1. Low dimensional Edge-localised- modes dynamics in JET tokamak Edge-localised-modes characterization through data analysis Francisco A. Calderon University of Warwick

2. Outline 1.Brief introduction to fusion High confinement and instabilities: ELMs 2.What is needed for?  ITER … DEMO 3.Description and results 4.Further work

3. Brief introduction to Fusion Controlled thermonuclear fusion reactions Inertial confinement Magnetically confined plasma Tokamak Stellerator Section 1

4. High confinement: ELMs First saw H-mode: ASDEX (1982) 1 H-mode is accompanied by many instabilities [1-3]. ELMs are more easily found in “divertor” geometry. They are a nonlinear bursting instability occurring in the edge of plasma. 1 Asdex-Upgrade tokamak

5. Why do we need to study ELMs? Challenge ITER, DEMO Human Well-Being Section 2

6. ITER Is a Tokamak Lab for burning plasma Prove DEMO feasibility Been built in: Caradache, Les Bouches du Rhône, southern France. Further info: www.iter.orgwww.iter.org Check for ITER newsletter!

7. Work and Results Section 3

8. Experimental data Analysis D  time trace (Lyman 656.3nm) Highly nonlinear Reduced number – few hundred per shot Low frequency (ELM type I) Time series analysis We found useful to use a new time series as defined by Schreiber et al. (2000) for spiky events in time series Greenhough (2003) states: “…[Need for] thresholding to define and quantify the individual ELM burts.”

9. Use time ocurrence(see figure) as new time series {t n }. We define the inter-ELM time interval as [6]:  t n = t n – t n-1. Construct delay plots. Make PDF of the inter- ELMs time intervals. Analysis

10. Delay plots Are not a phase space reconstruction as we used here Example: single pendulum, with a period 

11. Threshold scheme There are a few ELMs per time series, and they ranges from 67 - 196.

12. Gas puffing rate Reproduced from Calderon et al. (2013) [9]

13. First set with lower gas puffing rate Reproduced from Ref. [9]

14. Second set with higher gas puffing rate The population in the sharp peak increases with the gas puffing rate. Reproduced from Ref. [9]

15. Conclusions > Long-duration (~5s) quasi-stationary JET plasmas reveal significant variations in the ELMing process or processes along with the variations of the control parameter  — the gas puffing rate. > ELM population in each plasma enables us to characterize the dynamics, which is found to be low dimensional. > Demonstrating and quantifying the effectiveness of ELM control and mitigation techniques will be assisted by characterizing the measured sequences of inter-ELM time intervals in this way.

16. Further Work Webster et al. (2013)has recently found signs of Resonant behaviour in JET plasmas. - We see this as Stripes on Delay plots -Are ELMs coupling with Coils? Section 4

17. Why is this been seen now?

18. The End

19. References [1] A Loarte et al., Plasma Phys. Control. Fusion 45, 1549 (2003) [2] K Kamiya et al., Plasma Phys. Control. Fusion 49, S43 (2007) [3] R J Hawryluk et al., Nucl. Fusion 49, 065012 (2009) [4] www.iter.org Retrieved 15th june 2013.www.iter.org [5] J Greenhough, S C Chapman, R O Dendy, and D J Ward, Plasma Phys. Control. Fusion 45, 747 (2003) [6] T Schreiber and A Schimdt Physica D 142 346–382, (2000). [7] A Degeling, Y Martin, P E Bak, J B Lister, and X Llobet, Plasma Phys. Control. Fusion 43, 1671 (2001) [8] Webster et al. “Time-resonant tokamak plasma edge instabilities?” (2013), In press. [9] F A Calderon, R O Dendy, S C Chapman, A J Webster, B Alper et al., Phys. Plasmas 20, 042306 (2013)