Investigation of MHD Stability in KSTAR High Normalized Beta … · 2017. 1. 25. · 2 EX/P4-2 the mode starts to significantly limit high beta operation through confinement degradation.

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Investigation of MHD Stability in KSTAR High Normalized Beta Plasmas Y.S. Park1, S.A. Sabbagh1, J.W. Berkery1, J. Kim2, S.W. Yoon2, W.H. Ko2, Y.M. Jeon2, S.H. Hahn2, Y. In2, Y.S. Bae2, J.G. Bak2, J.M. Bialek1, S.C. Jardin3, M.J. Choi2, J.H. Kim2, J.Y. Kim4, K.D. Lee2, S.G. Lee2, J.G. Kwak2, G.S. Yun5, Y.K. Oh2, H.K. Park2,6 1 Department of Applied Physics, Columbia University, New York, NY, USA

2 National Fusion Research Institute, Daejeon, Korea 3 Princeton Plasma Physics Laboratory, Princeton, NJ, USA 4 University of Science and Technology, Daejeon, Korea 5 Pohang University of Science and Technology, Pohang, Korea 6 Ulsan National Institute of Science and Technology, Ulsan, Korea E-mail contact of main author: [email protected] Abstract: H-mode plasma operation in KSTAR reached high normalized beta, N, up to 4.3 which significantly surpassed the computed n = 1 ideal no-wall N limit, N

no-wall, by a factor of 1.6 with high ratios of N/li up to 6.3. Pulse lengths at maximum N were initially limited, but extended to longer pulse by utilizing improved equilibrium control. Recent device operation sustained the high N ~ 3.3 for the longest duration to date, 3 s, and was limited by a 2/1 tearing mode which onsets later in the discharge pulse, and consequently reduced N by 35%. At this N > N

no-wall, the low-n global kink/ballooning or RWMs were not detected. Ideal stability calculations shows that the measured total pressure profile at high N would be unstable based on ideal n = 1 modes but are stabilized by plasma rotation and the associated kinetic resonances when these effects are included. The MISK-calculated kinetic resistive wall mode (RWM) stability for experimental KSTAR equilibria and measured internal profiles shows the kinetic RWM to be stable due to the strong stabilization from trapped ion precession resonance, and the result agrees with the experimentally observed RWM stability at high N. The linear stability of the 2/1 tearing mode examined by the M3D-C1 code shows a stable mode growth rate while the equilibrium is experimentally unstable to the 2/1 mode. The result implies that the mode is classically stable, and the pressure driven terms could be dominant in the equilibria expected to have a non-negligible bootstrap current. A strong correlation is found between the 2/1 mode onset and the coinciding sawteeth. This indicates that the 2/1 mode onset can be avoided by altering the stability of the internal 1/1 mode leading to the NTM seeding. Stabilization of the 1/1 internal mode by rotation shear is investigated by linear stability calculation using M3D-C1. In the calculation, rotation shear is shown to be stabilizing to the 1/1 mode. 1. Introduction A major goal of the Korea Superconducting Tokamak Advanced Research, KSTAR [1-3], operation is the achievement of high performance plasma operation in steady-state through stabilization of deleterious MHD instabilities limiting high beta. The recent advances in device hardware including the neutral beam injection (NBI) system with increased heating power up to 5 MW and several diagnostics measuring key internal profiles warrant advanced physics studies of beta-limiting instabilities. Recent H-mode plasma operation in KSTAR reached high normalized beta, N, up to 4.3 that surpassed the n = 1 ideal MHD no-wall beta limit, N

no-wall, computed as close to N of 2.5 [4] when the plasma internal inductance, li is 0.7 for H-mode pressure profiles. The instabilities that usually limit plasma operation at high normalized beta are global kink/ballooning modes and resistive wall modes (RWMs) that can lead to major plasma disruption, and neoclassical tearing modes (NTMs) driven by a lack of local bootstrap current at low collisionality leading to confinement saturation and often mode locking by largely grown magnetic islands. Unstable RWMs have not yet been observed at N substantially above N

no-wall. Tearing instabilities have been routinely observed and have not placed a strong operational limit in KSTAR [5] however, as the plasma confinement improves,

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the mode starts to significantly limit high beta operation through confinement degradation. In this work, to investigate stability of KSTAR high N plasmas, the stability of major ideal and resistive MHD instabilities have been examined by best utilizing experimentally measured internal profiles which are critical for accurate stability calculations. Different physics models have been applied to major stability problems. For RWMs, the ideal n = 1 stability and its modification by kinetic effects is computed by using the MISK code [6]. The result estimates the impact of plasma toroidal rotation on particle kinetic resonances allowing for the observed RWM stabilized operation. A m/n = 2/1 tearing mode which onsets at high N is examined by using the M3D-C1 code [7] solving the linearized resistive MHD equations. The internal mode having m/n = 1/1 leads to seeding of NTMs by sawteeth, and as a potential means to avoid the non-linear 2/1 mode onset, change in the internal mode linear stability by varied toroidal rotation profile is investigated. 2. Achievement of high N plasmas KSTAR plasmas have reached a device record high N in the recent operations. Figure 1 shows the achieved equilibrium operating space displayed by stability-relevant parameters, N and li, from recent discharges made to explore sustained high N > N

no-wall. About 9,000 equilibria from 46 discharges are shown. Equilibrium reconstructions using external magnetic measurements [5, 8] have been used to evaluate the operating parameters presented. A typical

time interval between the equilibria shown is 25 ms. The high N has been achieved in discharges having lowered toroidal magnetic field, BT, in the range 0.9-1.3 T with plasma current of 0.35-0.47 MA. The plasma current was proportionally varied with BT to get a similar edge safety factor of between 4 < q95 < 4.5. The maximum plasma stored energy in these plasmas reached 0.34 MJ with the energy confinement time, E, at the highest N ranging from 50 to 70 ms. In earlier experiments, the highest N greater than 4 was transiently reached and sustained for longer than a few E. The ratio of N/li has reached 6.3 which is a high value for advanced tokamaks. Total pulse lengths of this high N discharges were initially limited to approximately 1.5 s, and it has

been clarified that the high N operation was terminated by radial movement of the plasma caused by equilibrium control that was not fully optimized at plasma conditions relevant to the high N. In KSTAR, a more typical duration for N ~ 2 plasmas is approximately 10 s (several current diffusion times) and the longest H-mode discharge duration to date is approximately 55 s.

In subsequent device operation, high N plasmas were significantly extended to longer pulse by utilizing fast plasma radial control and a discharge scenario made to avoid the earlier problems in the real-time equilibrium control. The evolution of the reconstructed plasma parameters for the shot that sustained the high N > 3 for the longest duration to date, 3 s, are shown in Fig. 2. The plasma current was initially maintained at a higher level of 470 kA and

Figure 1. KSTAR high N operational stabilityspace expressed in (li, N) for dischargesperformed to reach N > N

no-wall. The values at the2/1 mode onset are indicated by red diamonds.

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then was lowered to 430 kA at BT = 1.2 T for better equilibrium control at the earlier phase of the discharge, resulting in somewhat lower q95 around 4 compared to the target q95 of 4.5 chosen for higher plasma stability. The total neutral beam heating power (PNBI) from three beam sources is 4.5 MW with a beam modulation for the charge exchange spectroscopy diagnostic (CES) measuring plasma rotation and ion temperature profiles. The li value at N > 3 ranges from 0.8 to 1.4, indicating that many of the

equilibria operate above Nno-wall (Fig. 1). The time-averaged N and plasma stored energy

during this period are 3.3 and 270 kJ, respectively. The high N phase was limited by the onset of a 2/1 tearing mode around t = 4.3 s in the discharge. The mode amplitude measured by toroidal magnetic probe arrays measuring poloidal field perturbations at the outboard upper-midplane region reached 20 G. The mode onset reduced both N and the stored energy by ~35% but still maintained H-mode confinement. High N was limited by a 2/1 mode onset also in other discharges run with similar plasma conditions (Fig. 1). In these discharges, the mode onset occurred relatively earlier (t < 4 s) with N > 2.5 where li was still at relatively

high values. In these cases, mode onset stopped the plasma from going above the ideal MHD no-wall limit. Different mode onset times were created by varying plasma density by changing gas injection. The toroidal mode spectrum shown in Fig. 3 indicates that there is relatively weak mode activity at the highest confinement, which has been measured with a primary toroidal mode number n of 2. Measured electron temperature from the electron cyclotron emission (ECE) diagnostic suggests that there are strong sawteeth throughout the discharge. The 2/1 tearing mode was destabilized by successive sawtooth bursts with large amplitude which will be discussed in the next section. The presence of the sawteeth and coinciding frequency chirping in the

Figure 4. Rotation profile change due tothe 2/1 tearing mode onset at high N

measured by CES diagnostic.

Figure 3. The toroidal magneticspectrum in the high N discharge shownin Fig. 2.

Figure 2. KSTAR high N discharge evolution showing(a) plasma current and neutral beam heating power, (b)reconstructed N, (c) edge safety factor (q95) and li, (d)plasma stored energy and (e) mode amplitude.

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spectrogram indicates that there is a destabilized m/n = 1/1 internal mode with the safety factor on axis below unity (q0 < 1) in the discharge. In KSTAR H-modes, sawteeth are often observed and at high N values above the computed ideal MHD no-wall limit, a large sawtooth collapse leads to a degradation of energy confinement resulting in periodic reduction in N and stored energy, and eventually triggers a 2/1 mode that mostly limits high N operation.

The change in the rotation profile due to the mode onset, measured by CES is shown in Fig. 4. The saturated 2/1 mode and its interaction with the resistive wall passive conducting structure dragged the plasma rotation and consequently lead to global reduction in the rotation profile without bifurcation, unlike what is observed by more rapid rotation collapse due to the resonant mode locking [9]. The rotation reduction occurred on a relatively long time scale (~400 ms) after the mode onset, and the rotation profile recovers as the saturated mode amplitude decreases afterward. Typical small error bars on the CES diagnostic data ensures an accurate measurement of rotation profile as shown in the figure.

3. Ideal and resistive MHD stability at high N The global kink/ballooning or RWMs which usually limit high beta operation above N

no-wall have not yet been detected. The n = 1 ideal MHD stability of the achieved high N equilibria has been examined by the DCON [10] and M3D-C1 codes using experimental equilibria and measured internal profiles. The equilibria having N ~ 3.0 in the discharge shown in Fig. 2 closely positioned to the computed ideal stability no-wall limit are chosen to calculate stability. Reliable calculation of the ideal stability requires an accurate description of the pressure profile since N

no-wall strongly depends on the pressure peaking factor [11], Fp = p0/<p>, the ratio of central to volume-averaged pressure. Since the exact total pressure profile is not completely measured due to the missing ion density profile, total pressure is obtained by using measured ion and electron profiles, and the effective charge (Zeff) profile shapes representative of H-mode plasmas. Although the equilibrium reconstructions produce a fluid pressure profile that is consistent with the total plasma stored energy, the profile of fast particles in total pressure, which can produce a somewhat more core-peaked total pressure profile, is not considered in the calculation. Figure 5 shows the total thermal pressure profile from the measured partial kinetic profiles, along with pressure profiles from EFIT reconstructions varied to have different pressure peaking factors in the range of 2.65-3.88. The measured total pressure profile shown has Fp ~ 3.4. The ideal stability from DCON

Figure 5. (a) Reconstructed total pressure profiles used in the ideal stability calculations compared tothe measured pressure profile. (b) DCON computed perturbed B-normal for the unstable n = 1eigenfunction. The perturbed amplitude shown has been exaggerated for clarity. (c) The perturbedpoloidal flux of unstable mode from M3D-C1.

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shows the equilibrium to be unstable to n = 1 modes with Fp greater than 3.2 in the EFIT pressure profiles considered, whereas the equilibrium with a broader pressure profile having a lower Fp of 2.65 is computed to be stable. The DCON computed perturbed normal magnetic field for the unstable case with Fp = 3.3, which most resembles the measured pressure peaking, is shown in Fig. 5(b). The ideal mode linear stability is also examined by using the M3D-C1 code solving the linearized single fluid MHD equations. For a plasma with negligible resistivity, the solution from the M3D-C1 shows an unstable mode structure consistent with DCON, as shown by the perturbed poloidal flux in Fig. 5(c). The ideal conducting wall which defines the computational domain boundary in M3D-C1 has been chosen to give similar ideal mode stability criteria with DCON. The result indicates that the achieved high N equilibria can be unstable to the ideal n = 1 mode but remain stabilized by plasma rotation and the associated broad kinetic resonances [6, 12] which will be discussed in the next section.

The classical tearing stability of the achieved high N equilibria is also examined by using the M3D-C1 code. Resistive MHD equations are solved with the input resistivity profile determined by using the measured electron temperature from a Thomson scattering (TS)

diagnostic [13] using the Spitzer formula. Adaptive meshing in the code increases computational resolution around mode rational surfaces. The radial velocity eigenfunction from the linear stability calculation is shown in Fig. 6. In this result, the mode eigenfunction shows a clear tearing parity at q = 2 but the mode growth rates are negative. The negative mode growth rate implies that the mode is classically stable, and the pressure driven neoclassical terms [14] dominate over the current gradient term in the target equilibrium having p = 1.8, expected to have a non-negligible bootstrap current. The observed 2/1 mode onset at high N triggered by the neighboring core MHD activity also supports the idea of this mode being an NTM by considering the non-linear nature of the NTM stability which generally requires seeding events. Two fluid effects on tearing stability which might be relevant at this relatively low BT plasma due to larger ion gyro-radius have been found to be insignificant in this case.

4. RWM stability modified by kinetic effects

Kinetic modification of the ideal MHD n = 1 stability criterion, computed by the MISK code, has been used successfully to analyze RWM stability in NSTX [6, 9, 15]. This analysis generalizes the ideal MHD stability criterion by adding the effects of broad stabilizing kinetic resonances, and allows kink/ballooning and RWM stability above the ideal MHD no-wall limit. A similar analysis was performed on a high N equilibrium examined to be unstable to the ideal n = 1 mode (the discharge shown in Fig. 2 at 2.315 s) by using measured density, temperature and rotation profiles from TS and CES diagnostics. Figure 7

Figure 6. The radial velocityeigenfunction of a 2/1 tearingmode from M3D-C1.

Figure 7. MISK-calculated n = 1 RWM stabilitydiagram for an experimental N = 3 equilibrium(16295 @ 2.315 s) with scaled experimental rotation profiles.

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shows the MISK-calculated normalized kinetic RWM growth rate for this discharge, with the rotation profile scaled self-similarly in the analysis from 0.2 to 2 times the experimental value (/

exp = 1.0). The figure shows Im(WK) versus Re(WK), where WK is the change in potential energy due to kinetic effects that is calculated by MISK, and contours of constant normalized mode growth rate, w. This first examination of kinetic RWM stability for experimental KSTAR equilibria and measured internal profiles shows the entire range of variation to be stable, with the experimental rotation located close to the stability boundary contour of w = -0.3. The contribution from each component of Re(WK) shown in Fig. 8 shows that resonance

between the mode and the trapped thermal ion precession drift is the dominant stabilizing mechanism. The strong stabilization from trapped ion precession compared to other smaller destabilizing resonances moves the RWM stability away from the stability boundary as is lowered. This enhanced RWM stability at very low rotation is different than expected [8]. The result agrees with the experimentally observed RWM stability at high N, and explains the stability of the experiments above the ideal MHD limits discussed earlier. This analysis is under active development, including calculation with improved equilibrium reconstruction and the effect of energetic particles. In future experiments, RWM stability could be altered by changing plasma collisionality, and rotation profile in a controlled manner by neoclassical toroidal viscosity (NTV) which has been successfully demonstrated in KSTAR [16]. 5. Potential for 1/1 internal mode mitigation by plasma rotation

The 1/1 core instability can destabilize tearing modes by mode coupling [17] or seeding by resulting large sawtooth crashes [14, 18]. The NTM can grow from seed islands enhanced by a local bootstrap current deficit that opposes the stable tearing stability index, ′, producing non-linear island growth. It has been found that the 2/1 mode limiting the high N operation discussed previously was triggered by large sawteeth. At this high N, large and relatively infrequent sawtooth crashes typically lead to ~15% reduction in beta and stored energy as shown in Fig. 9. Each crash expels energetic particles from the core as measured by the fast ion loss detector [19]. Higher fast ion population due to the maximized NBI to the relatively low Ip plasma is expected to produce more detrimental sawteeth as the fast ion pressure generally mitigates the 1/1 mode leading to the long sawtooth period, saw, with large amplitude.

The onset of the 2/1 NTM is quantified in terms of saw and the time between the 2/1 onset and the

immediately preceding crash event measured in the high N experiment. As shown in Fig. 10,

Figure 8. Components of Re(WK)versus the scaled rotation profile forkinetic stabilization of the RWM inKSTAR discharge 16295 @ 2.315 s.

Figure 9. (a) Electron temperature, (b)fast ion loss and (c) plasma storedenergy during the high N phase shownin Fig. 2. Here the measured Te is fromthird harmonic ECE hence itsmagnitude is significantly lower thanthe TS measurement.

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most of the 2/1 onsets occurred within 1-10 ms after the preceding crash which is much shorter than the averagesaw ranging from 30-50 ms in these shots. This result implies that the observed 2/1 mode onset is strongly correlated with the seeding from sawteeth, and control of sawteeth is a possible way to avoid the non-linear triggering of 2/1 mode which would in turn enable sustained high beta operation.

The sawteeth can be avoided with q0 > 1 that can be produced by high non-inductive current drive not yet feasible in KSTAR. Therefore, as a potential way to mitigate the NTM seeding activities, the impact of plasma rotation on the linear stability of the ideal 1/1 internal mode has been examined by M3D-C1. Plasma rotation and rotation shear can modify the structure of instabilities, and the 1/1 mode can be linearly stable if the rotation and rotation shear around the q = 1 surface is sufficiently high [20]. The rotation shear altered the 1/1 linear stability for the rotation profiles tested. The linear mode growth rate with the profile with a higher shear shown in Fig. 11 is computed to be stable, and the mode becomes unstable with a reduced shear in the lowered rotation. In the calculation, rotation shear around the core region is reduced to model a relatively flat profile having reduced shear. The radial velocity eigenfunction of the resulting unstable 1/1 mode is also shown. The examined equilibrium is at high N where the global n = 1 ideal mode is marginally stable, hence future calculations will verify whether the calculated change in the 1/1 mode stability is affected by possible destabilization of the n = 1 ideal mode. 6. Conclusions KSTAR H-mode operational performance has reached and surpassed the ideal MHD n = 1 no-wall stability limit by a significant margin (up to 60%). The highest N value of 4.3 that was achieved for a limited duration has been extended in recent operations to longer pulse with N of 3.3 sustained for 3 s, exceeding MHD mode growth times by 2-3 orders of magnitude. Pulse lengths at maximum N were limited by a 2/1 tearing mode found to be triggered by coinciding large sawtooth crashes. The ideal and resistive MHD stability for the achieved high N equilibria are examined by different physics models. For N above the computed N

no-wall, pressure profiles having different peaking factors modeled from EFIT reconstructions are tested for the ideal n = 1 stability by using DCON, and it is found that a profile that most resembles the inferred pressure profile peaking obtained by using measured electron and ion kinetic profiles is unstable. Kinetic modification of the ideal n = 1 stability calculated by MISK is used for the first time on experimental KSTAR equilibria. The theoretical analysis agrees with the observed RWM stability at high N and somewhat unexpectedly, it shows

Figure 10. Relation of the averagesawtooth crash period with the timebetween 2/1 mode onset and theimmediately preceding crash.

Figure 11. (a) Rotation profiles resulting in different 1/1linear stability conditions. (b) The radial velocityeigenfunction of an ideal 1/1 mode from M3D-C1.

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enhanced RWM stability at very low rotation scaled from the experimental value. The M3D-C1 code solving linearized resistive MHD equations has been widely used for the stability problems discussed, and shows a consistent result with the ideal stability calculations. The linear tearing stability computed by M3D-C1 using a measured resistivity profile indicates the 2/1 mode limiting high N is classically stable, and the pressure driven effects could dominate over the current gradient term in the mode stability. Onset of the 2/1 NTM is quantified in terms of the mode onset time and the sawtooth crash period measured in the experiment and implies that the mode onset is strongly correlated with the perturbation due to sawteeth. The linear stability of the internal 1/1 mode causing sawteeth is calculated under varied rotation shear. The internal mode stability is altered by rotation shear that can stabilize the mode. Future device operation with elevated q, and controlled pressure and rotation profiles will eliminate the non-linear triggering of the 2/1 mode by sawteeth needed for high performance KSTAR equilibria. Ongoing stability analysis will include equilibrium reconstructions including the measured internal field line pitch. Future tearing stability calculation will be improved by employing neoclassical pressure driven terms in the model.

This research was supported by the U.S. Department of Energy under grant DE-FG02-99ER54524. References [1] LEE, G.S., KIM, J., HWANG, S.M., et al., Nucl. Fusion 40 (2000) 575. [2] KWON, M., OH, Y.K., YANG, H.Y., et al., Nucl. Fusion 51 (2011) 094006. [3] KWAK, J.G., OH, Y.K., YANG, H.Y., et al., Nucl. Fusion 53 (2013) 104005. [4] KATSURO-HOPKINS, O., SABBAGH, S.A., BIALEK, J.M., et al., Nucl. Fusion 50 (2010)

025019. [5] PARK, Y.S., SABBAGH, S.A., BIALEK, J.M., et al., Nucl. Fusion 53 (2013) 083029. [6] BERKERY, J.W., SABBAGH, S.A., BETTI, R., et al., Phys. Rev. Lett. 104 (2010) 035003. [7] JARDIN, S.C., BRESLAU, J. and FERRARO, N., J. Comput. Phys. 226 (2007) 2146. [8] PARK, Y.S., SABBAGH, S.A., BERKERY, J.W., et al., Nucl. Fusion 51 (2011) 053001. [9] SABBAGH, S.A., BERKERY, J.W., BELL, R.E., et al., Nucl. Fusion 50 (2010) 025020 . [10] GLASSER, A.H., Phys. Plasmas 23 (2016) 072505. [11] SABBAGH, S.A., BIALEK, J.M., BELL, R.E., et al., Nucl. Fusion 44 (2004) 560. [12] HU, B., BETTI, R. and MANICKAM, J., Phys. Plasmas 12 (2005) 057301. [13] LEE, J.H., OH, S.T. and WI, H.M., Rev. Sci. Instrum. 81 (2010) 10D528. [14] LA HAYE, R.J., Phys. Plasmas 31 (2006) 055501. [15] BERKERY, J.W., SABBAGH, S.A., BELL, R.E., et al., Nucl. Fusion 55 (2015) 123007. [16] SHAING, K.C., IDA, K. and SABBAGH, S.A., Nucl. Fusion 55 (2015) 125001. [17] NAVE, M.F.F., LAZZARO, E., COELHO, R., et al., Nucl. Fusion 43 (2003) 179. [18] SAUTER, O., WESTERHOF, E., MAYORAL, M.L., et al., Phys. Rev. Lett. 88 (2002) 105001. [19] KIM, J., KIM, J.Y., YOON, S.W., et al., Rev. Sci. Instrum. 83 (2012) 10D305. [20] MENARD, J.E., BELL, R.E., FREDRICKSON, E.D., et al., Nucl. Fusion 45 (2005) 539.