1. MHD in the Spherical Tokamak MAST authors: SD Pinches, I Chapman, MP Gryaznevich, DF Howell, SE Sharapov, RJ Akers, LC Appel, RJ Buttery, NJ Conway, G Cunningham, TC Hender, GTA Huysmans, R Martin and the MAST and NBI Teams NSTX authors: A.C. Sontag, S.A. Sabbagh, W. Zhu, J.E. Menard, R.E. Bell, J.M. Bialek, M.G. Bell, D.A. Gates, A.H. Glasser, B.P. Leblanc, F.M. Levinton, K.C. Shaing, D. Stutman, K.L. Tritz, H. Yu, and the NSTX Research Team 21 st IAEA Fusion Energy Conference, Chengdu, China, 2006 This work was jointly funded by the UK Engineering & Physical Sciences Research Council and Euratom Supported by Office of Science EX/7-2Rb EX/7-2Ra

2. MHD physics understanding to reduce performance risks in ITER and a CTF –Error field studies –RWM stability in high beta plasmas –Effects of rotation upon sawteeth –Alfvén cascades in reversed shear EX/7-2Ra EX/7-2Rb

3. Error field studies in MAST Four ex-vessel (ITER-like) error field correction coils wired to produce odd-n spectrum, I max = 15 kA·turns (3 turns) Mega Ampere Spherical Tokamak R = 0.85m, R/a ~ 1.3 Error fields: slow rotation, induce instabilities, terminate discharge EX/7-2Ra

4. Locked mode scaling in MAST [Howell et al. to be submitted Nucl. Fusion (2006)] [Buttery et al., Nucl. Fusion (1999)] B 21 is the m = 2, n = 1 field component normal to q = 2 surface: Error fields contribute to β N limit: n=1 kink EX/7-2Ra Similar density scaling observed on NSTX Extrapolating to a Spherical Tokamak Power Plant / Component Test Facility gives locked mode thresholds ≈ intrinsic error  prudent to include EFCCs

5. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb RWM active stabilization coils RWM sensors (B p ) Non-axisymmetric coil enables key physics studies on NSTX RWM active stabilization  Midplane control coil similar to ITER port plug designs  n > 1 studied during n = 1 stabilization RWM passive stabilization  Plasma rotation profile, ion collisionality, ii, important for stability Plasma rotation control  A tool to slow rotation,  , by resonant or non-resonant fields  Plasma momentum dissipation physics studied quantitatively RWM sensors (B r ) Stabilizer plates

6. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb RWM actively stabilized at low, ITER-relevant rotation First such demonstration in low-A tokamak  Long duration > 90/  RWM  Exceeds DCON  N no-wall for n = 1 and n = 2  n = 2 RWM amplitude increases, remains stable while n = 1 stabilized n = 3 magnetic braking to reduce    Non-resonant braking to accurately determine critical plasma rotation for RWM stability,  crit Sabbagh, et al., PRL 97 (2006) 045004. NN I A (kA)  B pu n=1 (G)  B pu n=2 (G)   /2  (kHz)  N >  N (n=1) no-wall 120047 120712   <  crit 92 x (1/  RWM ) 6 4 2 0 8 4 0 1.5 1.0 0.5 0.0 20 10 0 20 10 0 t(s) 0.40.50.60.70.80.9 Post-deadline paper at this conference, PD/P6-2

7. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb measured theory t = 0.360s 116931 axis n = 3 field T NTV (N m) 3 4 2 1 0 0.91.11.31.5 R (m) T NTV (N m) 3 4 2 1 0 Observed plasma rotation braking follows NTV theory First quantitative agreement using full neoclassical toroidal viscosity theory (NTV)  Due to plasma flow through non-axisymmetric field  Trapped particle effects, 3-D field spectrum important Resonant field amplification (RFA) increases damping at high beta  Computation based on applied field, or DCON computed mode spectrum Non-negligible physics for simulations of   in future devices (ITER, CTF) applied field only axis t = 0.370s 116939 With RFA (DCON) n = 1 field Zhu, et al., PRL 96 (2006) 225002. RFA =  B plasma  B applied

8. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Rotation profile shape important for RWM stability Benchmark profile for stabilization is  c =  A /4q 2 *  predicted by Bondeson-Chu semi- kinetic theory**  theory consistent with radially distributed dissipation Rotation outside q = 2.5 not required for stability  Applied n = 3 fields used to alter stable   profiles below  c Scalar  crit /  A at q = 2, > 2 not a reliable criterion for stability  variation of  crit /  A at q = 2 greater than measured   in one time step  consistent with distributed dissipation *A.C. Sontag, et al., Phys. Plasmas 12 (2005) 056112. **A. Bondeson, M.S. Chu, Phys. Plasmas 3 (1996) 3013.

9. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb  crit not correlated with Electromagnetic Torque Model Rapid drop in   when RWM unstable may seem similar to ‘forbidden bands’ theory  model: drag from electromagnetic torque on tearing mode*  Rotation bifurcation at  0 /2 predicted No bifurcation at  0 /2 observed  no correlation at q = 2 or further into core at q = 1.5  Same result for n = 1 and 3 applied field configuration NSTX  crit Database *R. Fitzpatrick, Nucl. Fusion 33 (1993) 1061. (  0  steady-state plasma rotation)

10. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Increased Ion Collisionality Leads to Decreased  crit (R. Fitzpatrick, et al., Phys. Plasmas 13 (2006) 072512.) Plasmas with similar v A Consistent with neoclassical viscous dissipation model  at low , increased ii leads to lower  crit  modification of Fitzpatrick “simple” model Similar result for neoclassical flow damping model at high collisionality ( ii > v transit ) (K. C. Shaing, Phys. Plasmas 11 (2004) 5525.) 121083 121071

11. Effects of rotation on sawtooth Increasing co-NBI  sawtooth period increases Increasing counter-NBI  sawtooth period decreases to a minimum, then increases I p = [680,740] kA, B T = [0.35,0.45] T n e = [1.6,2.2]  10 20 m -3 [Chapman, submitted to Nucl. Fusion (2006)] [Koslowski et al., Fusion Sci. Technol. 47 (2005) 260] [Nave et al., 31 st EPS (2004) P1.162] MAST #13369 1.61 MW (co) MAST #13575 1.56 MW (counter) EX/7-2Ra

12. Sawtooth Stability Modelling The resistive, compressional linear MHD stability code MISHKA that includes ion diamagnetic effects (  *i ) has been extended to include toroidal and poloidal flow profiles (MISHKA-F) In the case, v Φ << v A and s = (r/q)dq/dr ~ 1, (as in MAST) theory predicts that Doppler shifted mode frequency: In MAST, rotation at q = 1 is key parameter, not rotational shear  Precursor changes direction when, consistent with modelling [Mikhailovskii & Sharapov PPCF 42 (2000) 57] [Chapman, Phys. Plasmas 13 (2006) 065211] Increasing  *i Co-NBICounter-NBI EX/7-2Ra

13. JET data Marginal q=1 position with flow As sawtooth period,  st, increases, radial location of q = 1 increases Marginally stable q = 1 radius expected to correlate with  st Toroidal velocity at which q = 1 radius for marginal stability is minimised agrees with when sawtooth period is minimised Co-v Φ profile used Counter-v Φ profile used Experimental data MISHKA-F modelling q r 1 r(q=1) t Marginally stable q=1 radius Ongoing extension to this work to include fast ion kinetic effects to study fast ion stabilisation of sawteeth and NTM triggering EX/7-2Ra

14. MAST #15806 Log (δB) Frequency [kHz] Time [s] 0.1150.120 0.125 0.1300.135 -2.0 -3.0 -4.0 -5.0 170 160 150 140 130 120 Alfvén Cascades and q min (t) evolution Global shear Alfvén waves driven by fast beam ions –Lowered beam power to avoid nonlinear effects ACs occur when magnetic shear is reversed Characteristic frequency sweep determined by q min –Determine q min (t) Single Alfvén cascade eigenmode Transistion to TAE and frequency sweeping EX/7-2Ra Time [s] 0.090.100.110.130.120.14 Toroidal mode number, n 5 4 3 2 1 MAST #16149 Frequency [kHz] 140 120 100 80 60 q min (t) q min =7/2 5/28/37/3 3 2 3/1 0.08

15. Summary & Conclusions Error field studies highlight need for error field correction coils on Spherical Tokamak Power Plant or Component Test Facility Inverse dependence of  crit on ii indicates that lower collisionality on ITER may require a higher degree of RWM active stabilisation in advanced scenarios Similar inverse dependence of plasma momentum dissipation on ii in NTV theory indicates ITER plasmas will be subject to higher viscosity and greater   reduction Strong  B 2 dependence of quantitatively verified NTV theory shows that error fields and RFA need be minimized to maximize   Detailed sawtooth modelling agrees with experimental results and clarifies rôle of rotation in sawtooth stability Alfvén cascades have confirmed the sustainment of reversed magnetic shear and revealed the evolution of q min See posters EX/7-2Ra/b for more details

16. The End

17. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Non-axisymmetric fields amplified by stable RWM at high  N Toroidally rotating n = 1 fields used to examine resonant field amplification (RFA) when  N   N no-wall  propagation frequency and direction scanned  RFA increases when applied field rotates with plasma flow  consistent with DIII-D results and theoretical expectations Single mode model of RWM fit to measured RFA data  peak in fit at 45 Hz in direction of plasma flow RFA magnitude (n = 1) Applied frequency (Hz) Direction of plasma flow Counter plasma flow Single mode model fit RFA =  B plasma  B applied (H. Reimerdes, et al. PRL 93 (2004) 135002.)

18. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb RWM stabilized upon growth of other MHD modes n = 1 internal mode grows following unstable growth phase of n = 1 RWM Chordal USXR Data 0.41 0.420.43 t (s) 0.37 0.39 0.41 0.43 t (s) Edge Core RWM 0.360.380.400.42 DCON  W NN 6 4 2 0  B p (G)  B (G) 15 10 5 0 -10 0 t (s)  N >  N no-wall

19. v NBI v *i (co) v *i (counter) Sawtooth studies in MAST  High power NBI into small (low moment of inertia) plasma volume  fast rotation  Important to understand for future Component Test Facility (very high NBI power)  Studying effects of flow on sawtooth stability important for understanding slowly rotating ITER plasmas  Decoupling rotation from present-day results Combination of experimental studies and numerical modelling EX/7-2Ra

20. Reversed shear and Alfvén Cascades Alfvén Cascades observed on MAST showing duration of reversed shear Also seen on interferometry signals Plasma Current NBI Power #16095 #16149 Onset of AC with q min ~3 Onset of AC with q min ~2 Time (s) 0.000.050.10 0.150.200.25 MW 0.0 0.5 1.0 1.5 kA 800 600 200 400 0 ACs indicate shear reversal EX/7-2Ra

21. MAST #15806 Log (δB) Frequency [kHz] Time [s] 0.1150.120 0.125 0.1300.135 -2.0 -3.0 -4.0 -5.0 170 160 150 140 130 120 Alfvén Cascades in MAST Global shear Alfvén waves driven by super- Alfvénic beam ions –Lowered beam power to avoid nonlinear effects from strong drive ACs occur when magnetic shear is reversed Characteristic frequency sweep determined by q min –Enables determination of q min (t) Single Alfvén cascade eigenmode Transistion to TAE and frequency sweeping EX/7-2Ra

22. Alfvén cascades and q min evolution Time [s] 0.090.100.110.130.120.14 Toroidal mode number, n 5 4 3 2 1 MAST #16149 Frequency [kHz] 140 120 100 80 60 q min (t) q min =7/2 5/28/37/3 3 2 3/1 0.08 EX/7-2Ra

23. New Sensors Reveal High Frequency MHD [Appel et al., 31 st EPS (2004) P4.195] [Gorelenkov et al, Nucl. Fusion 42 (2002) 977] New TAE antenna currently being installed leaves MAST well-placed to probe fast particle stability at tight aspect ratio New high frequency sensors (<5 MHz) reveal modes similar to observations on NSTX MAST #16106 Log (δB) 0.0 -3.0 -4.0 -5.0 -2.0 -6.0 Frequency [kHz] 1000 800 600 400 200 Time [s] 0.2280.2300.2320.2360.2340.2380.2400.242 TAE modes EAE modes NAE modes High frequency modes

24. NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb NSTX supports ITPA / ITER locked mode threshold and disruption studies (1) Locked mode threshold(2) Disruption studies NSTX contributing low-A, low B data  density scaling nearly linear, similar to higher-A  Will contribute B, q scaling data for ITER size scaling (GA report A25385) NSTX data contributes dependence of current quench time,  CQ on A  Important test of theory for ITER, CTF   CQ independent of plasma current density when A dependence of plasma inductance is included n e [10 19 m -3 ] Applied 2/1 B  at lock (Gauss)  n e 0.93  n e 1.0 ITER Operating Range 9 MA 15 MA J. Menard, PPPL

25. Access to new regime Error field correction enables operation at previously inaccessible low densities to study current drive physics [Howell et al. to be submitted NF 2006] Locked mode grows up Still no locked mode EX/7-2Ra