MHD in the Spherical Tokamak

21 st IAEA Fusion Energy Conference, Chengdu, China, 2006

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, EX/7-2Ra 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 Office of Supported by Science

This work was jointly funded by the UK Engineering & Physical Sciences Research Council and Euratom 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 Error field studies in MAST EX/7-2Ra

Error fields: slow rotation, induce instabilities, terminate discharge Mega Ampere Spherical Tokamak R = 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) 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)] Non-axisymmetric coil enables key physics studies on NSTX RWM sensors (B r) RWM active stabilization • Stabilizer Midplane control coil similar to plates ITER port plug designs n > 1 studied during n = 1 stabilization • RWM passive stabilization Plasma rotation profile, ion ν collisionality, ii , important for stability • Plasma rotation control

A tool to slow rotation, ωφ, by resonant or non-resonant fields

Plasma momentum dissipation RWM sensors (B p) physics studied quantitatively RWM active stabilization coils

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb RWM actively stabilized at low, ITER-relevant rotation

γ 92 x (1/ RWM )

6 120047 • First such demonstration 4 β in low-A tokamak N β > βno-wall 2 N N (n=1) Long duration > 90/ γ 0 120712 RWM 8 ω Ω Exceeds DCON β no-wall φ < crit N 4 for n = 1 and n = 2 ω /2 π (kHz) 0 φ n = 2 RWM amplitude 1.5 I (kA) increases, remains stable 1.0 A while n = 1 stabilized 0.5 0.0 ∆ n=1 20 Bpu (G) • n = 3 magnetic braking to 10 reduce ωφ 0 Non-resonant braking to 20 ∆ n=2 Bpu (G) accurately determine 10 critical plasma rotation for RWM stability, Ω 0 crit 0.4 0.5 0.6 0.7 0.8 0.9 t(s) Post-deadline paper at this conference, PD/P6-2 Sabbagh, et al., PRL 97 (2006) 045004.

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Observed plasma rotation braking follows NTV theory 4 • First quantitative agreement n = 3 theory 116931 using full neoclassical toroidal 3 field viscosity theory (NTV) Due to plasma flow through (N (N m) 2 measured non-axisymmetric field Trapped particle effects, 3-D NTV

T field spectrum important 1 axis t = 0.360s • Resonant field amplification 0 (RFA) increases damping at 4 high beta n = 1 With RFA 116939 Computation based on applied 3 field field, or DCON computed mode spectrum With RFA applied δ (N (N m) 2 (DCON) field Bplasma RFA = δ only Bapplied NTV 1 axis T • Non-negligible physics for t = 0.370s ω 0 simulations of φ in future 0.9 1.1 1.3 1.5 devices (ITER, CTF) R (m) Zhu, et al., PRL 96 (2006) 225002.

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Rotation profile shape important for RWM stability

0.25 • Benchmark profile for stabilization is no applied field ω = ω /4 q2 * 0.20 n = 3 c A n = 3 max. braking A

predicted by Bondeson-Chu semi- ω 0.15 t crit - 10 ms / 2 kinetic theory** 1/(4q ) crit 0.10

theory consistent with radially Ω distributed dissipation 0.05 • Rotation outside q = 2.5 not required 0.00 for stability 1.5 2.0 2.5 3.0 3.5 4.0 Applied n = 3 fields used to alter stable q ω profiles below ω φ c 0.4 Ω ω no applied field • Scalar crit / A at q = 2 , > 2 not a n = 3 DC reliable criterion for stability 0.3 n = 1 DC A n = 1 traveling Ω ω ω

variation of / at q = 2 greater / crit A 0.2 n = 1 & n = 3 than measured ∆ωφ in one time step 2 crit 1/4q consistent with distributed dissipation Ω 0.1

*A.C. Sontag, et al., Phys. Plasmas 12 (2005) 056112. 0.0 **A. Bondeson, M.S. Chu, Phys. Plasmas 3 (1996) 3013. 1.0 2.0 3.0 4.0 q

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Ω crit not correlated with Electromagnetic Torque Model

• Rapid drop in ωφ when Ω RWM unstable may seem NSTX crit Database similar to ‘forbidden bands’ 1.0 theory n = 1 model: drag from 0.8 n = 3

electromagnetic torque on 0

ω 0.6

tearing mode* /

ω crit Rotation bifurcation at 0/2 0.4 predicted Ω ω 0.2 • No bifurcation at 0/2 observed 0.0 1.2 1.6 2.0 2.4 no correlation at q = 2 or further into core at q = 1.5 q Same result for n = 1 and 3 ω ≡ applied field configuration ( 0 steady-state plasma rotation)

*R. Fitzpatrick, Nucl. Fusion 33 (1993) 1061.

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Ω Increased Ion Collisionality Leads to Decreased crit

• Plasmas with similar vA 121071 121083 • Consistent with neoclassical Ω viscous dissipation model crit (km/s) (a) at low γ, increased ν leads to lower Ω ii crit modification of Fitzpatrick “simple” v model A (km/s) (K. C. Shaing, Phys. Plasmas 11 (2004) 5525.) (b) • Similar result for neoclassical flow damping model at high ν ν ii (kHz) collisionality ( ii > vtransit ) (c) (R. Fitzpatrick, et al., Phys. Plasmas 13 (2006) 072512.)

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Effects of rotation on sawtooth EX/7-2Ra

1.61 MW (co)

MAST #13369

1.56 MW (counter)

MAST #13575

I = [680,740] kA, B = [0.35,0.45] T Counter-NBI Co-NBI p T × 20 -3 ne = [1.6,2.2] 10 m • Increasing co -NBI ⇒ sawtooth period increases • Increasing counter -NBI ⇒ sawtooth period decreases to a minimum , then increases [Chapman, submitted to Nucl. Fusion (2006)] [Koslowski et al., Fusion Sci. Technol . 47 (2005) 260] [Nave et al. , 31 st EPS (2004) P1.162] Sawtooth Stability Modelling EX/7-2Ra

The resistive, compressional linear MHD stability code MISHKA that ω includes ion diamagnetic effects ( *i) has been extended to include toroidal and poloidal flow profiles (MISHKA-F)

Increasing In MAST, rotation at q = 1 is key ω parameter, not rotational shear *i In the case, v Φ << vA and s = (r/q)dq/dr ~ 1, (as in MAST) theory predicts that Doppler shifted mode frequency: ωωω ˆ*i ωωω ˆ*i ωωω ˆ*i ⇒ Precursor changes direction when,

Counter-NBI Co-NBI consistent with modelling [Mikhailovskii & Sharapov PPCF 42 (2000) 57] [Chapman, Phys. Plasmas 13 (2006) 065211] periodisminimised whenwithagrees sawtooth stabilityisminimised q whichToroidalvelocity at to studyto stabilisationion fast sawteeth of and NTM Ongoingworkextension includeto this to ion fast q 1 = 1radius = marginalfor t As As sawtooth period, r(q=1)

Marginally stable Marginally stable

q=1 radius Marginal r τ st q q , increases, radial location of = = 1 radius expected to correlate with q =1 position with flow Counter-v Experimentaldata MISHKA-F modellingMISHKA-F Φ profileused kineticeffects triggering Co-v

JET data q = = 1 increases Φ profileused τ st EX/7-2Ra Alfvén Cascades and qmin (t) evolution

MAST #15806 • Global shear Alfvén qmin =7/2 3/1 8/35/2 7/3 -2.0 waves driven by fast 1703 Single Alfvén beam ions cascade qmin (t) 160 eigenmode – Lowered beam 2 -3.0 MAST #16149 n B)

140 δ power to avoid 150 1 nonlinear effects 120 -4.0 140 2 ( Log

• ACs occur when [kHz] Frequency 100 130 Transistion to TAE 3 magnetic shear is -5.0 80 and frequency 4 reversed 120 sweeping Frequency [kHz] Frequency 60 5 • Characteristic 0.1150.08 0.09 0.120 0.100.125 0.110.1300.12 0.13 0.135 0.14 number, mode Toroidal frequency sweep TimeTime [s] [s]

determined by qmin

– Determine qmin (t)

EX/7-2Ra Summary & Conclusions • Error field studies highlight need for error field correction coils on Spherical Tokamak Power Plant or Component Test Facility Ω ν • 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 ν dissipation on ii in NTV theory indicates ITER plasmas will be subject to higher viscosity and greater ωφ reduction • Strong δB2 dependence of quantitatively verified NTV theory shows that error fields and RFA need be minimized to maximize ωφ • 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 The End Non-axisymmetric fields amplified by stable RWM at β high N δ Bplasma RFA = δ • Toroidally rotating n = 1 fields Bapplied used to examine resonant field amplification (RFA) when β > 1.8 β no-wall N N 1.6 propagation frequency and direction scanned 1.4 RFA increases when applied 1.2 field rotates with plasma flow 1.0 consistent with DIII-D results and theoretical expectations 0.8 Single mode (H. Reimerdes, et al. PRL 93 (2004) 135002.) model fit 0.6

• Single mode model of RWM fit 0.4 to measured RFA data RFA magnitude (n = 1) = (n magnitude RFA 0.2 Counter Direction of peak in fit at 45 Hz in direction plasma flow plasma flow of plasma flow 0.0 -120 -90 -60 -30 0 30 60 90 120 Applied frequency (Hz)

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb RWM stabilized upon growth of other MHD modes

Chordal USXR Data 2 EDGE 6 1 W Edge (a) δ N 4 0 β RWMRWM growth 2 βδw < 0β is unstableno-wall -1 N > N (a) DCON 0 -2 15 n = 1, RWM sensors (G) Inset Area

p 10 B 5 ∆ (b) 0 Core 10 CORE odd-n, f < 40kHz 0.370.37 0.38 0.390.39 0.40 0.410.41 0.42 0.430.43 0 timet (s) (s) B (G) B ∆ -10 121100 (c) (b) 0.360.36 0.380.38 0.400.40 0.420.42 t (s)

• n = 1 internal mode grows following unstable growth phase of n = 1 RWM 0.405 0.410.410 0.415 0.420.420 0.425 0.430.430 t (s)

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Sawtooth studies in MAST EX/7-2Ra

vNBI • High power NBI into small v (counter) (low moment of inertia ) *i 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 v*i (co) • Decoupling rotation from present-day results

Combination of experimental studies and numerical modelling Reversed shear and Alfvén Cascades

800 Plasma Current 600 kA ACs indicate shear reversal 400 Onset of Onset of 200 AC with AC with #16095 qmin ~3 q ~2 #16149 0 min

1.5 NBI Power

1.0 MW 0.5

0.0 0.00 0.05 0.10 0.15 0.20 0.25 Time (s) • Alfvén Cascades observed on MAST showing duration of reversed shear • Also seen on interferometry signals EX/7-2Ra Alfvén Cascades in MAST EX/7-2Ra

• Global shear Alfvén MAST #15806 waves driven by super- -2.0 170 Single Alfvén Alfvénic beam ions cascade – Lowered beam power 160 eigenmode -3.0

to avoid nonlinear B) 150 δ effects from strong -4.0 drive 140 ( Log Frequency [kHz] Frequency • ACs occur when 130 Transistion to TAE magnetic shear is and frequency -5.0 reversed 120 sweeping • Characteristic frequency 0.115 0.120 0.125 0.130 0.135 sweep determined by Time [s]

qmin – Enables determination

of qmin (t) Alfvén cascades and qmin evolution

qmin =7/2 3/1 8/35/2 7/3

qmin (t) 2 MAST #16149

140 n 1 120 2 100 3 Frequency [kHz] Frequency 80 4

60 5 number, mode Toroidal 0.08 0.09 0.10 0.110.12 0.13 0.14 Time [s]

EX/7-2Ra New Sensors Reveal High Frequency MHD

New high frequency sensors (<5 MHz) reveal modes similar to observations on NSTX MAST #16106

0.0 1000 High frequency modes -1.0 800 -2.0 B) δ

600 -3.0 Log ( NAE modes Frequency [kHz] 400 -4.0 EAE modes -5.0 200 TAE modes -6.0 0.228 0.230 0.2320.234 0.236 0.238 0.240 0.242 Time [s] New TAE antenna currently being installed leaves MAST well-placed to probe fast particle stability at tight aspect ratio [Appel et al., 31 st EPS (2004) P4.195] [Gorelenkov et al , Nucl. Fusion 42 (2002) 977] NSTX supports ITPA / ITER locked mode threshold and disruption studies (1) Locked mode threshold (2) Disruption studies

at lock (Gauss) lock at ∝∝∝ n 0.93

⊥ ⊥ e ⊥ ⊥

∝∝∝ 1.0 ne ITER Operating Range (GA report 9 MA 15 MA

Applied 2/1 B 2/1 Applied A25385)

19 -3 ne [10 m ] J. Menard, PPPL

• NSTX contributing low-A, low B data • NSTX data contributes dependence of current quench time, τ on A density scaling nearly linear, similar CQ to higher-A Important test of theory for ITER, CTF τ CQ independent of plasma current Will contribute B, q scaling data for density when A dependence of plasma ITER size scaling inductance is included

NSTX Pinches (Sontag): IAEA FEC 2006 – EX/7-2Rb Access to new regime EX/7-2Ra

Error field correction enables operation at previously inaccessible low densities to study current drive physics

30% lower density

Still no locked mode

0.0 0.1 0.2 0.3 0.4 Time [s] Locked mode grows up

[Howell et al . to be submitted NF 2006]