1. RFP Workshop Stockholm 9-11 / 10 / 2008 High Density Limit in RFP’s M Valisa and the RFX-mod team

2. RFP Workshop Stockholm 9-11 / 10 / 2008 OUTLINE Background on density limit in RFP’s New RFX-mod experimental results Discussion

3. RFP Workshop Stockholm 9-11 / 10 / 2008 Why are we interested in High Density plasmas? In a reactor P_fusion ~ n e 2 (provided T is around 10 keV) In RFX  E ~ n e The density limit is a commonality of all of the magnetic configurations.

4. RFP Workshop Stockholm 9-11 / 10 / 2008 Upper Density Limit in RFP’s known since many years Costa,De Angelis, Ortolani Puiatti, Nuc. Fusion 22, 1301 (1982). Radiation limit Ortolani & Rostagni 1983 Nucl. Instrum. Meth 207 35 Radiation limit around n/nG= 0.5 (I/N=2) Perkins & Hulse 1985 Phys. Fluids 28 1837 Bartiromo et al 2000 27th EPS Conf. Budapest http://epsppd.epfl.ch/Buda/pdf/p4_031.pdf Published in M. Greenwald’s review PPCF 2002 MST density limited regimes ( Wyman’s Thesis 2007) Rencent work : Puiatti et al Submitted to PoP Puiatti et al IAEA Conf 2008 Geneve Valisa et al IAEA Conf 2004 Villamoura Valisa et al IAEA Conf 2006 Chengdu

5. RFP Workshop Stockholm 9-11 / 10 / 2008 * RFX-Mod RFP and Tokamak share the same limit The Greenwald limit is an empirical law The Greenwald threshold is not an absolute limit but provides values in the right range In Tokamaks nG can be exceeded by a factor 2 by peaking the density profile. Some ITER scenarios assume n/nG ~ 1.2

6. RFP Workshop Stockholm 9-11 / 10 / 2008 JET Predicted pedestal DL (detachment) and Experimental In JET a pedestal DL is found overlap Borrass NF 2004 752 and is worse than the Greenwald limit

7. RFP Workshop Stockholm 9-11 / 10 / 2008 Stellarator : Sudo limit, much higher than nG RFX

8. RFP Workshop Stockholm 9-11 / 10 / 2008 In LHD the critical edge density that leads to complete detachment is well reproduced by the Sudo scaling with a factor 0.8. Pellet-fuelled plasmas with large density peaking factor  Ne(0)/ne Sudo up to 7 ! Core density can be increased until the core plasma locally collapses, as long as the edge density is kept below the Sudo scaling. Stellarators: Sudo Scaling The Sudo scaling is an edge density limit scaling. The operational limit is ne_ edge < ne Sudo J. Miyazawa. Nucl Fus 2008 and EPS 2008

9. RFP Workshop Stockholm 9-11 / 10 / 2008 New RFX-mod data New current regime Old RFX space Greenwald limit Runaway region

10. RFP Workshop Stockholm 9-11 / 10 / 2008 New on RFX-mod Confirmed the difficulty to keep the current derivative = 0 at high density Normalized Current derivativevs n/nG

11. RFP Workshop Stockholm 9-11 / 10 / 2008 Radiation pattern: a MARFE-like structure Toroidally localized, poloidally symmetric belt

12. RFP Workshop Stockholm 9-11 / 10 / 2008 New experiments with induced rotation of a strong artificial m=0 n=1 mode for a “3D” diagnostic of the relevant structures RFX-mod: DL experiments with induced m=o modes rotation

13. RFP Workshop Stockholm 9-11 / 10 / 2008 At the same relative position with respect to the Locked Mode (90 ° apart where the plasma shrinks): the radiating belt develops edge density accumulates due to the flow stagnation point ( and low diffusivity. Instead at the LM (m=1 modes) : Strong H  signal= main particle source, edge flow displacement due to m=0 radiation electron density HH m=1 toroidal angle plasma shrinking induced m=o modes rotation (Normalized to the Locked mode position) Locked mode position

14. RFP Workshop Stockholm 9-11 / 10 / 2008 New. Reconstruction of local flux structure Poincaré plot. Region where large radiation belts develop. The relationship between specific m=0 islands and radiaon belts still unclear. Measurements of Flow and radial electric field reversal are consistent. Possible explanation: the pattern of m=0 islands conveys the electron parallel flow to the wall in certain regions only. ( Carraro et al JNM 2003) (Bartiromo, Phys. Plasmas 5, 3342 (1998) Magenta line: toroidal flux function. m=0 islands develop around the reversal surface ( green line).

15. RFP Workshop Stockholm 9-11 / 10 / 2008 Edge Diffusivity is low with increasing n/nG Diffusion coefficient estimated from turbulence plotted as a function of normalized density This confirms old RFX measurements (Gregoratto et al NF 96)..

16. RFP Workshop Stockholm 9-11 / 10 / 2008 (open dots) Prad=Pohm as a function of n=nG ; m = 1 mode normalized amplitude vs n=nG : Squares : low- n modes n = 7 ¡ 9), Dots: high- n modes ( n = 10 ¡ 18). Prad/P_input ratio LOCALLY very high (full dots) Prad=Pohm taking into account the fraction of input power impinging on the toroidal portion of the radiating layer Radiating layers tend to manifest and grow beyond the dashed line

17. RFP Workshop Stockholm 9-11 / 10 / 2008 In the ULq case, appraoching and slightly exceeding the Greenwald limit is quite simple with flat current waveforms. The ULq case Well sustained current.

18. RFP Workshop Stockholm 9-11 / 10 / 2008 Summary of the RFX-mod experimental evidence With induced rotation of artificially produced modes At high density in the vicinity of m=0 modes ( not of the m=1 locked mode ) the composition of the radial Er procures a stagnation point for the toroidal flow Diffusion is sufficiently low to allow local density increase favoured by the RFP topology ( around the reversal parallel flow has no or little toroidal component) Density ( not necessarily impurity ) accumulation causes radiation to locally build up At high density localized radiation dissipation is experimenatlly comparable to the power flow to that region  possibility of a thermal instability.

19. RFP Workshop Stockholm 9-11 / 10 / 2008 Question What in absence of artificially induced m=0 modes (i.e. pure Clean Mode Control) ? 1) Fast TV images (1 kHz) show PWI patterns rapidly changing in space 2) 1D Simulation can be made to check the RFP response to an increase density in an axi-symmetric topology MST is more m=0 stable. Experiments could clarify the role of m=0 modes In RFX shallow F experiments at high desnity will be performed

20. RFP Workshop Stockholm 9-11 / 10 / 2008 1D Simulation of high density discharge ( Riport code) “Riport” code: - 1D ( cilindrical symmetry – does not include 3D effects of plasma deformations - Heat and particle equations ( including impurities solved self-consistently with Spitzer resistivity and  -dynamo term See Predebon et al submitted to PoP

21. RFP Workshop Stockholm 9-11 / 10 / 2008 Simulated RFP discharge with a linearly increasing influx 1D Simulation od high density discharge ( Report code) Increased resistivity causes the current to decrease unless the dynamo term is proportionally augmented

22. RFP Workshop Stockholm 9-11 / 10 / 2008 Conclusions 1 New experimental evidence in RFX—mod confirms that localized radiation belts develop in the region where m=0 islands are formed. The evolution is favoured by converging toroidal flow of particles and low edge diffusivity. ULq reaches quite easily the Greenwald DL with well sustained current ( despite general transport is worse). NB: In ULq’s the m=0 resonance is no longer in the plasma In RFX-mod best performance is with QSH which is instead prefers regimes at high Lundquist ~ Te3/2/ ne1/2 We must learn how to to make QSH and high ne compatible..

23. RFP Workshop Stockholm 9-11 / 10 / 2008 Conclusions 2 In Tokamak, Stellarators and RFP’s exceeding a density threshold triggers some kind of instability processes at the egde: typically involving radiation cooling.at the edge (except TEXT : DL due to transport change.D. Brower et al PRL 67, 200 (1991) ) In Tokamaks MARFE structures can lead to a disruption. In the Stellarator and in the RFP (including ULq) the consequences are not disruptive In the RFP current sustainement becomes critical even before nG is reached unlike the ULq  The density limit is originated by similar physics, but modulated by the topological and stability properties of each configuration.

24. RFP Workshop Stockholm 9-11 / 10 / 2008 Conclusions 3 Questions: Would an m=0 controlled RFP plasma avoid the Greenwald density limit? Is the RFP intrinsically limited in density due to its topology and the need of an internal dynamo? In Tokamaks and Stellarators average densities well above the “DL” have been achieved. Can we conceive a high density RFP with peaked profiles and sufficiently low edge density to overcome the Greenwald limit? Try with internal fuelling (pellet/ power beams )& edge recycling control