1. MHD Limits to Tokamak Operation and their Control Hartmut Zohm ASDEX Upgrade credits: G. Gantenbein (Stuttgart U), A. Keller, M. Maraschek, A. Mück DIII-D credits: E.J. Strait, R.J. La Haye JET credits: S. Pinches JT-60U credits: A. Isayama (JAERI), K. Nagasaki (Kyoto U) Introduction The density limit  -limit in conventional scenarios: NTMs  -limit in advanced scenarios: RWMs Conclusions Invited talk at 30th EPS Conference on Controlled Fusion and Plasma Physics, St. Petersburg, Russia, 08 July, 2003

2. Tokamaks and their operational space To obtain the goal of nuclear fusion, tokamaks have to maximise the energy confinement time  E (  I p or 1/q for fixed B-field) the fuel density n (P fus  n 2  v  or (nT) 2 at optimum T of 10-20 keV) the normalised pressure  = p kin /p mag (P fus  p kin 2 or  2 at fixed B-field)

3. Tokamaks and their operational space To obtain the goal of nuclear fusion, tokamaks have to maximise the energy confinement time  E (  I p or 1/q for fixed B-field) the fuel density n (P fus  n 2  v  or (nT) 2 at optimum T of 10-20 keV) the normalised pressure  = p kin /p mag (P fus  p kin 2 or  2 at fixed B-field) ITER operational space simulation

4. Tokamaks and their operational space MHD instabilities can be ideal (  A = ~  s) or resistive (  R = ~ ms) Examples: Disruptions at low q and high density (current driven islands) Neoclassical Tearing Modes (‚pressure driven‘ islands) Resistive wall modes (current and pressure driven ideal kink) Two strategies: Avoid – natural tendency, but limits operational space Control – needs active tools, but increases op. space q, n and  are limited by the occurrence of large scale MHD instabilities (free energy of poloidal field and plasma pressure)

5. The density limit is often accompanied by a disruption Actual limitation is a power balance problem at the edge radiative instability (MARFE) excessively cools edge edge current is drastically reduced – gradient drives tearing modes neighbouring chains of islands lead to loss of confinement temperature collapse increases resistance – current cannot be sustained Density limit scales as n max = I p /(  a 2 ) = n G (Greenwald limit) ASDEX Upgrade, W. Suttrop et al., NF 97

6. Practical density limit: onset of confinement degradation Well before disruptive termination, confinement starts to degrade H-mode confinement drops when n comes close to Greenwald limit H-L back transition due to reduced edge temperature Practical density limit is a confinement issue, not an MHD issue! Note: 'accidents' will still lead to disruptions – mitigation techniques needed ASDEX Upgrade, V. Mertens et al., EPS 99ASDEX Upgrade, J Stober et al., EPS 99

7.  -limit in conventional scenarii: Neoclassical Tearing Modes Once seeded, island is sustained by lack of bootstrap current (flat p(r))...predicts  * p -scaling of onset  N (bad news for ITER) Equilibrium current profile Bootstrap drive Finite   /   Polarisation current ASDEX Upgrade, H. Zohm et al., PPCF 96

8. Dimensionless NTM onset scaling for JET and ASDEX Upgrade M. Maraschek et al., this conference

9. Active control or avoidance of NTMs Active control or avoidance is possible by reducing the local  p – may not be a free parameter in a reactor preventing seed island formation (e.g. suppress sawteeth) tailoring the equilibrium current profile (e.g. LHCD, ECCD) generating a localised helical current in the island (e.g. ECCD)

10. Active control or avoidance of NTMs Active control or avoidance is possible by reducing the local  p – may not be a free parameter in a reactor preventing seed island formation (e.g. suppress sawteeth) tailoring the equilibrium current profile (e.g. LHCD, ECCD) generating a localised helical current in the island (e.g. ECCD)

11.  N can be increased above onset level (ASDEX Upgrade) Complete stabilisation of (3,2) NTM with P ECCD / P tot = 10% Mode comes back due to deposition mismatch (Shafranov shift) deposition must be exact within island half width (1-2 % of major radius) H. Zohm et al., Phys. Plasmas 01

12. 'Search and suppress' adjusts B t or R until (3,2) mode vanishes DIII-D has successfully implemented radial feedback R.J. La Haye et al., Phys. Plasmas 02

13. Rational surface inferred from local minimum in ECE perturbation JT-60U: feedback control of launching mirror A. Isayama et al., IAEA FEC 02

14. (2,1) stabilisation needs more power (DIII-D) Required power substantially higher than for (3,2) – ok for ITER? mode stabilised with 2.8 MW of ECRH power at  N = 2.1 'search and suppress' also works for this mode (3,2)(2,1) R.J. La Haye et al., this conference

15. In ASDEX Upgrade, (2,1) NTM usually occurs at high   and locks to wall target plasma has power step-down to obtain rotating (2,1) at lower   (2,1) stabilisation needs more power (ASDEX Upgrade) G. Gantenbein et al., this conference

16. At  N = 1.9, ECCD power of 2.0 MW just sufficient for stabilisation (2,1) stabilisation needs more power (ASDEX Upgrade)

17. Injection of ECCD before NTM onset in JT-60U Application of ECCD before mode onset is advantageous for same ECCD power, saturated amplitude during ECCD is smaller explanation must be based on nonlinearity in stability curve K. Nagasaki et al., to appear in NF

18. Modelling of NTM stabilisation ECCD current (e.g. Fokker-Planck) inserted in temporal evolution equation use Rutherford equation or 2d nonlinear resistive MHD code agreement with experiment gives some confidence for extrapolation Largest uncertainty in prediction to ITER lies in NTM stability, not ECCD [Q. Yu et al., Phys. Plasmas 01]

19. first demonstrated on JET with ICRH current drive [O. Sauter, PRL 2002]

20. Experiments with slow B t -ramp, 0.8 MW co-ECCD and 5.1 MW NBI: increase of sawtooth period for deposition outside inversion radius decrease of sawtooth period for deposition inside inversion radius Ctr-ECCD shows inverse behaviour Sawtooth tailoring by ECCD in ASDEX Upgrade A. Mück et al., this conference

21. Removal of sawteeth avoids NTM during ECCD pulse B t ramp + feedback controlled  -ramp maintain correct ECCD deposition

22.  -limit in advanced scenarii: Resistive Wall Modes When ideal kink is wall stabilised, RWM can grow on wall time scale rotation w.r.t. wall can stabilise the RWM if  rot >> 1/  W balance between wall drag and (rotating) plasma drag on mode Ideal regime: Ideal kink stable if wall is close enough RWM regime: RWM is stable when slipping between mode and wall is large enough Ideal branch RWM branch A. Bondeson et al., PRL 94

23. Without nearby conducting wall, external kink is observed ASDEX Upgrade: very low  -limit (  N = 1.8) with strongly reversed shear Stability analysis and experimental data suggest coupling to infernal mode S. Günter et al., NF 00

24. With conducting wall, ideal  -limit can be exceeded DIII-D: with fast plasma rotation,  N no-wall is substantially exceeded Below threshold value, mode penetrates wall and becomes a RWM Threshold value of few % of Alfvén speed consistent with theory E.J. Strait et al., NF 03

25. Above no-wall limit, plasma amplifies error fields If  exceeds no-wall limit, external perturbation is strongly amplified amplification of intrinsic error fields slows down rotation if  >  no-wall can be interpreted as resonant amplification by marginally stable RWM Similar findings on JET confirm this picture  Rotational stabilisation may not work in steady state!

26. Direct RWM stabilisation by active coils Saddle coils for direct stabilisation different feedback schemes exist first results look promising new experiments with in-vessel coils under way on DIII-D

27. Summary and conclusions Tokamak operational space restricted by large scale MHD instabilities Present strategy aims at avoiding current and density limit ITER aims at operation within intrinsically stable space  -limit in conventional (NTM) and advanced scenarii (RWM) too low Strategies for active control are under development based on good physics understanding involves local j(r) control by ECCD for NTMs may ultimately need active saddle coil feedback for RWM

29. Error field correction results in sustained rotation Continuous high beta by error field compensation