Wall Stabilized Operation in High Beta NSTX Plasmas

1. Supported by Wall Stabilized Operation in High Beta NSTX Plasmas Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics NYU ORNL PPPL PSI SNL UC Davis UC Irvine UCLA UCSD U Maryland U New Mexico U Rochester U Washington U Wisconsin Culham Sci Ctr Hiroshima U HIST Kyushu Tokai U Niigata U Tsukuba U U Tokyo JAERI Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec S. A. Sabbagh1, A.C. Sontag1, R. E. Bell2, J. Bialek1, D.A. Gates2,A. H. Glasser3, B.P. LeBlanc2, J.E. Menard2, W. Zhu1, M.G. Bell2, T.M. Biewer2, A. Bondeson4, C.E. Bush5, J.D. Callen6, M.S. Chu7, C. Hegna6, S. M. Kaye2, L. L. Lao7, Y. Liu4, R. Maingi5, D. Mueller2, K.C. Shaing6, D. Stutman8, K. Tritz8, C. Zhang9 1Department of Applied Physics, Columbia University, New York, NY, USA 2Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA 3Los Alamos National Laboratory, Los Alamos, NM, USA 4Institute for Electromagnetic Field Theory, Chalmers U., Goteborg, Sweden 5Oak Ridge National Laboratory, Oak Ridge, TN, USA 6University of Wisconsin, Madison, WI, USA 7General Atomics, San Diego, CA, USA 8Johns Hopkins University, Baltimore, MD, USA 9Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China 20th IAEA Fusion Energy Conference 1-6 November 2004 Vilamoura, Portugal

2. Wall stabilization physics understanding is key to sustained plasma operation at maximum b • High bt = 39%, bN = 6.8 reached • Operation with bN/bNno-wall > 1.3 at highest bN for pulse >> twall bN/li = 12 10 8 6 112402 wall stabilized 4 wall stabilized bN bN core plasma rotation (x10 kHz) 0 n=1 (wall) dW 10 n=1 (no-wall) 20 DCON EFIT 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 li t(s) • Global MHD modes can lead to rotation damping, b collapse • Physics of sustained stabilization is applicable to ITER

3. 1.0 0.5 0.0 -0.5 -1.0 0.0 0.5 1.0 1.5 Wf Theory provides framework for wall stabilization study Fitzpatrick-Aydemir (F-A) stability curves • This talk: Resistive Wall Mode physics • RWM toroidal mode spectrum • Critical rotation frequency, Wcrit • Toroidal rotation damping • Resonant field amplification (RFA) • Theory • Ideal MHD stability – DCON (Glasser) • Drift kinetic theory (Bondeson – Chu) • RWM dynamics (Fitzpatrick – Aydemir) Phys. Plasmas 9 (2002) 3459 ideal wall limit wall stabilized n*= mode strength s no-wall limit stable stable plasma rotation plasma inertia dissipation mode strength wall response wall/edge coupling S* ~ 1/twall

4. Unstable RWM dynamics follow theory • Unstable n=1-3 RWM observed • ideal no-wall unstable at high bN • n > 1 theoretically less stable at low A • F-A theory / experiment show • mode rotation can occur during growth • growth rate, rotation frequency ~ 1/twall • << edge Wf > 1 kHz • RWM phase velocity follows plasma flow • n=1 phase velocity not constant due to error field • Low frequency tearing modes absent growth w/o mode rotation mode rotation during growth bN n=1 no-wall unstable n=1-3 no-wall unstable n=2,3 |dBp|(n=1) (G) mode growth |dBp|(n=2) (G) |dBp|(n=3) (G) (deg) fBp(n=1) mode rotation (f<40 kHz, odd-n) Bz(G)

5. Camera shows scale/asymmetry of theoretical RWM Theoretical DBy (x10) with n=1-3 (DCON) RWM with DBp = 92 G • Visible light emission is toroidally asymmetric during RWM • DCON theory computation displays mode • uses experimental equilibrium reconstruction • includes n = 1 – 3 mode spectrum • uses relative amplitude / phase of n spectrum measured by RWM sensors 114147 t = 0.268s 114147 114147 (exterior view) (interior view) Before RWM activity 114147 t = 0.250s

6. 2 1 0 -1 3 5 4 -2 0.0 0.5 1.0 1.5 2.0 Soft X-ray emission shows toroidal asymmetry during RWM USXR separated by 90 degrees Bay G array (0 deg) Bay J array (90 deg) RWM growth 8 Chord 3 DCON n = 1 mode decomposition 6 yn = 0.4 Intensity (arb) 4 yn:0.13 0.24 0.4 2 2 m=2 0 Z(m) Chord 4 m=3 6 4 5 (arb) 6 1 Intensity (arb) 4 m=1 2 yn = 0.24 0 0 0.2 0.4 0.6 0.8 1.0 0.0 Chord 5 6 yn 4 Intensity (arb) • Experiment / theory show RWM not edge localized • Supported by measured DTe 2 yn = 0.13 0 R(m) 0.27 0.29 0.28 114024, t=0.273s bN = 5 t(s)

7. stabilized 1/(4q2) not stabilized 0.5 0.4 0.3 0.2 0.1 0.0 4 5 1 2 3 Experimental Wcrit follows Bondeson-Chu theory Phys. Plasmas 8 (1996) 3013 • Experimental Wcrit • stabilized profiles: b >bNno-wall (DCON) • profiles not stabilized cannot maintain b > bNno-wall • regionsseparated by wf/wA =1/(4q2) • Drift Kinetic Theory • Trapped particle effects significantly weaken stabilizing ion Landau damping • Toroidal inertia enhancement more important • Alfven wave dissipation yields Wcrit = wA/(4q2) wf/wA(q,t) profiles wf/wA q

8. 0.06 0.05 0.04 0.03 0.02 0.01 0.00 8 10 2 4 6 stabilized 1/(4q2) not stabilized Wcrit follows F-A theory with neoclassical viscosity • Experimental Wcrit • stabilized points: b >bNno-wall (DCON) • points not stabilized cannot maintain b > bNno-wall • regionsseparated by wf/wA =1/(4q2) • F-A Theory • Standard F-A theory has Wcrit ~ 1/q • neoclassical viscosity includes toroidal inertia enhancement (K. Shaing, PoP 2004) • yields Wcrit ~ 1/q2 wf/wA in F-A inertial layer (edge) wf/wA q95

9. Evolution detail differs for other modes no momentum transfer across rational surfaces no rigid rotor plasma core (internal 1/1 mode) 0.8 1.0 1.2 1.4 1.6 R(m) 1.0 1.2 1.4 1.6 R(m) see EX/P2-26 Menard Plasma rotation damping described by NTV theory • Neoclassical toroidal viscosity (NTV) ~ dB2*Ti0.5 • Rapid, global damping observed during RWM • Edge rotation ~ 2kHz maintained • Low frequency tearing modes absent initial rotation evolution 25 t(s) 0.266 0.276 20 Wf/2p (kHz) 15 40 full rotation evolution 10 t(s) 0.226 0.236 0.256 30 5 axis edge Wf/2p (kHz) 0 20 theory measured 0.4 -rR2(dWf/dt) TNTV 10 0.3 114452 0.2 Td (N m-2) 0.1 0.0 -0.1 113924 t = 0.276s -0.2

10. Resonant Field Amplification increases at high bN • Plasma response to applied field from initial RWM stabilization coil pair • AC and pulsed n = 1 field • RFA increase consistent with DIII-D • Stable RWM damping rate of 300s-1 measured bNno-wall (n = 1) plasma DBp / applied Bp bN Sensors Initial RWM stabilization coils Completed coils will be used to suppress RFA, stabilize RWM, sustain high b

11. Wall stabilization research at low aspect ratio illuminates key physics for general high b operation • Plasma bt = 39%, bN = 6.8, bN/li = 11 reached; bN/bNno-wall > 1.3 • Unstable n = 1-3 RWMs measured (n > 1 prominent at low A) • Critical rotation frequency ~ wA/q2 strongly influenced by toroidal inertia enhancement (prominent at low A) • Rapid, global plasma rotation damping mechanism associated with neoclassical toroidal viscosity • Resonant field amplification of stable RWM increases with increasing bN (similar to higher A) • Evidence for AC error field resonance observed (see poster) • Effect of rotation on equilibrium reconstruction evaluated (see poster) Completed RWM active stabilization coil to be used for research in 2005