narrower than that during ELMy phase, while no substantialdifference in the fast ion energy and population will be expected during both phases.Among several theoretical models, the mode structure of the edge drift ballooning modewith the poloidal rotation provided by the Reynolds stress predicts the pedestal width asρpol a2 3 1 3/ / , with which DIII-D data are also found to fit well [3].   Although with this width scalingthe pedestal pressure in the database can be fitted similarly well as in Fig. 1, Reynolds stress isactually expected to be too weak to suppress the turbulence.  Many of the remaining theoreticalpredictions based on the suppression of micro turbulence suggest that the width should scale asρtor  instead of ρpol .  Thus, in these models, plasma current dependence, which is observed inmany machines, must be appropriately explained.4. Width scaling with ρtor  and its current dependenceIn this section, we propose a new width scaling with ρtor .  The underlying physics is thatthe edge transport barrier is formed where the turbulence growth rate is balanced by a stabilizingExB shearing rate, which is dominantly produced by a steep pressure gradient during a welldeveloped H-mode phase. The magnetic shear S also plays an essential role under this conditionthrough the fact that the critical pressure gradient for the ideal ballooning mode is increased andthe turbulence growth rate is decreased with increasing the shear.  Here let us employ verysimplified expressions for both turbulence growth rate γ s  and stabilizing ExB shearing rate γ ExBarising from the critical pressure gradient.  The stabilizing condition can be written as γ γExB s≥ .  Assuming that the dominant contribution to theradial electric field is the pressure gradient, which isdetermined by the ideal ballooning mode, γ ExB isexpressed as in Eq. (1).   Here, cs  and x0  are thesound velocity and the width scale length,respectively. We have assumed a simplified S− α  γ ρExB tor sScx≈02   (1)  γ χ κ ρ ρ κs GB tor s tor sc x Scx S≈ ≈ ≈⊥ ⊥20201 1  (2)  ∆ ∝ ρtorS2        (3)diagram for the ballooning stability. For the turbulence growth rate,  we will assume a  simplifiedexpression  for the gyro-Bohm type transport including the stabilising effect due to the magneticshear as in Eq. (2), where κ ρ⊥ ≈tor Ο  ( )1  is assumed.  From Eqs (1),(2), the pedestal width ∆scales as Eq. (3).  Pedestal pressure evaluated with this width is very consistent with the scalingderived in JET recently [11].  Although this is derived by very simplified assumptions, manyexperimental features seem qualitatively consistent with this expression.  For instance, withincreasing plasma current Ip , the edge shear decreases, so that the width scales inversely with Ip(ion poloidal-Larmor-radius like dependence).  The shear increases with δ , which increases thewidth as observed in C-MOD [7].  The ion mass dependence can be retained through thetoroidal Larmor radius. Examinations of this scaling with C-MOD and JET data show that it can26th EPS CCFPP 1999 ; M.Sugihara et al.: Studies on the Scaling of H-mode Pedestal width in the ITER ...1452reproduce the data at least similarly well as the scaling based on ρpol .   Fig. 3 shows the Tpedwith changing the pedestal density nped  for fixed IP (=2.5 MA) and BT (=2.3 T) in JET [4](closed squares).  Dotted and dashed lines are expected Tped , when the width are constant andpoloidal Larmor radius like, respectively.  Open circles show the expected Tped  when the width isevaluated by Eq. (3) using the experimental shear values.  Although the evaluated points showsome scatter due mainly to the scatter of shears calculated by EFIT code, they reproduce theexperimental tendency reasonably well. Thisis realised by the decrease of shear withdecreasing nped  and increasing Tped . Themost likely mechanism of this systematicdecrease of shear is the effect of bootstrapcurrent.  Larger bootstrap current is expectedto flow when nped  decreases, since collision-ality strongly decreases.  This larger bootstrapcurrent decreases the edge shear, which makesthe deviation of the pedestal pressure fromLarmor radius dependence of the width.  Thisbootstrap current may not directly influencethe shear value in the EFIT calculation.However, it can modify the equilibrium evenfor fixed BT  and IP , which can resultantlymodify the shear value. More comprehensiveequilibrium code calculation includingbootstrap current self-consistently is neededto confirm this mechanism, which is beyondthe scope of this paper and deserves futureFig. 3 Experimental pedestal temperature (closedsquare) for fixed toroidal field and current discharge inJET.  Open circles, dotted line and dashed line showexpected pedestal temperature by width scaling of Eq.(3), constant width and poloidal Larmor dependentwidth, respectively.study. DIII-D data in the database are not reproduced reasonably well by this scaling. Thereason for this discrepancy is somewhat trivial when we consider that the DIII-D pedestals are inthe 2nd stability regime. Then, the relation between critical gradient and shear cannot beexpressed as simply proportional to shear, which modifies the shear dependence of Eq. (1)greatly.  To derive the width scaling for these regimes, full treatment of the ballooning stabilityincluding the effect of bootstrap current is needed. Note that by considering the spatial structureof the shear, a size dependence can be derived, which results in Tped ≈3-4 keV for ITER based onan example model profile for shear.	Examinations of the ITER multi-machine pedestal database show that the pedestal heightsduring ELM-free, EDA and Type-I ELMy phases have a good correlation with the criticalgradient for the ideal ballooning times poloidal Larmor radius, though they are clearly separateddepending on the discharge regimes and probably size.  Scaling with toroidal Larmor radius andmagnetic shear could explain many features of the width experimentally observed, and furtherinvestigation is to be done in parallel with more systematic data archiving in the database.  	[1] G. Janeschitz,  et al., 26 th EPS Conf. on Contr. Fusion Plas. Physics, Maastrich, 1999.[2] A. E. Hubbard, R. L. Boivin, R. S. Granetz, et al., Phys. Plasmas 5 (1998) 1744.[3] T. H. Osborne, K. H. Burrell, R. J. Groebner, et al., J. Nucl. Mat. 266-269 (1999) 131.[4] J. Lingertat, V. Bhatnager, G. D. Conway, et al., J. Nucl. Mat. 266-269 (1999) 124.[5] Y. Kamada, et al., 17th IAEA Fus. Energy Conf. 1998, IAEA-F1-CN-69/CD2/EX9/2.[6] W. Suttrop, et al., Plasma Phys. Control. Fusion 39 (1997) 2051.[7] R. S. Granetz,  et al., 17th IAEA Fus. Energy Conf., 1998, IAEA-F1-CN-69/EX6/2.[8] T. Hatae, Y. Kamada, S. Ishida, et al., Plasma Phys. Control. Fusion 40 (1998) 1073.[9] V. Parail, H. Y. Guo and J. Lingertat, to be published in Nucl. Fusion, 1998.[10] Y. Kamada, et al., 16th IAEA Fus. Energy Conf., Montreal, 1996, IAEA-CN-64/A1-6.[11] G. Saibene, L. D. Horton, R. Sartori, et al., submitted to Nucl. Fusion (1999).

Studies on the scaling of h-mode pedestal width in the ITER multi-machine pedestal database

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Studies on the scaling of h-mode pedestal width in the ITER multi-machine pedestal database

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