Andrew, P.

Bombard, B.

Coad, J.

Erents, K.

Felton, R.

Fundamenski, W.

Hidalgo, C.

Huber, A.

Lipschultz, B.

Matthews, G.

Mertens, P.

Pitts, R.A.

Silva, C.

Stamp, M.

Strachan, J.

Whyte, D.

DSpace@MIT

PSFC/JA-03-23           A Study of JET SOL Radial Transport Based on Particle Balance  Lipschultz, B., Andrew, P.2, Coad, J.2 Erents, K.2, Felton, R.2, Fundamenski, W.2, Hidalgo, C.3, Huber, A.4, LaBombard, B., Matthews,G.2, Mertens, P.4, Pitts, R.A.5, Silva, C.6, Stamp, M.2, Strachan, J.7, Whyte, D.8  18 February 2004          1Plasma Science and Fusion Center, MIT, Cambridge, MA  02139 USA 2UKAEA, Culham, UK 3Asociación EURATOM-CIEMAT para Fusión, E-28040 Madrid, Spain   4KFA Research Centre 52425 Jülich, Germany 5CRPP EURATOM-Confédération Suisse, EPFL, 1015 Lausanne, Switzerland 6EURATOM/IST, Centro de Fusão Nuclear, 1049-001 Lisboa, Portugal  7PPPL Princeton NJ 08453 USA 8U. Wisc. Madison WI, USA      This work was supported by the U.S. Department of Energy, Cooperative Grant No.  DE-FC02-99ER54512. Reproduction, translation, publication, use and disposal, in whole  or in part, by or for the United States government is permitted.   Submitted for publication to Nuclear Fusion. Figure 1: D chordal brightness (dah) used tocalibrate the simulated camera D chord, BTOT.Also shown are the contributions from the inner(BIN) and outer edges (BOUT) of the plasma.Figure 2: The separatrix is shownin red. The limiter shadow that theRCP samples is bounded at twopoints ‘a’ and ‘b’.A Study of JET SOL Radial Transport Based on Particle BalanceB. Lipschultz1*, P. Andrew2, J. Coad2, K. Erents2, R. Felton2, W. Fundamenski2, C.Hidalgo3, A. Huber4, B. LaBombard1, G. Matthews2, P. Mertens4, R.A. Pitts5, C. Silva6, M.Stamp2, J. Strachan7, D. Whyte81MIT Plasma Science & Fusion Center, Cambridge Ma 02139, USA, 2UKAEA, CulhamUK, 3Asociación EURATOM-CIEMAT para Fusión, E-28040 Madrid, Spain , 4KFAResearch Centre 52425 Jülich, Germany, 5CRPP EURATOM-Confédération Suisse,EPFL, 1015 Lausanne, Switzerland, 6EURATOM/IST, Centro de Fusão Nuclear, 1049-001 Lisboa, Portugal, 7PPPL Princeton NJ 08453 USA, U. Wisc. Madison WI, USA*This work supported by US Dept. of Energy under grant #DE-FC02-99ER54512A. IntroductionRadial transport in a tokamak Scrape Off Layer (SOL) is important in determining anumber of aspects of tokamak operation including recycling, impurity sources andtransport, divertor dynamics, and potentially playing a role in the determining the densitylimit. This work represents an initial effort to apply an interpretive method [1] to JETplasmas to determine the underlying radial fluxes and transport in the outer SOL.B. Experimental measurementsA prerequisite to the radial transportanalysis is to have a measure of the SOLprofiles of ne, Te and the ionization source.SION. ne and Te are obtained in JET using theRCP scanning probe. We developed a measureof the ionization profile by digitizing a wideangle camera view of the main chamber(‘KL1’). That provides us with anunnormalized brightness profile for visibleemission across the midplane of the plasma.An emissivity profile is obtained through Abelinversion. A chordal integration along a major radius isthen done to simulate the midplane D measurementview, ‘dah’. A comparison of the simulated and ‘real’chordal D measurements then determines the cameracalibration, Figure 1. The Monte-Carlo neutral code,KN1D [2], using only the plasma SOL ne and Te profilesand the midplane pressure, has been utilised to modelthe same emissivity profiles. The modelled profilesmatch those derived from the wide-angle camera fairlywell in both magnitude and general shape.BDα (1x1019/m2 /s)58 60 62 64 66 68time (sec)56893c00720.jpglines 165:1740.00.51.01.52.02.5Dα chord brightnessBTOTBOUTBIN56893: 64.9sRCP1.5 2.0 2.5 3.0 3.5 4.0major radius (m)-2-1012z(m)abThe ion flux to the vessel surfaces outside the divertor serves as a boundary conditionfor the radial flux analysis. We derive the value for the radial flux at the limiter radius,,i, from radial profile measurements of ne and Te and a model by LaBombard [3].During the RCP sweep the probe samples plasma in the shadow of structures within themain chamber. Through field line mapping we were able to delineate the outline of thisshadow region. As illustrated in Figure 2 this ‘window frame’ through which the radialflux passes, is bounded poloidally by a toroidal ring of tiles at the top of the machine andthe poloidal limiters at the outer midplane. Given that SION <  in the limiter shadow,the radial ion flux is then  ,lim =2  ||,0  nL||=2  nlim,0  cs  n  R  qwhere nlim,0 is thedensity at the limiter radius. The typical values for the JET limiter shadow are n ~ 14mm, Te ~ 10 eV, ~ 2.9 m, q ~ 3.5. This gives ,i ~ 28xnlim,0 (m-3). The following tablesummarizes the radial ion flux reaching the limiters radius for the time slices studied. Theinward neutral flux, 0., determined from the midplane pressure is shown as well.Shot Time n e(m-3) nlim (m-3) i. (m-2/s) Pmidplane (mT/Pa) 0. (m-2/s)56836 60.52 1.2x1019 2.5x1017 7x1018 .0042/.00055 2x101956836 62.53 1.2x1019 2.5x1017 7x1018 .0044/.00058 2.1x101956836 66 1.9x1019 8x1017 2.24x1019 .0086/.0011 4.1x101956836 68 2.3x1019 1x1018 2.8x1019 .021/.028 1.x102056893 58.24 1.5x1019 1x1017 2.8x1018 .0035/.00046 1.2x101956893 60.24 2.5x1019 1.5x1017 4.2x1018 .008/.001 3.8x101956893 62.22 3.4x1019 8x1017 2.24x1019 .015/.002 7.1x101956893 64.23 3.7x1019 1.2x1018 3.4x1019 .022/.029 1.x1020All fluxes increase with increasing n e. We see that ,i ~ 0./3. It appears that the ionflux to the chamber surfaces, although substantial, does not account for all of the midplaneneutrals (pressure). The remaining neutrals could then come from divertor leakage.C. Radial flux analysisWe can expand our analysis of radial fluxes to all points in the SOL. The derivationof the underlying radial transport is based on particle balance between ionisation sourceand parallel and perpendicular particle losses [1,4]. We start with the basic continuityequation for quantities averaged over the SOL:   +||  || = SION (1)(r) = SION (r) Mn(r)cs(r) /L||[ ]sepr  dr + ,sep (2),sep = SION (r)[ ]0sep  dr + fc Mn(r)cs(r) /L||[ ]sepwall  dr (3),wall = SION (r)[ ]0wall  dr  (1 fc )M n(r)cs(r) /L||[ ]sepwall  dr (4)where M is Mach number, cs~(kTe/mi)1/2 is sound speed, L// is the field line length betweendivertors, SION is the volumetric ionization source rate. fc is the fraction of ion flux into thedivertor that recycles and enters the core. The divertor leakage flux fraction is then (1-fc).The boundary condition for this analysis is the wall flux measurement of the previousFigure 3: Radial transport analysis for a set of 8 time slices over two shots – 56836 (Ip=1MA, BT=1T)and 56893 (Ip=2MA, BT=2T), described in the above table.Figure 4: Dimensionless scaling comparison of JET and Alcator C-Mod. The JET data are dashed lines.The C-Mod data are solid lines + symbols. Dimensionless parameters for the JET (56836) and C-Moddischarges shown in a-c. JET and C-Mod SOL parameters are shown in 4d-f (56836) and  4g-i (56893).section. We assume a Mach profile based on measurements [4-8] that is 0.2 at theseparatrix rising rapidly to M=0.4 at r-rsep=17 mm, constant for greater r-rsep. The value offc assumed was 0.9. However, it has little effect on the analysis once the ,wall is known[4]. Figure 3 shows the plasma profiles input to this analysis (a-c) as well as the radial ionflux (d). The effective transport coefficients are derived assuming diffusive (e) - (r) = -Deffn(r), or convective (f) - (r) = n(r)veff(r) transport. The radial ion flux, , isconstant or dropping across the SOL. Deff and veff both increase with distance from theseparatrix. The values of Deff and veff do not seem affected by changing plasma conditions.56836 568930.010.101.00a) ne (1019/m3)1020b) Te (eV)0.100c) SION (1021/m3/s)0.0101.0000.0010.010d) Γ⊥ (1021/m2/s)0.11.0e) Deff (m2/s)0 20 40 60 80r-rsep (mm) 0 20 40 60 80r-rsep (mm)101000.010.101.0010200.1000.0101.0000.0010.0100.11.010100f) veff (m/s)a) ne (1019/m3)b) Te (eV)c) SION (1021/m3/s)d) Γ⊥ (1021/m2/s)e) Deff (m2/s)f) veff (m/s)C. Dimensionless scaling analysisThe radial flux analysis shown in figure 3 shows little or no variation in the inferredtransport coefficients even though the SOL characteristics have changed considerably. Weuse a dimensionless similarity scaling approach [9-10] as a vehicle to discuss the role of101001.00 1.04 1.08 1.12r/a1.00 1.04 1.08 1.12r/a1.00 1.04 1.08r/a10-710-610-510-40.11.0.001.0002a) ν*b) ρ*c) β1070e) Te (eV)10100 f) veff (m/s)d) ne (1020/m3)h) Te (eV)i) veff (m/s)g) ne (1020/m3)plasma and atomic physics. The profiles of *, *, and  are shown in figure 4a-c for theone JET shot already discussed (56836, dashed lines) as well as for three density casesfrom Alcator C-Mod (1 MA, 5.3 T). The Alcator C-Mod and JET (56836) shots havedimensionlessly similar SOLs. Note also the * and  variation within a shot as thedensity is varied,.We can use the dimensionless scaling to directly compare the JET SOL characteristicswith that from C-Mod, Figure 4d-i. The ne profiles show some similarity, shorter e-foldinglengths in the ‘near’ SOL (1.< r/a < 1.02) than in the SOL ‘far’ from the separatrix. Thedimensionless scaling between C-Mod and JET appears to predict the veff profile to withina factor of 2. The JET shot at higher toroidal field (56893, 4g-i) has lower * and . Butthis substantial change only lowers veff slightly compared to 56836.But what of the role of neutrals? The mean free path for neutrals (ionization + CX),when normalized by the machine size, 0,mfp/a, should scale as a. Thus the JET SOLshould be much more transparent to neutrals than C-Mod. Since the transport is so similaron the two experiments we believe that the difference in profile shapes (generally flatteron C-Mod, Fig. 4) is due to a radial 'high-recycling' condition whereby the neutralpressure, and ionization in the far SOL, must be much higher in C-Mod due to the poorprobability of their reaching the core plasma.D. SummaryThe JET SOL profiles evidence some of the same characteristics of other tokamaks.There are 'near' and 'far' SOL regions with short and long e-folding lengths. The 'far' SOLne profile flattens with increasing density. The flattening is less pronounced in JET.Radial transport analysis using particle balance has been done. It shows that the radialion flux is dropping slowly or flat across the SOL. The effective transport coefficients,Deff and veff, both increase across the SOL by factors of 2-10. Deff and veff, are similar tothat found for C-Mod and DIII-D.Dimensionless scaling analysis indicates that *, *, and  are not strong factorscontrolling the transport. The dimensionless scaling from JET to C-Mod works well.Neutrals do not appear to play a role in setting the transport coefficients- large changes inneutral midplane densities do not correlate with changes in veff or Deff. However, shorternormalized neutral mean free path, 0,mfp/a does correlate with flattening of ne profile.References[1] LaBombard, B., et al., Phys. Plasmas 8 (2001) 2107.[2] LaBombard, B. MIT report PSFC-RR-01-03.[3] LaBombard, B., et al., Nucl. Fusion 40 (2000) 2041.[4] Lipschultz, B., et al, 'Comparison of ion transport in the Scrapeoff Layer plasmas ofAlcator C-Mod and DIII-D', to be submitted to PPCF.[5] LaBombard, B., et al., J. Nucl. Mater. 241-243 (1997) 149.[6] deKock. L., et al., 1989 Proc. 12th Int'l Cong. on Plasma Phys. & Contr. Nucl. Fs. Res.vol 1 (IAEA) 467.[7] Loarte, A., 1993 Proc. 20th European Conf. on Contr. Fus. & Plasma Phys. vol 17C(Lisboa) 555.[8] Asakura, N., Plasma Phys. & Control. Fusion 44 (2002) 2101.[9] Connor, J.W., Taylor, J.B., Nucl. Fusion 17 (1977) 2047.[10] Kadomtsev, B.B., Sov. J. Plasma Phys. 1 (1975) 295.

A Study of JET SOL Radial Transport Based on Particle Balance

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A Study of JET SOL Radial Transport Based on Particle Balance

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