1. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 MHD in Tokamak Plasmas Guido Huysmans Association Euratom/CEA Cadarache, France with contributions from: T. Hender (UKAEA, Culham, UK) Y. Liu (Göteborg, Sweden) H. Lutjens (Ecole Polytechnique, Paris, France) S. Sharapov (UKAEA, UK) J. Lonnroth (JET, UK) S. Saarelma(UKAEA, UK) M. Becoulet (CEA Cadarache, France) P. Maget(CEA Cadarache, France)

2. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 ITER relevant MHD Edge Localised Modes (ELMs) –Can cause large heat loads on plasma facing components –Need to be controlled Neo-classical tearing modes (NTMs) –Can cause pressure limit well below ideal MHD stability limits Resistive wall modes (RWMs) –The relevant modes (external kink modes) for broad current profiles typical for advanced scenarios Disruptions –Need to be avoided Fast particle modes, TAE modes –Efficiency of alpha particle heating Sawteeth –Source of seed islands …

3. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Outline Ideal (linear) MHD –Waves, MHD Spectroscopy TAE modes Resistive wall modes –MHD Stability limits Global (Internal transport barriers) Local (ELMs) Resistive, extended, non-linear, etc. MHD –Neoclassical tearing modes –MHD in steady state plasmas... I wish to deal with a model which: respects the main physical conservation laws has a decent mathematical structure permits analysis in complicated geometries Ideal MHD is the only model so far that satisfactorily combines these features J.P. Goedbloed (1983)

4. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Ideal MHD The ideal MHD model is very successful in describing and predicting important aspects of MHD phenomena in tokamaks: –Global MHD stability limits Disruptions in advanced tokamak discharges –Local MHD stability limits Edge Localised Modes (ELMs) –Frequencies (spectrum) of stable global modes (waves) TAE modes Modelling tools : linear MHD codes (CASTOR, MISHKA)

5. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 MHD Spectroscopy Diagnostics of the q(r)- profile in toroidally rotating plasmas Neutral Beam Injection on JET drives a significant toroidal plasma rotation Frequencies of waves with mode number n in laboratory reference frame, f n lab, and in the plasma, f n 0, are related through the Doppler shift : n f rot (r) f n lab = f n 0 + n f rot (r) For TAEs frequency does not depend on n, so that f n 0  V a / (2 q R) On the other hand, TAE with mode number n is located at q TAE (r)=(m+1/2)/n Correspondence between f rot (r) and q TAE (r) can be inferred from TAE and the toroidal rotation profile measurements (charge-exchange) S. Sharapov … through continued improvement of both numerical calculations and experimental observations we may witness the birth of a, new kind of spectroscopy, properly called MHD spectroscopy, in the coming decade. J.P.Goedbloed (1993)

6. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 MHD Spectroscopy Magnetic field perturbation measurements at vessel wall (JET #40369) –High frequency TAE modes (300-400 kHz) –TAE antenna signal –Low frequency MHD instabilities (0 – 80 kHz)

7. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 MHD Spectroscopy TAEs observed with magnetic pick-up coils Resulting q-profile: TAE’s EFIT Rotation profile Radius [m]

8. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Resistive wall modes (RWMs) The broad current profile of advanced scenarios leads to a relatively low MHD stability limit due to global kink mode External kink stabilised by ideally conducting wall, unstable when wall is resistive Excitation by external perturbation, plasma response (resonant field amplification) depends on closeness to stability limit : MHD spectroscopy MARS code Y. Liu, Göteborg

9. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Resistive Wall Modes Excitation of JET resistive wall mode: –Resonant field amplification (RFA), comparison experiment with MARS simulations T. Hender, Y. Liu, IAEA, 2004

10. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Disruption Limit Peaked pressure profile due to transport barrier in advanced scenarios causes disruption at a low MHD stability limit Good agreement with predicted ideal MHD stability limit Good agreement with calculated ideal MHD and observed mode structures (JET) 3.8 R [m] 3.1 0.0.20.40.6 time [ms] Electron temperature contours SXR n=1 Stability limit exp. trace

11. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Edge Localised Modes (ELMs) Periodic relaxations of the large pressure gradient at the edge of the plasma (H-mode): centre edge pedestal pedestal density pedestal temperature energy divertor D  A. Kirk, PPCF(2005) High speed video image from MAST pressure profile

12. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Ideal MHD Stability Limits Ideal MHD stability limits to the pressure gradient due to medium n (~10) ballooning modes agree well with observed maximum pressure gradient. S. Saarelma, PPCF,2005  shear JET #55937 0.9 1.0 Edge Electron temperature density radius current density

13. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Medium n ballooning mode Mode structure of ideal MHD ballooning mode (n=10) : perpendicular velocity poloidal harmonics perpendicular velocity 0.7 radius 1.0 S. Saarelma, PPCF,2005

14. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Peeling modes and the separatrix Peeling modes are localised external kink modes driven by the edge current density. The stability of peeling modes depends sensitively on q at the edge. What happens to peeling modes in the presence of an x-point where q goes to infinity? Limit towards separatrix, ideal MHD: Finite current gradient Finite edge current MISHKAFlux at boundary

15. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Influence of separatrix Resistive MHD peeling modes are also strongly stabilised by the approach to the separatrix An additional instability (so-called peeling-tearing mode) remains unstable in the presence of an X-point. peeling modepeeling-tearing mode CASTOR

16. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 X-point Geometry Non-linear MHD code (JOREK) –Includes separatrix geometry, open and closed field lines –Flux surface aligned finite element grid –Reduced MHD in toroidal geometry –Fully implicit time evolution –under development

17. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Peeling modes in X-point Geometry Peeling mode stability in X-point geometry agrees with CASTOR results in the limit to the separatrix: Ideal and resistive peeling modes are completely stabilised by the separatrix Resistive peeling-tearing mode remains unstable  =0.99  =0.998 X-point Growth rate(n=1) Current perturbation

18. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Non-linear evolution of peeling modes Peeling-tearing mode saturates non-linearly –Line tied boundary conditions –strong deformation density profile, small perturbation of flux surfaces JOREK kinetic magnetic

19. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Neo-classical Tearing modes NTMs are non-linear instabilities : An island created by another instability (sawtooth) flattens locally the pressure profile:  reduction of the bootstrap current inside the island  further growth of the island  loss of confinement and limit to pressure Example NTM JET Heating power Plasma Energy MHD temperature density SXR Electron temperature profile Radius [m]

20. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Neo-classical Tearing Modes (NTMs) Tore Supra: MHD mode triggered after monster sawtooth Tearing mode with mode numbers m/n=3/2 Slow decay on resistive time scale ~1sec.

21. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Neo-Classical Tearing Modes Simulations XTOR code : –resistive MHD (including transport and bootstrap current) in toroidal geometry. –H. Lutjens and J.F. Luciani (Ecole Polytechnique Paris) Evolution island size

22. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 NTM Theory versus Simulations Reasonable agreement for small island widths (thresholds) Disagreement on island saturation size Comparison 0D theory with full numerical simulations (XTOR):

23. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 MHD in Plasmas with Current Drive Tore Supra, steady state discharges Neutron (x10 10 /s) Z eff T i (0) (keV) Line density (x10 19 m -2 ) LH Power (MW) Transformer flux (Wb) T e (0) (keV) Plasma stable until small (harmless) MHD instability sets in at t=258s Discharge duration : > 6 min Injected energy : > 1 GJ q Hard-X 75 keV (a.u.)

24. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Quietoscillations giant oscillationsMHD Oscillations in Tore Supra The interaction between the deposition of the driven current, the temperature, q-profile and the (improved) confinement can lead to an oscillatory regime: double tearing mode

25. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Tore Supra : MHD regime Tore Supra steady state scenario sensitive to MHD instabilities –reversed q-profile with q min ~2 –Linear tearing mode and later double tearing almost always unstable. –relevant stability criterion : full reconnection of the double tearing mode P. Maget

26. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Current Holes Current holes are formed with a strong off-axis current drive. –Off-axis current tends to drive central current density to negative values –Central current density fixed close to zero by an n=0/m=1 internal kink instability (2D non-linear MHD simulations) In JET, sawtooth like crashes are observed in plasmas with a current hole. –Crashes not due to n=0/m=1 mode –n=1 postcursors observed –3D simulations of JET current hole plasmas n=0/m=1 internal kink mode A current hole is the absence of toroidal current in the central part of the plasma. JOREK perturbed current profile

27. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Current Holes The reversed q-profile of current hole plasmas can be unstable to double tearing modes –in this example, a complete reconnection occurs in between the outer q=2 surface and the radius of the current hole –the current hole survives the crash –density profile shows a fast collapse

28. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Conclusions The relevance of (and interest in) MHD in tokamak fusion plasmas has grown significantly over the past years. Linear Ideal MHD is surprisingly accurate for a number of applications in tokamak plasmas MHD Spectroscopy is now a valuable diagnostic for the q-profile Non-linear and extended MHD is becoming more relevant/necesary for comparison with experiment Interaction between MHD and current deposition profile is important  combined MHD transport simulations

29. G.Huysmansworkshop : Principles of MHD 21-24/3/2005 Discussion Challenges (to Physics and Numerics): –Simulation of complete ELM cycle Different ELM types : I, II, III etc. –Trigger of Neo-classical tearing modes FIR NTM regime (NTM interaction) Island rotation –Convergence MHD models – Turbulent Transport models –Kinetic effects in reconnection –Sawteeth models –Fast particle physics –Integrated tokamak modelling