Edge stability in tokamak plasmas

1. Edge stability in tokamak plasmas S. Saarelma, C. Gimblett, T. Hender, A. Kirk, H. Meyer and MAST Team, UKAEA Fusion, UK H. Wilson, University of York, UK S. Günter, L. Horton, IPP Garching, Germany Y. Andrew, M. Kempenaars, A. Korotkov, A. Loarte, E. de la Luna, P. Monier-Garbet,V. Parail and Contributors to EFDA-JET work programme O.J. Kwon, Daegu University, Gyungbuk, South Korea

2. Outline • “Standard” ELM-model • JET, ASDEX Upgrade • MAST, difference to other machines • Detailed analysis of MAST edge stability • Peeling-model for ELMs

3. MAST JET ELMs • Short bursts of edge plasma • Remove impurities and help controlling plasma density, but • Can cause unacceptable erosion on divertors • From experiments we know, what the ELMs look like: • Da-signal, • Changes in profiles, • Camera pictures, • etc.

4. Purpose of the edge stability analysis • The stability analysis tries to answer to two questions: • What triggers the ELMs ? • Is there a way to control the ELMs ?

5. 4 3 Bootstrap current builds up 2 Edge current density Peeling limit 1 Ballooning limit Stable Edge pressure gradient “Standard” ELM-model (Connor, Hastie, Wilson, Miller, PoP, 1998)

6. MHD stability analysis method • Using experimental data construct an equilibrium with self-consistent bootstrap current. • Investigate the stability of the equilibrium using MHD stability codes such as • GATO , only low-n • MISHKA, low- to intermediate-n • ELITE, intermediate- to high-n • Vary the edge pressure gradient (a) and current density (jf~1/shear) to find stability boundaries near the experimental point.

7. ASDEX Upgrade & JET • The standard ELM model is tested on experimental AUG and JET plasmas. • The model is tested for Type I, II and III ELMs.

8. JET ELMs JET #55937, Type I ELMs, MISHKA n=10 mode amplitude Fourier decomposition of the mode

9. JET gas scan y=0.98, the most unstable mode number plotted = high-n ballooning unstable Type I ELMs • Type I ELMs: At the intermediate-n peeling-ballooning stability boundary. • Type III ELMs: Below the first ballooning stability boundary • Power scan, similar results for Type I and Type III ELMs. Type III ELM The result reproduced using ELITE by O.J. Kwon !

10. AUG, Type II ELMs • Type II ELMs: • High triangularity (d), high q95, close to double null configuration. • Edge pressure gradient comparable to Type I ELMy plasmas. GATO (n=3): Type II conditions cause the unstable mode to become more localised to the edge Smaller ELMs

11. MAST ELMs • MAST parameters : • R=0.85m, a=0.65, Bt=0.52 T • Ip=1.35 MA (achieved), 2MA (design) • PNBI=3.3 MW (achieved), 5 MW (design) • Small aspect ratio • A lot of NBI power for a small volume: • Fast rotation

12. MAST ELM Stability analysis #8901 high resolution Thomson scattering density and temperature profiles 15 ms before an ELM • MAST has very good diagnostics for Te and ne profiles. • Current is assumed to be a combination of inductive and bootstrap current. Density Temperature

13. n=7 MAST edge instabilities (1) • The MAST equilibria can have two types of instabilities • If D = mqedge-n is very small, peeling modes can become unstable. • The peeling modes have very narrow width and its stability is very sensitive to the edge value of q. • Unlikely a trigger for ELMs. Mode localised near the x-points. ELITE:

14. n=6 MAST edge instabilities (2) • With increased pressure, a more robust peeling-ballooning mode becomes unstable. • It is not sensitive to the edge value of q. • It has wider radial extent, across the whole pedestal.

15. Edge stability and pressure D=m-nqsurf D=0.5 D=0.1 • With experimental profiles, only very narrow peeling modes with small growth rate are unstable. • Increasing edge pressure gradient drives wider peeling-ballooning modes with larger growth rate unstable. • Peeling-ballooning modes are the likely triggers of ELMs in MAST

16. MAST edge stability diagram MAST #8209, y=0.99

17. Sensitivity to the pedestal position ysteepest gradient=0.987 ysteepest gradient=0.991

18. Pedestal position scan • If instead of the pedestal height, the pedestal position is varied, the wide peeling-ballooning modes become destabilised within the error margin of the pedestal position. Peeling-ballooning modes: n of the most unstable mode increases with pedestal position: n=6 most unstable at y=0.996 and n=25 at y=0.999. Peeling modes: Small-n (n=1-3) modes are the most unstable.

19. Single null vs. double null (1) • Experiment: no ELMs in single-null discharges. • Is the shape reason for the change in stability boundaries ? • Stability analysis, same profiles, varying plasma shape: No stability difference due to the boundary shape

20. Single null vs. double null (2) • But using the profiles from a single-null discharge (#7508), the wide peeling-ballooning modes with large growth rate are stable when the pedestal position is varied. • Also increasing the pedestal height by 100 % does not change the stability. • The different temperature and density profiles responsible for the change in stability and ELM-free behaviour. Still unknown: Why are the profiles different in single-null discharges ?

21. Experimental level Stabilisation through velocity shear • Before an ELM, the edge toroidal velocity changes from 25 km/s to 0 km/s within less than 1 cm. • During an ELM, the velocity shear flattens. • What is the effect of velocity shear on the stability ? Growth rate (peeling-ballooning mode) vs. vped Experimental toroidal rotation profile The rotation shear has a stabilising effect. However, the rotation shear required for the complete stabilisation is slightly higher than the experimental value

22. MAST ELM model Velocity profile Pressure profile with stability limits Flux surfaces near the plasma edge 1. The edge pressure gradient exceeds the stability limit for a static plasma. 2. Plasma reaches the stability limit for a rotating plasma and the instability starts to grow. Low-n modes become unstable first because they are the least affected by the sheared rotation stabilisation. 3. The growing instability ties the adjacent flux surfaces together and flattens the rotation profile. High-n modes become dominant. 4. The growth of the mode becomes even faster as the rotation shear disappears.  ELM crash

23. Aspect ratio and rotation • Does the same ELM model work with conventional tokamaks? • No, ELMy JET plasma is not affected by edge rotation shear. • The reason: The stabilising effect of rotation shear becomes weaker as the aspect ratio increases. • Even in spherical tokamaks, relatively fast edge rotation (~20% of sound speed) is needed for the stabilisation • The rotation has little effect on conventional tokamak ELMs. • The standard ELM model still works for conventional tokamaks or with spherical tokamaks with no or weak beams. ELITE: circular plasma with an edge mode n=10 e=a/R

24. j(r) r ELM model for Type III ELMs • Let us assume that Type III ELMs are current-driven peeling modes (in any case they are well below the ballooning stability boundary) • During an ELM crash, the current starts relaxing in outer annular region. • The relaxation produces a negative surface skin current which has a stabilising effect on the peeling modes. All peeling modes at certain radial width become stable. Pre-ELM current profile Post-ELM current profile Post-ELM skin currents

25. Use the toroidal peeling criterion + width prediction to compute DWELM/WPED from the model: (MAST parameters, no trapped particles, parabolic pressure profile) More in: C.G. Gimblett, R.J Hastie, P. Helander 31th EPS, Tarragona, 2005

26. Conclusions • Standard ELM model agrees with experimental observations in conventional tokamaks • Edge plasmas are unstable to peeling-ballooning modes. • Before an ELM, MAST edge plasma is • unstable against narrow peeling modes with low growth rate • close to the stability limit for wider peeling-ballooning modes • The high-n modes are stabilised at experimental edge rotation profiles suggesting a modification to the ELM model for STs. • An analytical model for peeling modes and skin currents can explain destabilisation and stabilisation of the edge during the ELM cycle.

27. Future challenges • X-point effects on the stability • Near x-point, the magnetic field becomes ergodised • No flux surfaces • A limit for current MHD stability codes • New tools needed for modelling n=10