Magnetic Fields and Resistive MHD Stability Analysis in KSTAR * Y.S. - PowerPoint PPT Presentation

Supported by Plasma Rotation Alteration by Non-axisymmetric Magnetic Fields and Resistive MHD Stability Analysis in KSTAR * Y.S. Park 1 , S.A. Sabbagh 1 , W.H. Ko 2 , Y.M. Jeon 2 , Y.S. Bae 2 , J.G. Bak 2 , J.W. Berkery 1 , J.M. Bialek 1 , M.J. Choi 3 , S.H. Hahn 2 , S.C. Jardin 4 , J.H. Kim 2 , J.Y. Kim 2 , J. Ko 2 , J.G. Kwak 2 , S.G. Lee 2 , Y.K. Oh 2 , H.K. Park 5 , J.C. Seol 2 , K.C. Shaing 6 , H.L. Yang 2 , S.W. Yoon 2 , K.-I. You 2 , G.S. Yun 3 , and the KSTAR Team 1 Department of Applied Physics, Columbia University, New York, NY, USA 2 National Fusion Research Institute, Daejeon, Korea 3 POSTECH, Pohang, Korea 4 Princeton Plasma Physics Laboratory, Princeton, NJ, USA 5 UNIST, Ulsan, Korea 6 National Cheng Kung University, Tainan, Taiwan presented at the KSTAR Conference 2014 February 24-26, 2014 National Fusion In collaboration with Research Institute *Work supported by the U.S. Department of Energy under contract DE-FG02-99ER54524. V3.0 1

Plasmas exceeding the ideal MHD no-wall stability limit mark initial KSTAR advanced tokamak operation  Motivation  Understanding and maintenance of MHD stability at high b N , over long pulse duration are key KSTAR, ITER goals  Altering plasma rotation to study MHD stability, and to operate in most ITER relevant low rotation regime are key  Outline  High b N results exceeding the n = 1 ideal no-wall limit  Open loop control of plasma rotation using 3D fields  Tearing mode stability analysis using different numerical methods (asymptotic matching and full resistive MHD)  Advances in global mode stabilization power requirement calculations 2

Plasmas have reached and exceeded the predicted “closest approach” to the n = 1 ideal no-wall stability limit I p scan performed to  determine “optimal” b N vs. I p b N /l i = 4  B T in range 1.3 - 1.5 T  b N up to 2.9 b N /l i = 3.6 b N /l i > 4 (80% increase  n = 1 with-wall limit from 2011) Recent n = 1 no-wall limit operation  A high value for advanced (2012) tokamaks Mode stability   Target plasma is at Previous max. b N * published computed ideal First n = 1 no-wall stability limit ** (2011) H-mode (DCON) (2010)  Plasma is subject to RWM instability, depending on plasma rotation profile  Rotating n = 1, 2 mode Normalized beta vs. internal inductance from EFIT reconstruction activity observed in core *Y.S. Park, et al., Nucl. Fusion 53 (2013) 083029 during H-mode ** O. Katsuro-Hopkins, et al., Nucl. Fusion 50 (2010) 025019 3

n = 2 non-axisymmetric field used to alter plasma rotation profile non-resonantly in using in-vessel control coil Test plasma characteristics vs. toroidal rotation by slowing plasma with  non resonant n = 2 NTV using IVCC I p , I IVCC , P NBI (a.u.) I p = 0.65 MA (B T = 1.5 T) 1 2 3 4 Step-up n = 2 field Step # Step-down n = 2 field P NBI = 2.8 MW Time (s) NB dropouts for CES measurement KSTAR in-vessel control coil (IVCC) Simplified expression of NTV force (“1/  regime”) Top IVCC     1 1 p 3          1 i i 2 e B R ( ) I     t NC 2 3 / 2 t B R  Middle ( 1 / ) t i – – + + IVCC Steady-state velocity K.C. Shaing, et al., 5/2 T i PPCF 51 (2009) 035004 Inverse aspect ratio Bottom IVCC Pre-requisite for study of NTV physics in  KSTAR – comparison to NSTX (low A.R.) Applied n = 2 even parity configuration 4

Clear reduction in CES measured toroidal plasma rotation profile with applied n = 2 field With IVCC n = 2 field No IVCC n > 0 field KSTAR 8062 CES KSTAR 8061 CES Rotation reduction Rotation profile oscillates due to core mode activity & plasma boundary movement The rotation slows further at later times CES data in courtesy of W.H. Ko (NFRI)  Significant reduction of rotation speed using middle IVCC coil alone  Significant alteration in rotation pedestal at the edge during braking  Slowed rotation profile resembles an L-mode profile (H-mode is maintained)  Edge rotation reduces first by NTV, then the core follows due to momentum diffusion 5

Change in the measured steady-state rotation profile is analyzed by torque balance Torque balance relation in steady-state    ≈ constant at each n = 2 current step  No existing tearing mode d ( I ) KSTAR 8062       T T T T 0 flux-calibrated CES  B NBI D NTV J dt NBI torque Momentum diffusion NTV torque - Equation in flux coordinate ( i = ion)    2  R Not in torque n       2 2 i Step-up n = 2 field balance n m R R m n m      i i i i i (not included) t t t  1        V V     Step #   2 n m R      1 2 3 4      i i     t N N  1          V V           2 2 n m R ( ) T              i i N torque  Since the plasma boundary is not     N N N N stationary, rotation at constant ( V = volume,   = toroidal momentum diffusivity) normalized flux surface is computed by assuming J.D. Callen, et al., Nucl. Fusion 49 (2009) 085021 by using high time resolution EFIT  2      R n V      flux grid at every time point shown i 0 then the equation reduces to          t t t N  1            V V             2 2 2 ( ) n m R n m R T T               i i i i N NBI NTV     t N N N N 6

Reduced formulation of the steady-state torque balance problem         - In steady-state profiles ,  0     t  1          V V            2 2 0 n m R ( ) T T              i i N NBI NTV     N N N N          2             C1 C2 0 T T    0 C3 C4 T T     NBI NTV     NBI NTV   2 N N N N Express T NTV as non-resonant (damping scales with   )    (Resonant field amplification is insignificant as b N < b N P ( K = function of T i ) T K B no-wall )  NTV  constant T NBI C3, C4 are assumed to be constant over time at fixed flux surface, then by taking difference of the equation between steady-state NTV steps,               2 2                  P P C5 C6 K B B               2 2 j 2 j 1     N N N N j 2 j 1 j 2 j 1 ( j = steady-state step #)     2  B     I , , with and from flux-calibrated CES profiles      IVCC 2 N N 7

Change in rotation profile gradient by applied n = 2 Analysis of increasing n = 2 current steps (shot 8062)   At constant normalized flux surface, profiles having similar <n e > and T i between comparing steady-state steps are chosen in accordance with assumptions | D T i | < 90 eV | D n e |< 0.47E19 Flux-calibrated T i at fixed  N = 0.58 Chosen profile points for analysis  Rotation gradient change calculated from measured profiles yErr = 1 s d   /d  N (  N = 0.58) d 2   /d  2 N (  N = 0.58) 3 2 Step #1 4 Rotation profile flattens as braking increases 4 Step # Change in the 2 nd order derivative 1 3 smaller than error (similar profile curvature) 2  Use only “C5” dependence Increasing I n = 2 yErr = 1 s 8

Steady-state profile analysis to examine NTV dependence on  B Resulting NTV correlation with different power in  B P   B 2  B 2  N = 0.58  N = 0.56 Slope  " K/C5" Smaller number of samples Estimate slope between step #1-2 (largest D I n=2 ) in step #3 may cause relatively then propagate it to other steps large deviation Step #1 Step #2 Step #3 Step #4 Step #1 Step #2 Step #3 Step #4  For the different normalized flux surfaces, T NTV scales well with  B 2   2 T NTV B 9