1. NSTX WZ – XP524 - NSTX Results Review ‘05 Supported by Office of Science 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 XP524: Physics and Control of Toroidal Rotation Damping in NSTX W. Zhu 1, S.A. Sabbagh 1, A.C. Sontag 1, J. Bialek 1, R.E. Bell 2, J.E. Menard 2, D.A. Gates 2, C.C. Hegna 3, B.P. LeBlanc 2, K.C. Shaing 3, D. Battaglia 3, and the NSTX Research Team 1 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ 3 University of Wisconsin, Madison, WI v1.0 NSTX Results Review December 12th, 2005 Princeton Plasma Physics Laboratory

2. NSTX WZ – XP524 - NSTX Results Review ‘05  Produce low rotation (ITER relevant) target plasmas  Good control by current timing / magnitude  Study physics of plasma rotation damping due to applied field / RWM  n=1 and n=3 fields used 6 ex-vessel non-axisymmetric field coils 64206420 32103210 NN I RWM (kA) 0.4 0.3 0.2 0.1 0.0 0.4 0.3 0.2 0.1 0.0 V/V A Core region Edge region 116924 116930 116931 0.0 0.2 0.4 0.6 0.8 Time (s) n=3 DC field pulse R=1.08m R=1.30m Non-axisymmetric fields used to study plasma rotation damping

3. NSTX WZ – XP524 - NSTX Results Review ‘05 Attention placed on studying non-resonant rotation damping physics  Non-resonant  Global profile control by pulsing the applied field  Resonant  Local JxB torque can explain damping by tearing modes  Outward momentum transfer across rational surface  Leads to rigid rotor core 0.9 1.0 1.1 1.2 1.3 1.4 1.5 R (m) 40 30 20 10 0 40 30 20 10 0 F t (kHz) Spin-down Spin-up ! 116937 Time (s) 0.345s 0.355s 0.365s 0.375s 0.385s Time (s) 0.405s 0.415s 0.425s 0.435s 0.9 1.0 1.1 1.2 1.3 1.4 1.5 R (m) 40 30 20 10 0 F t (kHz) 10 0 -10 -20 -30  F t (kHz) 116190 Time (s) 0.345s 0.355s 0.365s Time (s) 0.345-0.355s 0.355-0.365s n = 1 tearing mode resonant dampingnon-resonant damping q = 2

4. NSTX WZ – XP524 - NSTX Results Review ‘05 Neoclassical toroidal viscosity (NTV) theory tested as non-resonant damping mechanism Torque balance: (Set = 0 here - tearing modes avoided.) Damping caused by kinked field K.C. Shaing, Phys. Fluids 29 (1986) 521.; E. Lazzaro Phys. Plasmas 9 (2002) 3906. measured computed T i 1/2 profiles collisionality factor

5. NSTX WZ – XP524 - NSTX Results Review ‘05 NTV theory applied to different periods in discharge  Plasma  N at or below no-wall limit Resonant Field Amplification (RFA) 64206420 16 12 8 4 0 NN  B p (G) 32103210 I RWM (kA) Unstable RWM NN  B p (G) I RWM (kA) 2.5 2.0 1.5 1.0 0.5 0.0 Applied field  Plasma  N above no-wall limit  Applied field is amplified by stable RWM Applied fieldRFA12 0.30 0.35 0.40 0.45 0.50 0.55 Time (s) n = 3 applied fieldn = 1 applied field 543210543210 50 40 30 20 10 0 0.350.400.450.30 Time (s)

6. NSTX WZ – XP524 - NSTX Results Review ‘05 Applied field alone yields moderate, global rotation damping  n = 3 DC field (800A)  Damping reduced at large R due to reduction in T i  n=1-15 field components included  Resonant denominator in NTV theory might be overemphasized  Function of collisionality Time 0.375s 0.395s Time 0.375-0.395s 116935 1.0 1.1 1.2 1.3 1.4 1.5 Radius (m) 40 30 20 10 0 0.4 0.3 0.2 0.1 0.0 F t (kHz) T (N m -2 ) Vacuum Field n 2 b r 2 (VALEN) n=3 n=9 n=15 measured T NTV K = 8

7. NSTX WZ – XP524 - NSTX Results Review ‘05 RFA enhances, broadens rotation damping  n = 1 DC field (800A)  n=5 torque larger than n=1 torque ( n 2 b 2 scaling)  n=1-15 components included  Broadening damping profile Time 0.355s 0.365s 0.375s 1.0 1.1 1.2 1.3 1.4 1.5 Radius (m) 40 30 20 10 0 0.4 0.3 0.2 0.1 0.0 F t (kHz) T (N m -2 ) Time 0.355-0.365s 0.365-0.375s 116939 n=1 n=5 n=11 n=7 Vacuum Field n 2 b r 2 (VALEN) measured T NTV K = 8

8. NSTX WZ – XP524 - NSTX Results Review ‘05 RWM eigenfuction can explain broader damping  DCON n = 1 (m = -12 to 26) RWM calculated eigenfunction  No-wall boundary condition  Need to evaluate with-wall boundary condition; inclusion of measured n = 2 component Time 0.365-0.375s 0.375-0.385s Time 0.355s 0.365s 0.375s 0.385s 0.395s 0.405s 40 30 20 10 0 F t (kHz) RWM mode decomposition 0.0 0.2 0.4 0.6 0.8 1.0 |  n | B n (arb) 1.0 0.5 0.0 -0.5 m = 1 m = 2 3456 116939 116939 t = 0.39s T (N m -2 ) measured T NTV

9. NSTX WZ – XP524 - NSTX Results Review ‘05 Control of plasma rotation profile allows study of rotation damping physics  Applied n=1,3 DC and AC fields used to alter plasma rotation profile in a controlled fashion  Plasma rotation recovers if applied field reduced before RWM critical rotation profile reached  Rotation damping profile from applied n = 1,3 fields and RFA follows neoclassical toroidal viscosity (NTV) theory  NTV theory tested, including n scaling, reduced damping at low T i, global/non-resonant mechanism  Continued work to resolve magnitude (multiplicative factor, K)  At APS ‘05, K ~ 8 - 10; trapped particle effects may reduce to 2 – 3 (K.C. Shaing)  Lazzaro, et al. estimate trapped particles increase NTV by (646/q 2 )

10. NSTX WZ – XP524 - NSTX Results Review ‘05 Full calculation of NTV theory giving quantitative agreement with experiment Since APS ’05  Computation in Hamada coordinates Cylindrical approximations eliminated  Fourier decomposition of mod(B)  Full NTV plateau regime computation Multiplicative factor K ~ 3.4 Need to re-run analysis for shots taken in XP 524  Added full trapped particle computation (Shaing, PoP 2003) to NTV Computed and compared to XP for the first time Multiplicative factor K ~ 0.5 Hamada coordinate grid 0.0 0.5 1.0 1.5 -0.5 -1.5 Z(m) R(m) 0.60.21.01.4 116939 t = 0.39s