1. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti1 Particle transport and density profile behaviour on JET L. Garzotti with contributions from G. Corrigan, X. Garbet, D. Heading, T. T. C. Jones, P. Lang, P. Mantica, H. Nordman, V. Parail, B. Pégourié, G. Saibene, J. Spence, P. Strand, M. Valovič, J. Weiland (work performed within the JET TF-T particle transport working group)

2. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti2 Motivation of the work Study particle transport in different scenarios Investigate the mechanisms leading to density profile peaking (in particular the existence of an anomalous pinch velocity) Compare with predictions of existing theories

3. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti3 Description of the work Many scenarios analysed: L-modes, H modes both stationary, quasi-stationary and transient JETTO transport code with different models employed: completely empirical, semi-empirical (mixed Bohm/gyro-Bohm) and physics based (Weiland’s ITG and TE modes) Particular attention paid to the density profile peaking and possible effects of an anomalous pinch

4. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti4 Discharges analysed

5. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti5 Model description (1) mixed Bohm gyro-Bohm electron/ion thermal conductivity particle diffusivity pinch velocity (Ware pinch always present) (trapped electron modes, turbulence equipartition)

6. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti6 Model description (2) Weiland’s ITG and trapped electron instabilities growth rate for each point of the radial mesh transport matrix obtained by quasi-linear theory combined with saturation level estimate the presence of terms like  T/T,  n/n and  B/B introduces off-diagonals elements in the transport matrix

7. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti7 L-mode 51034 - Steady state plasma heated by radio-frequency only 49030 - Multiple deep pellet injection 51084 - shallow pellet, optimised shear 55804 - shallow pellet, non-optimised shear

8. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti8 Shot 51034 only RF heating Mixed Bohm/gyro-Bohm: V = Ware pinch V = c T D  T/T c T = -0.25 V = c q D  q/q c q = 0.75 Weiland’s + off-diagonal elements Similar results are obtained for shot 49030 (deep pellet fuelling).

9. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti9 Shot 55804 - standard shear Analytical D (~ 0.6 m 2 /s) V = Ware pinch V = -c T D  T/T c T = 0.25 V = c q D  q/q c q = 0.5 Weiland’s + off-diagonal elements × Interferometer (KG1)  Thomson scattering (LIDAR) JPN 55804 Simulation of shot 51084 (shallow pellet, optimised shear) doesn’t need any pinch velocity.

10. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti10 Comments on the analysis of L-modes Equivalence between: mixed Bohm gyro-Bohm + anomalous pinch Weiland’s + off-diagonals elements Compatibility with pinch velocity: V = -Dc T  T/T 0.125 < c T < 0.25 V = Dc q  q/q 0.25 < c q < 0.75 (5 to 10 times larger than the Ware pinch) Off-diagonals elements in Weiland’s model provide the correct particle convection

11. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti11 H-modes 47744 - steady state sawtoothing plasma, mainly radio frequency heated 52979 - steady state sawtoothing plasma, mainly NBI heated, slow puffing

12. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti12 Shot 47744 mainly RF heating Mixed Bohm/gyro-Bohm: V = Ware pinch V = -c T D  T/T c T = 0.125 V = c q D  q/q c q = 0.125 Weiland’s: without off-diagonals elements with off-diagonals elements

13. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti13 Shot 52979 slow puffing sawteeth Mixed Bohm/gyro-Bohm: V = Ware pinch V = -c T D  T/T c T = 0.125 V = c q D  q/q c q = 0.25 Weiland’s: without off-diagonals elements with off-diagonals elements

14. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti14 Comments on the analysis of H-modes In the mixed Bohm/gyro-Bohm model, due to the fact that D is much lower than in L-mode, the effect of the pinch velocity is strongly reduced. Particle convection becomes compatible with neo-classical Ware convection. In some case this is in agreement with the experiment in some other it is not. Why? A similar effect is observed in the Weiland’s model. The effect of the off-diagonal elements is not clear. Sometimes they are needed sometimes they aren’t. Why? In general Weiland’s model seems to do better than the mixed Bohm/gyro-Bohm in the gradient zone (0.5 < r/a < 0.9)

15. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti15 Conclusions (1) Particle transport has been analysed in different scenarios. The JETTO code has been employed with analytical, semi-empirical and physics based transport model. The semi-empirical mixed Bohm gyro-Bohm works well in L-mode. The physics based Weiland’s model is as good as mixed Bohm gyro-Bohm and gives a better reproduction of the gradient zone in H-mode (although the role of the off-diagonal elements is still not clear)

16. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti16 Conclusions (2) Convective velocity –L-mode simulations are compatible with an anomalous pinch velocity 5 to 10 times greater than the neo-classical Ware pinch. (Reasonably well established) –Dependence on q-profile detected in shallow pellet simulations –H-mode simulations are less clear: sometimes the expected lower convection (comparable with the Ware pinch) is in agreement with experiments sometimes it is not

17. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti17 Shot 49030 pellet injection Mixed Bohm/gyro-Bohm: V = Ware pinch V = -c T D  T/T c T = 0.125 V = c q D  q/q c q = 0.25 Weiland’s

18. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti18 Shot 51084 - optimised shear Simulation with analytical D and without anomalous pinch D (~ 0.3 m 2 /s) fitted to have a density profile evolution compatible: –with the temperature pulse propagation –with the integral line density measured by the interferometers chords JPN 51034

19. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti19 Shot 52961 slow puffing no sawteeth Mixed Bohm/gyro-Bohm: V = Ware pinch V = -c T D  T/T c T = 0.125 V = c q D  q/q c q = 0.25 Weiland’s

20. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti20 Partial conclusions for cold pulses Optimised shear. No anomalous pinch. (As in H-mode). Standard shear. Anomalous pinch (5-10 times the Ware pinch). (As in L-mode).

21. 9 th EU-US Transport Task Force Workshop, Córdoba, Spain, 9-12 September 2002Luca Garzotti21 Model description (1) mixed Bohm gyro-Bohm electron/ion thermal conductivity particle diffusivity pinch velocity (Ware pinch always present) (trapped electron modes, turbulence equipartition)