Transient transport studies have long been recognised as a valuable complement to steady-state analysis for the understanding of transport mechanisms. Recently, transient transport data have proved to be a powerful tool to test the validity of physics-based transport models. In this paper, results from transient heat transport experiments in JET and their modelling will be presented. Edge cold pulses and modulation of ICRH (in Mode Conversion scheme) and NBI power have been used to provide detectable electron (Te) and ion (Ti) temperature perturbations. The experiments have been performed either in conventional plasma regimes or in Advanced Tokamak regimes, in the presence of an Internal Transport Barrier (ITB). In conventional plasmas issues such as stiffness, influence of Te/Ti, non-locality have been addressed. In ITB plasmas, insight into the physics of ITBs and the ITB formation mechanisms has been gained. The use of edge perturbations for ITB triggering has been explored. Modelling of the experimental results has been performed using both empirical models and physics-based models. Results of cold pulse experiments in ITBs have also been compared with turbulence simulations

Coffey, I.

Dux, R.

Garbet, X.

Garzotti, L.

Gorini, G.

Imbeaux, F.

JET EFDA Contributors

Joffrin, E.

Kinsey, J.

Mantica, P.

Mantsinen, M.

Mooney, R.

Parail, V.

Sarazin, Y.

Sozzi, C.

Suttrop, W.

Tardini, G.

Van Eester, D.

English

MPG.PuRe

1 EX/P1-04Transient Heat Transport Studies in JET Conventional and AdvancedTokamak PlasmasP.Mantica1, I.Coffey2, R.Dux3, X.Garbet4, L.Garzotti5, G.Gorini6, F.Imbeaux4 E.Joffrin4,J.Kinsey7, M.Mantsinen8, R.Mooney2, V.Parail2, Y.Sarazin4, C.Sozzi1 W.Suttrop3,G.Tardini3, D.Van Eester9 and JET EFDA contributors*1) Istituto di Fisica del Plasma, EURATOM-ENEA-CNR Association, Milan, Italy2) Euratom/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxon, UK3) Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching, Germany4) Association Euratom-CEA, CEA Cadarache, St Paul-lez-Durance Cedex, France5) Istituto Gas Ionizzati, EURATOM-ENEA-CNR Association, Padova, Italy6) INFM, Dept. of Physics, Univ. of Milano-Bicocca, Milano, Italy7) Lehigh University, Bethlehem, Pennsylvania, US8) Helsinki Univ. of Technology, Association Euratom-Tekes, P.O.Box 2200, Finland9) LPP-ERM/KMS, Association Euratom-Belgium, TEC, B-1000 Brussels, Belgium* see Annex 1 in PAMELA, J., et al., "Overview of JET results", Fusion Energy 2002 (Proc.19th Int. Conf. Lyon, 2002), OV/1-4, IAEA, Vienna.e-mail contact of main author: mantica@ifp.cnr.itAbstract. Transient transport studies are a valuable complement to steady-state analysis for the understanding oftransport mechanisms and the validation of physics-based transport models. This paper presents results fromtransient heat transport experiments in JET and their modelling. Edge cold pulses and modulation of ICRH (inmode conversion scheme) have been used to provide detectable electron and ion temperature perturbations. Theexperiments have been performed in conventional L-mode plasmas or in Advanced Tokamak regimes, in thepresence of an Internal Transport Barrier (ITB). In conventional plasmas, the issues of stiffness and non-localityhave been addressed. Cold pulse propagation in ITB plasmas has provided useful insight into the physics of ITBformation. The use of edge perturbations for ITB triggering has been explored. Modelling of the experimentalresults has been performed using both empirical models and physics-based models. Results of cold pulseexperiments in ITBs have also been compared with turbulence simulations.1. IntroductionThe understanding of heat transport remains a high priority area in thermonuclear fusionresearch. Transient transport studies have proved to be powerful tools for separating differenttransport mechanisms and testing the validity of physics-based transport models [1-3].In this paper, results from transient heat transport experiments in JET and their modellingare presented. The perturbative techniques consisted of a) cold pulses using Ni laser ablationor deuterium shallow pellet injection; b) modulated ICH in the mode conversion scheme. Thecomprehensive set of JET diagnostics and the long transport time scales make JETparticularly suited for such studies, in particular providing the possibility of monitoring theion component. The experiments have been performed either in conventional L-mode plasmasor in Advanced Tokamak regimes, in the presence of an Internal Transport Barrier (ITB).Modelling of the experimental results has been performed using both empirical models andphysics-based models such as IFS-PPPL, MM-95, GLF23. Results of cold pulse experimentsin ITBs have also been compared with turbulence simulations using the TRB [4] code.2. Transient transport in JET conventional L-mode plasmasIn JET conventional L-mode plasmas, the issues of stiffness and non-locality have beenaddressed by Te modulation and cold pulse experiments. ICH in D plasma with ~15-20% of3He results in mode conversion of fast waves into short wavelength waves, thereby providingefficient direct electron power deposition with good localization [5]. A scan of electron heatflux by changing ICH position and NBI power has been carried out. Figs.1-2 show the range ofelectron power density and heat flux profiles obtained.2 EX/P1-04FIG.1. a) power deposition and Te profiles for 4 discharges from the heat flux scan experiments;b) electron heat flux profiles for the 4 discharges shown in a).FIG.2. a) Te and Ti profiles in log scale for the 4 dischargesshown in Fig.1; b) profiles of ∇ Te / Te for the same discharges.In Fig.2a the Te and T i profiles are plotted in log scale, showing that a maximum value ∇ T/T~ 2.2m-1 is never exceeded in the core plasma (ρ<0.6). In Fig.2b the profiles of ∇ Te /Teare shown. Assuming a critical value ∇ Te /Te ~ 1.8 m-1 as the threshold for the onset of stifftransport (this is justified below), one can see that in shots 55802 (black) and 55805 (red)∇Te/Te is above threshold in the whole region ρ>0.1 (except for a small region around ρ~0.4 inshot 55805 where an MHD island flattens the profile). In shot 55811 (green) ∇ Te/Te is belowthreshold throughout the plasma, while in shot 55809 (blue) it crosses the threshold value.FIG.3. Heat wave amplitude (a) and phase (b) profiles at 1st harmonic (15 Hz) for 3discharges from the heat flux scan experimentConsidering now the modulation data, the issue is to identify whether the heat wavepropagates differently in regions above or below threshold. The analysis concerns the electronchannel alone, since with mode conversion no significant ion perturbation is excited, asconfirmed by active CX spectroscopy. Fig.3 shows profiles of amplitude (A) and phase (ϕ) ofthe heat wave at f=15 Hz for 3 of the above discharges. In both A and ϕ plots, two slopes are01234560 0.2 0.4 0.6 0.8 100.511.5255802 slightly off-axis ICH 3.7 MW NBI 2 MW55805 slightly off-axis ICH 3.7 MW NBI 3.2 MW55809 well off-axis ICH 3.7 MW NBI 9 MW55811 well off-axis ICH 3.7 MW LH 3 MWTe [keV]pe [Mw/m3]ρ00.020.040.060.080 0.2 0.4 0.6 0.8 155805 broader ICH55802 peaked ICH55809 off-axis ICH +NBI55811 off-axis ICHqe [MW/m2 ]ρ00.511.522.533.540 0.2 0.4 0.6 0.8 155805 broader ICH55802 peaked ICH55809 off-axis ICH+NBI55811 off-axis ICH∇Te/Te [m-1]ρ0.010.020.030.040.050.060 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8A [keV]ρ55805 - 55809 - 55811all below thresholdpart above thresholdpart below thresholdall above thresholdradius of critical gradient?MHD island50607080901001101201300 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8phi [deg]ρ55805 - 55809 - 55811all below thresholdpart above thresholdpart below thresholdall above thresholdradius of critical gradient?0.91234560 0.2 0.4 0.6 0.8 155802 peaked ICH55805 broader ICH55809 off-axis ICH+NBI55811 off-axis ICHTi [keV]ρmax ∇T/T value ~ 2.2 m-10.91234560 0.2 0.4 0.6 0.8 155802 peaked ICH55805 broader ICH55809 off-axis ICH +NBI55811 off-axis ICH Te [keV]ρmax ∇T/T value ~ 2.2 m-13 EX/P1-04observed (the slopes are indicative of the 1/ √ χepert value [6]). A steeper slope is observed inregions below threshold, corresponding to a low value of χepert which is found to coincidewith the power balance value, while a flatter slope is observed above threshold, with a ratioχepert /χePB exceeding 10. The transition between the two modes of propagation appears quitesharp, as can be noticed in particular in shot 55809 (blue) where the heat wave is observed tocross the threshold and change abruptly its propagation speed. The data have been modelledusing the 1D transport code ASTRA [7] and an empirical model for χe featuring the onset ofstiff transport above a critical value of the inverse electron temperature gradient length [8]: χe = χ 0 +λ Te3/ 2 |∇Te |Te− κ        βH|∇Te |Te−κ        (1)where H is the Heaviside function, χ0 isthe residual (constant) χ value below thethreshold κ, λ and β quantify stiffness.FIG.4. Experimental (dots) and simulated (lines) profiles of A and ϕ at 1st (black) and 3rd (red)harmonics and steady-state Te for shot 55809 using the model of Eq.(1).Indeed the model reproduces well the observations, with κ=1.8 m-1 (R/LTc=5.4), λ=2 m3s-1keV-3/2, β=0.8. The fit in the case of shot 55809 is shown in Fig.4. In summary, modulation results areconsistent with the existence of athreshold in the inverse critical gradi-ent length R/LTc~5.4, and a "medium"level of stiffness in the electronchannel, as shown also in Fig.5. Theresults are in good agreement withresults from AUG concerning electronstiffness [9]. Also, it has been shown[10] that they are not inconsistentwith the recently derived ITPA two-term confinement scaling law [11].FIG.5. Electron heat flux vs ∇Te/Te at ρ=0.2 for thedischarges shown in Fig.1. The line represents theempirical model that fits the modulation data.Cold pulse perturbations performed in the same shots of Fig.1 are observed to travel almostinstantaneously (within the experimental noise level) from edge to core, crossing at high speedalso the regions below threshold where the modulation heat wave is observed to propagateslowly and where the simulation with the critical gradient model would predict a measurabledelay (Fig.6). Similar observations of prompt responses of the core to edge perturbations werealready reported for JET [12,13]. Here this is observed in a plasma without sawtooth activity(easier to diagnose in the core) and together with modulated heat waves featuring slowerpropagation. The observations suggest that, although stiffness can explain fast propagation inouter regions above threshold, stiffness alone is not enough to explain the fast response of thecore to edge perturbations. Alternative explanations are "non-local" transport via the existenceof radial structures connecting edge to core or via mode coupling, or avalanche-like processestriggered by the edge cold pulse and carrying with them a fast propagating turbulence front.01020304050600 0.2 0.4 0.6 0.8 1A [eV]ρ55809 λ=2 keV-3.2 m3 s-1κ=1.8 m-1β=0.850607080901001101201300 0.2 0.4 0.6 0.8 1phi [deg]ρλ=2 keV-3.2 m3 s-1κ=1.8 m-1β=0.8558090123450 0.2 0.4 0.6 0.8 1Te [keV]ρλ=2 keV-3.2 m3 s-1κ=1.8 m-1β=0.85580900.020.040.060.080.10.5 1 1.5 2 2.5 3 3.5 4qe [MW/m2]∇Te/Te (m-1)558115580955802ρ=0.255805fit to modulation data4 EX/P1-04FIG.6. Experimentaland simulated(using critical gradient model Eq.(1)) Te time traces for cold pulse propagation in shot 55809.3. Transient transport in JET Advanced Tokamak PlasmasThe only cases where a slowing down of the cold pulse has been observed in the core regionare Advanced Tokamak plasmas with low or reversed magnetic shear. These observations havebeen reported in detail in [3], both during an ITB phase and in the absence of an ITB. In thelatter case, the cold pulse is observed to slow down in the core, but its amplitude grows (atvariance with simple diffusive propagation). Existing first-principles models such as IFS-PPPL, GLF23 and MM95 have been tested against the data and found not able to reproducethe whole set of observations for ions and electrons, although they can reproduce subsets ofthe observed features. Qualitatively, the observations are consistent with a region of stabilisedtransport due to low or reverse shear, which slows down the pulse but may be damaged by itsarrival, giving rise to an increase in transport leading to an increase of the cold pulse amplitude.Consistent with these observations, but possibly more dramatic in their consequences, arethe observations of cold pulse propagation in the presence of an ITB. Fig.7 shows Te timetraces for one case with laser ablation, Fig.8 shows Te profile evolution in a similar case withshallow pellet. The profiles of Te variation for both cases are shown in Fig.9. One can noticethat when the cold pulse meets the ITB foot its amplitude is enhanced in the outer ITB part,and is then damped strongly in the inner ITB portion. This suggests that the ITB is indeed aregion of reduced heat diffusivity, which is however easily deteriorated by the increase oftemperature gradient driven by the cold pulse. In the cases shown the ITB was strong enoughto maintain its confinement capabilities in spite of the outer erosion. Weaker ITBs arehowever easily killed by cold pulses, and presumably the same type of phenomenon underliesthe dramatic effect observed with ELMs, which lead rapidly to the loss of the ITB [14]. Theseobservations bring additional elements for the understanding of ITB onset mechanisms, inparticular regarding the issue whether experiments support more a 1st order or 2nd order typeof transition, as discussed in [4]. In fact erosion due to transient enhancement of temperaturegradient would be more easily compatible with a 2nd order transition scheme. Theoreticalmodelling of cold pulse propagation in ITB plasmas is being addressed via turbulencesimulations. First results using the 3D ITG/TEM fluid turbulence code TRB are reported in[4] and are indeed in good agreement with experimental observations.Finally, the issue of triggering ITBs by means of edge cold pulses has been investigated.Although in some cases an apparent coincidence in time has been observed [15], ITB triggeringin JET is more strongly connected with the appearance of rational surfaces [15,16]. When thecold pulse is fired far from suitable conditions in terms of rational locations, it causes at most aweak increase in central Te which does not develop into a proper ITB [3].44.24.4Te [keV]ρ=0.1133.13.23.33.4Te [keV]ρ=0.31.31.41.5Te [keV]ρ=0.60delay from edge to centre ~ 22 ms0.50.60.71 1.02 1.04 1.06 1.08T e [keV]t [s]ρ=0.87SIMULATION4.34.44.54.6Te [keV]ρ=0.1155809 2.72.82.9Te [keV]ρ=0.31.41.51.6Te [keV]ρ=0.60delay from edge to centre < 4 ms0.40.50.650.1 50.12 50.14 50.16 50.18Te [keV]t [s]ρ=0.87EXPERIMENT5 EX/P1-04Fig.8: Time evolution of experimentalprofiles of ECE Te following the coldpulse in ITB in shot 53682.Fig.7: Experimental time traces of electron temperatures for a Ni laser ablation cold pulse (shot51581, t=6.2 s) in a strong ITB. The channel at ITB foot is marked thickFIG.9: Time evolution of experimental profiles of ECE ∆Te following (a) a shallow pellet coldpulse in shot 53682 and (b) a laser ablation cold pulse in shot 51581. The ITB region is shaded.4. ConclusionsTe modulation experiments in conventional L-mode plasmas show the existence of athreshold above which electron transport is characterised by a "medium" degree of stiffness.The results are not inconsistent with ITPA global confinement scaling laws. Cold pulseexperiments show fast propagation from edge to core, requiring additional mechanisms thanstiffness alone to be explained. Cold pulses are slowed down in regions of low or reverseshear. Physics based models have been tested against cold pulse data with non satisfactoryresults. Cold pulses in ITBs induce an erosion of the ITB outer edge and are damped furtherinside. The result is well reproduced by ITG/TEM turbulence simulations. Cold pulse inducedITB triggering decoupled from the role of rational surfaces could not be obtained.References[1] KINSEY, J..E., et al. Phys. Plasmas 6 (1999) 1865.[2] TARDINI, G., et al., Letter for Nuclear Fusion, Vol. 42 (2002), L11.[3] MANTICA, P., et al., Plasma Phys. Control. Fusion 44 (2002) 2185.[4] GARBET, X., et al., this conference, TH/2-1, to be submitted to Nucl. Fusion.[5] MANTSINEN M., et al., Proc. 28th EPS Conf., Funchal (Madeira), Portugal, 2001, Vol. ECA 25A, 1745.[6] JACCHIA, A., et al., Phys. Fluids B 3 (1991) 3033.[7] PEREVERZEV, G., YUSHMANOV, P.N, Max-Planck-IPP Report, IPP 5/98 (2002).[8] IMBEAUX F., et al., Plasma Phys. Control. Fusion 43 (2001) 1503.[9] RYTER, F., et al., this conference, EX/C4-2Ra.[10] GARBET, X., private communication.[11] CORDEY, J., et al., this conference, CT/P-02.[12] GALLI, P., et al., Nucl. Fusion 38 (1998) 1355.[13] PARAIL, V. V., et al. 1997 Nucl.Fusion 37 481.[14] SARAZIN, Y., et al. “Edge issues in ITB plasmas on JET”, submitted to Plasma Phys. Control. Fusion.[15] JOFFRIN, E., et al., Plasma Phys. Control. Fusion 44 (2002) 1739.[16] JOFFRIN, E., et al., this conference, EX/P1-13.-0.8-0.6-0.4-0.200 0.2 0.4 0.6 0.8 1536825 ms10 ms20 ms30 ms50 ms75 ms∆T [keV]ρ-0.4-0.3-0.2-0.100.10 0.2 0.4 0.6 0.8 14 ms8 ms12 ms20 ms30 ms∆T [keV]ρ51581123456786.1 6.2 6.3 6.451581Te [keV]t (s)ρ=0.2ρ=0.8246810120.1 0.2 0.3 0.4 0.5 0.6 0.753682 10.000 s10.005 s10.010 s10.020 s10.040 sT e [keV]ρITB foot