MHD in the Spherical Tokamak

1. Office of Science Supported by 21st IAEA Fusion Energy Conference, Chengdu, China, 2006 MHD in theSpherical Tokamak EX/7-2Ra 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 EX/7-2Rb This work was jointly funded by the UK Engineering & Physical Sciences Research Council and Euratom

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

4. Locked mode scaling in MAST EX/7-2Ra Error fields contribute to βN limit: n=1 kink B21 is the m = 2, n = 1 field component normal to q = 2 surface: • 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 [Howell et al. to be submitted Nucl. Fusion (2006)] [Buttery et al., Nucl. Fusion (1999)]

5. Non-axisymmetric coil enables key physics studies on NSTX RWM sensors (Br) • 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, nii, important for stability • Plasma rotation control • A tool to slow rotation, wf, by resonant or non-resonant fields • Plasma momentum dissipation physics studied quantitatively Stabilizer plates RWM sensors (Bp) RWM active stabilization coils

6. no-wall bN > bN (n=1) 0.4 0.5 0.6 0.7 0.8 0.9 t(s) RWM actively stabilized at low, ITER-relevant rotation 92 x (1/gRWM ) • First such demonstration in low-A tokamak • Long duration > 90/gRWM • Exceeds DCON bNno-wall for n = 1 and n = 2 • n = 2 RWM amplitude increases, remains stable while n = 1 stabilized • n = 3 magnetic braking to reduce wf • Non-resonant braking to accurately determine critical plasma rotation for RWM stability, Wcrit 6 120047 4 bN 2 0 120712 8 wf < Wcrit 4 wf/2p (kHz) 0 1.5 IA (kA) 1.0 0.5 0.0 DBpun=1 (G) 20 10 0 20 DBpun=2 (G) 10 0 Post-deadline paper at this conference, PD/P6-2 Sabbagh, et al., PRL 97 (2006) 045004.

7. 116939 n = 1 field With RFA 4 With RFA (DCON) applied field only 3 axis 2 t = 0.370s 1 116931 n = 3 field theory 0 0.9 1.1 1.3 1.5 measured axis t = 0.360s dBplasma RFA = dBapplied Observed plasma rotation braking follows NTV theory 4 • 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 wf in future devices (ITER, CTF) 3 TNTV (N m) 2 1 0 TNTV (N m) R (m) Zhu, et al., PRL 96 (2006) 225002.

8. Rotation profile shape important for RWM stability • Benchmark profile for stabilization is wc = wA/4q2 * • 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 wf profiles below wc • Scalar Wcrit/wA at q = 2 , > 2 not a reliable criterion for stability • variation of Wcrit/wA at q = 2 greater than measured Dwf 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. Wcrit not correlated with Electromagnetic Torque Model • Rapid drop in wf when RWM unstable may seem similar to ‘forbidden bands’ theory • model: drag from electromagnetic torque on tearing mode* • Rotation bifurcation at w0/2 predicted • No bifurcation at w0/2 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 Wcrit Database (w0º steady-state plasma rotation) *R. Fitzpatrick, Nucl. Fusion 33 (1993) 1061.

10. Increased Ion Collisionality Leads to Decreased Wcrit • Plasmas with similar vA • Consistent with neoclassical viscous dissipation model • at low g, increased nii leads to lower Wcrit • modification of Fitzpatrick “simple” model • Similar result for neoclassical flow damping model at high collisionality (nii > vtransit) 121071 121083 (K. C. Shaing, Phys. Plasmas 11 (2004) 5525.) (R. Fitzpatrick, et al., Phys. Plasmas 13 (2006) 072512.)

11. Effects of rotation on sawtooth EX/7-2Ra 1.56 MW (counter) MAST #13575 1.61 MW (co) MAST #13369 Counter-NBI Co-NBI • Increasing co-NBI sawtooth period increases • Increasing counter-NBI sawtooth period decreases to a minimum, then increases Ip = [680,740] kA, BT = [0.35,0.45] T ne = [1.6,2.2] 1020 m-3 [Chapman, submitted to Nucl. Fusion (2006)] [Koslowski et al., Fusion Sci. Technol. 47 (2005) 260] [Nave et al., 31st EPS (2004) P1.162]

12. Sawtooth Stability Modelling EX/7-2Ra 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 MAST, rotation at q = 1 is key parameter, not rotational shear Increasing *i In the case, vΦ << vA ands = (r/q)dq/dr ~ 1, (as in MAST) theory predicts that Doppler shifted mode frequency:  Precursor changes direction when, Counter-NBI Co-NBI consistent with modelling [Mikhailovskii & Sharapov PPCF 42 (2000) 57] [Chapman, Phys. Plasmas13 (2006) 065211]

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

14. Alfvén Cascades and qmin(t) evolution MAST #15806 qmin=7/2 8/3 5/2 7/3 3/1 -2.0 170 3 qmin(t) 160 -3.0 2 MAST #16149 150 140 Frequency [kHz] 1 Log (δB) -4.0 120 140 2 100 Toroidal mode number, n 3 Frequency [kHz] 130 -5.0 80 4 120 5 60 0.115 0.120 0.130 0.135 0.125 0.08 0.09 0.10 0.11 0.12 0.13 0.14 Time [s] Time [s] • 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 qmin • Determine qmin(t) Single Alfvén cascade eigenmode Transistion to TAE and frequency sweeping EX/7-2Ra

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 Wcrit on nii 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 nii in NTV theory indicates ITER plasmas will be subject to higher viscosity and greater wf reduction • Strong dB2dependence of quantitatively verified NTV theory shows that error fields and RFA need be minimized to maximize wf • 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 qmin See posters EX/7-2Ra/b for more details

16. The End

17. RFA magnitude (n = 1) Single mode model fit Counter plasma flow Direction of plasma flow Applied frequency (Hz) dBplasma RFA = dBapplied Non-axisymmetric fields amplified by stable RWM at high bN • Toroidally rotating n = 1 fields used to examine resonant field amplification (RFA) when bN > bNno-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 (H. Reimerdes, et al. PRL 93 (2004) 135002.)

18. 6 4 2 0 RWM stabilized upon growth of other MHD modes Chordal USXR Data • n = 1 internal mode grows following unstable growth phase of n = 1 RWM Edge bN DCON dW RWM bN > bNno-wall 15 DBp (G) 10 5 0 Core 10 0.37 0.41 0.39 0.43 t (s) DB (G) 0 -10 0.36 0.38 0.40 0.42 t (s) 0.42 0.43 0.41 t (s)

19. Sawtooth studies in MAST EX/7-2Ra vNBI v*i (counter) v*i (co) • 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

20. Reversed shear and Alfvén Cascades Alfvén Cascades observed on MAST showing duration of reversed shear Also seen on interferometry signals 800 Plasma Current 600 ACs indicate shear reversal kA 400 Onset of AC with qmin~3 Onset of AC with qmin~2 #16095 200 #16149 0 NBI Power 1.5 1.0 MW 0.5 0.0 0.00 0.05 0.10 0.15 0.20 0.25 Time (s) EX/7-2Ra

21. Alfvén Cascades in MAST EX/7-2Ra MAST #15806 -2.0 170 160 -3.0 150 Frequency [kHz] Log (δB) -4.0 140 130 -5.0 120 0.115 0.120 0.130 0.135 0.125 Time [s] • 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 qmin • Enables determination of qmin(t) Single Alfvén cascade eigenmode Transistion to TAE and frequency sweeping

22. Alfvén cascades and qmin evolution qmin=7/2 8/3 5/2 7/3 3/1 3 qmin(t) 2 MAST #16149 140 1 120 2 Frequency [kHz] 100 Toroidal mode number, n 3 80 4 60 5 0.08 0.09 0.10 0.11 0.12 0.13 0.14 Time [s] EX/7-2Ra

23. New Sensors Reveal High Frequency MHD MAST #16106 0.0 High frequency modes 1000 -1.0 800 -2.0 Frequency [kHz] Log (δB) 600 -3.0 NAE modes -4.0 400 EAE modes -5.0 TAE modes 200 -6.0 0.228 0.230 0.232 0.234 0.236 0.238 0.240 0.242 Time [s] New high frequency sensors (<5 MHz) reveal modes similar to observations on NSTX New TAE antenna currently being installed leaves MAST well-placed to probe fast particle stability at tight aspect ratio [Appel et al., 31st EPS (2004) P4.195][Gorelenkov et al, Nucl. Fusion42 (2002) 977]

24.  ne0.93 Applied 2/1 B at lock (Gauss)  ne1.0 ne[1019m-3] NSTX supports ITPA / ITER locked mode threshold and 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 (1) Locked mode threshold (2) Disruption studies ITER Operating Range (GA report A25385) 15 MA 9 MA J. Menard, PPPL • NSTX data contributes dependence of current quench time, tCQ on A • Important test of theory for ITER, CTF • tCQ independent of plasma current density when A dependence of plasma inductance is included

25. Access to new regime EX/7-2Ra 30% lower density 0.0 0.3 0.4 0.1 0.2 Time [s] Error field correction enables operation at previously inaccessible low densities to study current drive physics Still no locked mode Locked mode grows up [Howell et al. to be submitted NF 2006]