Y.S. PARK et al.

1

STABILITY, TRANSPORT, AND ACTIVE MHD MODE CONTROL ANALYSIS OF KSTAR HIGH PERFORMANCE PLASMAS SUPPORTING DISRUPTION AVOIDANCE

Y.S. PARK, S.A. SABBAGH, J.H. AHN, J.W. BERKERY, Y. JIANG, J.M. BIALEK, J.D. RIQUEZES Department of Applied Physics and Applied Mathematics, Columbia University New York, NY, USA Email: ypark@pppl.gov B.H. PARK, J. KIM, H.S. HAN, S.H. HAHN, J.G. BAK, Y.M. JEON, W.H. KO, M.J. CHOI, J.S. KO, H.S. KIM, H.H. LEE, J.H. LEE, L. TERZOLO, S.J. WANG, J.G. KWAK, S.W. YOON National Fusion Research Institute Daejeon, Republic of Korea M.D. BOYER, Z.R. WANG, J.-K. PARK, N.M. FERRARO, S.C. JARDIN, F. POLI, S. SCOTT Princeton Plasma Physics Laboratory Princeton, NJ, USA A.H. GLASSER Fusion Theory and Computation, Inc. Kingston, WA, USA

Abstract

H-mode plasma operation in KSTAR has surpassed the n = 1 ideal MHD no-wall beta limit computed to occur at N = 2.5 with li = 0.7. High N operation produced N of 3.3 sustained for 3 s, limited by tearing instabilities rather than resistive wall modes (RWMs). High fidelity kinetic equilibrium reconstructions (EFIT) have been developed to include Thomson scattering, charge exchange spectroscopy data, and an allowance for fast particle pressure. In addition, motional Stark effect data are used to produce reliable evaluation of the safety factor, q, profile. The reconstructed equilibria can exhibit significant variation of the q-profile dependent upon the broadness of the bootstrap current profile as computed by TRANSP analysis. TRANSP analysis indicates that the non-inductive current fraction can reach up to 75% while its profile can vary significantly depending upon plasma operational scenario. The classical stability of the m/n = 2/1 tearing mode that limited high N operation is examined using the resistive DCON code and by the M3D-C1 code using the kinetic EFIT reconstructions as input. For equilibria at high N > 3, the tearing stability index, ′, is more unstable compared to that of equilibria at reduced N. However calculations of instability of stable lower N equilibria indicate that the neoclassical components of tearing stability need to be invoked to produce consistency with experiment. MISK code analysis which examines global MHD stability modified by kinetic effects shows significant passive kinetic stabilization of the RWM in these plasmas. Predict-first TRANSP analysis was conducted to design KSTAR plasma operation with 100% non-inductive fraction at N above 4. Active RWM control has additionally been enabled on KSTAR. To accurately determine the dominant n-component produced by RWMs expected to onset at higher beta utilizing the new second NBI system, an algorithm has been developed that includes magnetic sensor compensation of the prompt applied field and the field from the induced current on the passive conductors. This analysis on stability, transport, and control provides the required foundation for disruption prediction and avoidance research on KSTAR.

1. INTRODUCTION

H-mode plasma operation in KSTAR has surpassed the n = 1 ideal MHD no-wall beta limit, βNno-wall, computed to

occur at normalized beta, βN = 2.5 when the plasma internal inductance, li, = 0.7 for H-mode pressure profiles [1]. Figure 1 shows the achieved βN and li values from dedicated experiments to explore βN > βN

no-wall over long pulse lengths in the recent device operations. The computed βN

no-wall boundary was substantially exceeded by increased neutral beam injection power. Compared to the earlier machine operation, high βN plasma was extended to longer pulse exceeding several seconds in duration by utilizing improved real-time plasma control resulting in βN of 3.3 sustained for ~3 s during the discharge pulse length of 6.5 s (discharge 16295 in FIG. 1). The ratio of N/li has surpassed 6 which is a high value for advanced tokamaks. The observed high βN plasmas were limited by m/n = 2/1 resistive tearing mode instabilities. Although tearing modes have been routinely observed in KSTAR [2-4], the modes at high βN have notably large amplitude up to 20 G determined by magnetic probes measuring poloidal field perturbations at the outboard upper-midplane region, consequently reducing both βN and the stored energy by up to ~35%. The mode onset points in several high βN discharges are shown in the figure. In these discharges run with similar plasma conditions, the mode onset occurred at βN > 2.5 with li at relatively high values between 0.85 and 1.07. In many cases, the mode onset relatively early in the discharge stopped the plasma from achieving βN above the ideal MHD no-wall limit. Global kink/ballooning or resistive wall modes (RWMs) have

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not been observed at high βN. The disruptivity of these plasmas during the programmed current flattop period is presently low [5]. However, as the neutral beam heating power continues to be upgraded (~1.5 MW planned for 2018, with an additional 3 MW in 2019), the disruption probability due to these instabilities may increase. To achieve plasma operation at high beta without disruptions, the estimation of stability and unique equilibrium and transport properties supporting stability analysis and disruption prediction is crucial. The paper describes recent progress in development of the analysis components necessary for reliable estimation of stability in KSTAR. Equilibrium reconstructions now include constraint from measured internal profiles including electron and ion temperature, electron density, and magnetic pitch angle profiles. Reconstructed realistic pressure profiles relevant to H-mode plasma operation enable reliable estimation of stability driven by the global shape of pressure profile and local details of

the pressure gradient. Determination of plasma current density profiles shows regions of low shear appear at varied safety factor, q, values in different operational regimes. Interpretive transport analysis using the TRANSP code computes high non-inductive current fraction up to 75% in these plasmas while its profile can vary significantly, which is studied as a function of plasma parameters. The change in the non-inductive current profile leads to significant changes in q-profile and shear which can be used to optimize the stability at high non-inductive current fraction. The ideal and resistive stability at high βN is examined by using the resistive DCON code and by the M3D-C1 code with the kinetic EFIT as input. The tearing stability index, ′, is computed and compared to the measured experimental stability. MISK code analysis examining global MHD stability modified by kinetic effects can explain how RWMs at the achieved βN > βN

no-wall can remain stable. The new magnetic probe sensor sets for active RWM control have been implemented for operation at higher beta utilizing the new second NBI system. To accurately determine RWM dynamics and to actively stabilize these modes, an algorithm has been developed that utilizes the entire three toroidal sensor arrays at different poloidal locations with sensor compensation of the prompt applied field as well as the AC field generated from the induced current in the device passive stabilizing plates and other conducting components.

2. KINETIC EQUILIBRIUM RECONSTRUCTION USING MEASURED INTERNAL PROFILES

High fidelity kinetic equilibrium reconstructions, which are an essential requirement for accurate stability and transport analyses, have been developed to support steady-state, high confinement operation in KSTAR. The work significantly expands prior magnetics-only equilibrium reconstruction capability [2, 6]. Unlike analysis that uses

only external magnetic measurements, kinetic equilibrium reconstructions provide measurement constraints internal to the plasma including the plasma temperature and density. KSTAR kinetic EFIT reconstructions include Thomson scattering (TS) data up to 27 radial channels [7], charge exchange spectroscopy (CES) data up to 32 radial channels [8], allowance for fast ion pressure, external magnetics and shaping field current data, and inclusion of vacuum vessel and passive plate currents. The q-profile is a key parameter in optimizing confinement and determining stability. In KSTAR, up to 25 radial channels of motional Stark effect (MSE) diagnostic data are equipped to measure the local magnetic pitch angle at the midplane [9]. The recent addition of the MSE background polychrometer diagnostic installed in the device will improve the measurement by preventing the desired beam-generated signal from pollution caused by background light due to reflection on hot in-vessel surfaces [10]. These MSE data provide constraints for reliable evaluation of the q-profile. By adopting the partial kinetic reconstruction approach which has been used successfully for years in NSTX [11], the profile functions composing the total pressure profile are computed from directly measured quantities such as electron pressure and ion temperature, and either modeled or estimated quantities with large error bars such as ion density and the fast ion pressure. The fast ion pressure is estimated by using the

FIG. 1. The KSTAR equilibrium operating space and ideal stability limits in (li, βN) space.

FIG. 2. Reconstructed (a) pressure and (b) q-profile from the reconstructions with and without measured internal profile constraints.

Y.S. PARK et al.

3

electron pressure with a large bar assigned to allow greater flexibility in fitting the total pressure profile.

The reconstructed high performance plasma equilibria can exhibit significant variation of the reconstructed q-profile dependent upon the plasma operational scenario due to the broadness of the bootstrap current profile as computed by TRANSP analysis. Figure 2 shows the reconstructed pressure and the q-profile for an equilibrium having βN ~ βP > 2 with q95 = 6 and qmin =1.3. Sawteeth were absent throughout the discharge flattop. The reconstructed pressure profile using the partial kinetic reconstruction approach shows a realistic broad profile shape expected of H-mode plasmas and observed in the kinetic measurements. Weak q shear regions are found to form in different parts of the profile, both farther out in the profile at higher q, or closer to the core at lower q dependent on plasma scenario. These less conventional q-profiles are attributed to the broadness of the non-inductive current which can generate radially peaked / broadened toroidal current profiles depending on current drive sources which will be discussed in the next section. The non-inductive current profile and the resultant weak local q-shear may alter the stability of tearing modes destabilized by local current density perturbations. Especially, a weakly positive magnetic shear and large local pressure gradient enhances the growth of the neoclassical tearing mode (NTM) which is a major instability limiting high beta in the present device operation.

3. TRANSPORT ANALYSIS FOR FULLY NON-INDUCTIVE, HIGH PERFORMANCE OPERATION

High performance plasma operation with high non-inductive current fraction, fNI, by replacing inductively driven plasma current with non-inductive current such as NBI current and pressure-gradient driven bootstrap current is highly desired for continuous advanced tokamak operation. Interpretive and predictive TRANSP [12] calculations for KSTAR high performance plasmas have been conducted to investigate a disruption-free path to the device design target operation having βN up to 5 with fully non-inductive current drive. The TRANSP code computes solutions to time-dependent 1.5D transport equations describing poloidal magnetic field diffusion, particle balance, power balance and momentum balance as desired. The newly developed kinetic equilibrium reconstructions have been used as input to TRANSP, and the ion density is calculated by assuming a flat effective plasma charge, Zeff = 3 profile with carbon as the only impurity. The result of the interpretive runs indicates that the non-inductive current fraction can reach up to 75%. Figure 3(a) shows the non-inductive current density profiles in the high βN > 4 equilibrium (FIG. 1) that has a fairly broad bootstrap current profile with fNI of 67%. The equilibrium with a transient high N of 2.7 shown in FIG. 3(b) has ~15% higher plasma current than the higher βN case. The distinctive high bootstrap current in the edge region increases fNI up to 71% in this case. This result suggests that while the non-inductive current fraction can be high in different operating conditions, the bootstrap and total non-inductive current profile shapes can vary significantly. This can lead to significant changes in safety factor profile and shear as shown in the reconstructed q-profiles in FIG. 2, which in turn leads to different stability at high non-inductive fraction. Synthetic scans of Zeff show that fNI remains high regardless of its value due to the complementary dependence of the neutral beam-driven current and neoclassical bootstrap current on Zeff.

Predictive capabilities of the TRANSP code have been applied to investigate and develop scenarios plausible to maintain higher performance plasma operation enabled by the increased NBI heating power, PNBI. In addition to the existing NBI system (NBI-1), a new tangential off-axis NBI system (NBI-2) having three beam sources (one injected from below the midplane is being installed for 2018, and two from above the midplane and from the midplane, repectively, will be installed in 2019) will be available in KSTAR. In the predictive calculations, the experimental electron density profile is scaled to match a given Greenwald fraction, fGW, and the electron temperature profile is scaled to match a given energy confinement enhancement factor, H98y2. The change in fNI is calcuated with varied fGW and H98y2 with an increased PNBI of 6.5 MW from the two NBI systems (PNBI = PNBI-1 + PNBI-2 where PNBI-1 = 5 MW, PNBI-2 = 1.5 MW). The fNI increases as H98y2 is increased up to the experimentally achieved value of the reference plasma, 1.25, due to a larger amount of bootstrap and beam-driven current generated. Interpretive TRANSP runs calculate fGW ranging from 0.4 to 0.8 in existing experimental equilibria with different plasma parameters, hence the fGW values used in the predictive runs are chosen in this range. The bootstrap current is increased at higher fGW however, degraded external currrent drive efficiency reduces the overall fNI at higher fGW.

TRANSP

KSTAR 16325 @ t = 2.05 s

N = 2.7

fNI

= 71%

FIG. 3. Toroidal current density profiles from TRANSP for (a) high βN > 4 and (b) intermediate βN = 2.7 equilibria.

(a)

(b)

TRANSP

KSTAR 16295 @ t = 1.75 s

N = 4.3

fNI = 67%

PNBI = 4.5 MW

PNBI

= 4.5 MW

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Figure 4(a) shows that near fully non-inductive plasma current can be achieved with fNI increased from 71% (FIG. 3(b)) to 96% when PNBI is increased from 4.5 MW to 6.5 MW. The total plasma toroidal current density is shown by the black solid line in the figure. Both the beam-driven current and bootstrap current are increased and they replace the inductive current to reach fully non-inductive plasma current. The total plasma current of 490 kA, fGW of 0.5 and H98y2 of 1.25 from the interpretive run (FIG. 3(b)) are maintained in the preditive run. The βN is calculated to increase to a higher value of 3.4. In further analysis, the toroidal magnetic field strength (BT) was reduced from 2.0 T to 1.7 T to further increase βN along with the increased PNBI. The result shown in FIG. 4(b) indicates that with the plasma current similar to the experimental value, βN can be raised above 4 with similar high fNI. The results from these projections show that fully non-inductive plasmas can be obtained at present levels of global energy confinement quality and Greenwald density fraction with βN highly above βN

no-wall by using only a fraction of the planned PNBI increase which will eventually be increased to a total PNBI of 11 MW and beyond.

4. STABILITY OF HIGH BETA KSTAR PLASMAS

The ideal and resistive stability of the discharges shown in FIG. 1, for which the equilibrium and transport characteristics have been analyzed in this paper, is now examined by using different physics

models. The kinetic EFIT reconstructions are used as input to stability analysis for full discharge time evolution. This enables reliable calculation of the global mode stability which requires an accurate description of the pressure and q-profiles since βN

no-wall strongly depends on the pressure peaking factor [13] as well as li. The ideal n = 1 stability, calculated by using the DCON code [14], is shown in FIG. 5. Negative total perturbed potential energy by n = 1, δWno-wall

n=1 , indicates an unstable n = 1 mode with no surrounding wall. The equilibria having sustained βN ~ 2.0 in current flattop in FIG. 5(a) show δWno-wall

n=1 consistently stays below the stability boundary and the n = 1 ideal mode remains stable throughout the long discharge pulse. For equilibria having a higher βN that exceeds the computed βN

no-wall in FIG. 5(b), the ideal mode is computed to be unstable while the RWM is experimentally stable in the discharge. The βN

no-wall depends on li which is in the range 0.8 - 1.1 in the high βN equilibria in the discharge flattop, and many equilibria at high βN/li ratio ~ 4 and above violate the ideal mode no-wall stability criteria. The small deviations in the reconstructed profiles possibly due to the benign n = 2 activity in the high βN phase are thought to be responsible for reduced equilibrium convergence causing the scatter in δWno-wall

n=1 shown in FIG. 5(b).

The stability of the observed 2/1 tearing mode at high βN is computed by using the resistive DCON code [15] and the M3D-C1 code [16]. The kinetic EFIT reconstructions with MSE data allow reliable determination of tearing stability by enabling proper estimation of the plasma profiles and their gradient near the mode rational surface. Figure 6 shows the resistive stability examined by the resistive DCON code. For equilibria at high βN > 3 in which tearing mode onsets were observed in similar discharges in the experiment, the linear tearing stability index, ′, at the q = 2 surface is more unstable compared to that of equilibria at reduced βN later in the discharge, which is consistent with the observed stability. At βN above the ideal stability boundary, the computed ′ is found to be

FIG. 5. The evolution of the n = 1 no-wall stability criteria computed by DCON for the two discharges shown in FIG. 1 each having (a) intermediate βN and (b) higher βN values, respectively. Unstable equilibria are displayed in orange color.

DCON (a) KSTAR 16325 KSTAR 16295

DCON (b)

N = 2

N > 3

TRANSP (Predictive)

FIG. 4. (a) Toroidal current density profiles from the predictive TRANSP run using an increased PNBI of 6.5 MW. (b) The calculated N by varying IP when BT is lowered to 1.7 T.

(a)

(b)

TRANSP (Predictive)

Projected from KSTAR 16325

N = 3.4

fNI = 96%

PNBI

= 6.5 MW

BT = 2 T

PNBI

= 6.5 MW

BT = 1.7 T

Y.S. PARK et al.

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more sensitive to the equilibrium profiles than in the case of lower βN. Comparative results for the intermediate βN equilibria shown in FIG. 6(a) that are experimentally stable to tearing modes but show an unstable value of ′ indicate that stabilizing components of the NTM stability such as the effect of the polarization current and the field curvature [17] combined with sheared toroidal rotation need to be invoked to produce consistency with experiment. In terms of NTM triggers, the presence of the co-existing sawteeth observed only in the high βN phase in FIG. 6(b) can provide necessary seeding to trigger NTMs. The resistive DCON analysis shown used the outer region solution which needs to be matched to the resistive layer inner solutions to better determine resistive mode stability in future analysis. The linear stability calculation using the M3D-C1 code shows a marginally stable tearing mode for the high βN > 3 equilibria. A simplified input plasma resistivity is used in the M3D-C1 calculations which could cause the somewhat different mode stability, and should be improved for more analogous stability comparison between the numerical models. Although tearing stability is not completely determined solely by ′ in this result, this initial evaluation of the classical tearing stability using kinetic equilibrium reconstructions of sufficient accuracy is an important foundation for reliable analysis of NTM stability in the presence of significant toroidal flow shear observed in KSTAR [2, 4].

The global MHD stability modified by kinetic effects is examined using the MISK code [18]. This analysis generalizes the ideal MHD stability criterion by adding the effects of broad stabilizing kinetic resonances, and allows kink/ballooning mode and RWM stability above the ideal MHD no-wall limit. MISK calculations were performed to explain the observed RWM stability at equilibria examined to be unstable to the ideal n = 1 mode by using measured density, temperature and rotation profiles from TS and CES diagnostics. MISK analysis shows the equilibria to be stabilized by kinetic effects in agreement with experiment. Figure 7 shows the MISK-calculated normalized kinetic RWM growth rate, 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 examination of kinetic RWM stability shows the entire range of variation to be stable in both equilibria at different βN while the scaled experimental rotation located closest to the stability boundary contour (w = 0) is different. The contribution from resonance between the mode and the trapped thermal ion precession drift is found to be the dominant stabilizing mechanism. The strong stabilization from trapped ion precession compared to other destabilizing resonances including that with trapped ion bounce, trapped electron and circulating ion moves the RWM stability away from the stability boundary. The effect of energetic particles on stability is shown in FIG. 7(a). Only trapped beam ions with an isotropic distribution across pitch angle are considered. The kinetic effects of energetic particles are stabilizing by making the magnetic flux more rigid and resistant to change by RWM [19]. The result suggests that RWM stability could be altered by

FIG. 6. Resistive DCON computed ′ for equilibria having (a) intermediate βN and (b) higher βN values (FIG. 1).

R-DCON (a) KSTAR 16325 KSTAR 16295

R-DCON(b)

N = 2

N > 3

Susceptible to tearing mode onset

FIG. 7. MISK-calculated n = 1 RWM stability diagram for equilibrium at (a) intermediate βN and at (b) high βN with varied rotation profiles. The RWM stability boundary is shown in red contour.

MISK (a) KSTAR 16325 KSTAR 16295

MISK (b)

N = 2 N = 3

w/ energetic particles

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changing the plasma rotation profile by neoclassical toroidal viscosity which has been demonstrated in KSTAR by using the central electron cyclotron heating [20] and applied 3D fields with various field spectra [4, 21].

5. ACTIVE RWM FEEDBACK SYSTEM DEVELOPMENT FOR HIGH BETA OPERATION

In preparation for plasma operation at higher beta utilizing the second NBI now installed on the device, three sets of new magnetic field sensors will be used for RWM active feedback control. The newly available RWM feedback sensors are shown in FIG. 8. The new sensors measure poloidal magnetic field perturbations at the inside of the top and bottom passive stabilizing plates. Among the total of 20 sensors in three toroidally distributed sensor arrays, 12 sensors (MPZU03 and MPZU04 array) are located at two poloidal positions above the midplane and 8 sensors (MPZL20 array) are at a single poloidal position below the midplane. These sensors are computed to have a negligible mutual coupling to the RWM feedback coils compared to other device magnetic sensors [22] which supports RWM control using “Mode control” [23] feedback logic requiring compensation of the prompt applied fields. However, due to strong mutual coupling between the sensors to the neighboring conducting structures, including the highly conductive copper passive plates to which the sensors are

mounted, compensation of the fields from the induced eddy currents in the conducting structures from the sensor measurement is critical and challenging. An example of the high sensor mutual coupling to the passive plates is illustrated in FIG. 9. Here, toroidally rotating n = 1 fields in various frequencies are applied from the RWM coils without plasma. A significant amount of magnetic field mostly from the plate eddy currents remains even after compensation of the magnetic fields directly applied from the coils (DC compensation) as shown in FIG. 9(c). An algorithm has been developed that includes sensor compensation of the induced current on the passive conductors (AC compensation) by following the approach used in NSTX. The AC compensation term for the i-th sensor is

computed by evaluating the formula, δBAC,i(t) = ∑ ∑ pi,j,k

LPFdIRWM, j(t)

dt;τAC,k

3k=1

4j=1 , where j is an index over the four

RWM coil currents, k is an index over the three time constants, AC, used for low-pass-filtering (LPF) of RWM coil current time derivative, and p is an AC pickup coefficient. Three AC values are determined to minimize the

amount of magnetic field remaining after the DC compensation, which are in the range 3 - 215 ms. Although adding more AC time constants is typically beneficial, it results in higher computational load on real-time computers, and the determined three AC values well compensate the magnetic fields from the induced currents as shown in FIG. 9(d). For the entire RWM sensors, the magnitude of the uncompensated magnetic field components when the DC and the AC compensations are applied is less than 2 G in this case which is tolerable considering the typical error bars of the measurement, and that experience on other devices indicates that the RWM will not become highly problematic on KSTAR until the n = 1 amplitude exceeds 20 G. For n = 1 RWM identification, two toroidally opposing sensors (FIG. 8) in the sensor arrays are paired and their signals are subtracted from each other to eliminate the n = 0 component. The resulting 10 sensor differences are then multiplied by the mode decomposition matrix to calculate the amplitude and phase of the n = 1 component of the perturbation produced by RWM. The mode identification algorithm including the required sets of variables for the sensor compensation and the mode decomposition matrix have been implemented in the real-time plasma control system (PCS) in KSTAR.

It is beneficial to use the entire set of available RWM sensor arrays simultaneously for a mode identification more robust against individual sensor failures. Additionally, measuring the mode at multiple poloidal positions above and below the midplane can do a

FIG. 8. VALEN-3D finite element model showing toroidal distribution of the RWM feedback sensors installed on the passive stabilizing plates, and RWM feedback coils viewed from the top of the device.

FIG. 9. (a) RWM coil current and (b) corresponding Bp measured by an RWM sensor. (c) The measured Bp when DC prompt applied fields from the coils are compensated, and (d) when both DC and AC compensations are applied.

Coil current

Sensor Bp

DC compensated Bp

(a)

(b)

(c)

DC/AC compensated Bp (d)

Y.S. PARK et al.

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better job of control since the RWM eigenfunction can have varying helicities of the perturbed mode field structure in the outboard region. In KSTAR, the feedback coils are at the midplane whereas the mode measurement is made at the off-midplane region, hence the effect of varied mode helicities on the optimal feedback phase can be mitigated when the mode phases measured at above and below the midplane are combined. Use of multiple sensor arrays is enabled by modifying the sensor toroidal angles assumed in mode decomposition. This gives the effect of toroidally rotating the sensor arrays with respect to each other. To determine the proper amount of angle shift, the poloidal field perturbation by a simulated unstable RWM is analyzed with varied mode growth rate represented by varying βN. Figure 10(a) shows the poloidal field perturbation from a projected unstable RWM on an unwrapped plasma surface with the positions of the RWM sensors and coils overlaid. Although the MPZU03 and MPZU04 arrays are positioned closely to each other at the region where the phase of the perturbed mode field does not significantly change along the poloidal direction, the mode phase measured by these arrays in 3D space computed by the VALEN-3D code [24] can be significantly different. In FIG. 10(b), the change in the toroidal phase of the measured mode field with respect to the phase measured at the outboard midplane is shown. The phase difference between the midplane and off-midplane region changes with βN as the response of the wall increases with faster mode growth at higher βN. The

magnitude of this change according to βN is greater in the MPZU03 and MPZL20 arrays compared to the MPZU04 array. The phase difference can vary by up to 7o in these sensor arrays at the βN values examined. In the case with no electromagnetic response of the wall, the phase difference is nearly constant for each sensor array as shown by the dashed lines in the figure. The mode decomposition matrix which computes the amplitude and the toroidal phase of the RWM is generated by considering these sensor phase shifts. In calculating the phase of the applied feedback coil current, the difference in the phase between the perturbed poloidal field and the perturbed radial field must be taken into account.

A developed method of mode identification using the compensated magnetics data was tested experimentally using an n = 1 MHD that rotates slowly enough to be measured by the RWM sensors. In the discharge shown in FIG. 11, a tearing mode that saturates drags the plasma rotation down to the mode bifurcation point and the mode consequently locks to the wall. The measured mode amplitude and phase at the point of the mode locking are shown in the figure. Further analysis on mode identification and feedback will be carried out when the RWM is destabilized at higher performance plasmas expected to be produced in future experiments.

6. CONCLUSIONS

The KSTAR H-mode operational performance has reached and surpassed the ideal MHD n = 1 no-wall stability limit with a βN value higher than 3 sustained for duration longer than 3 s. Kinetic equilibrium reconstructions including MSE data have been developed for accurate reconstruction of plasma profiles. The reconstructed low-q shear observed in high performance equilibria can affect stability, and the non-inductive current profiles that produce the less conventional q-profiles are calculated by TRANSP analysis. A high non-inductive current fraction up to 75% is calculated for the experimental equilibria, and the predictive capabilities of TRANSP show that high βN > 4 operation can be achieved with fully non-inductive plasma current over a range of plasma parameters by using the increased neutral beam heating power recently installed on the device. The ideal and resistive MHD stability examined by different physics models are compared between equilibria having different plasma parameters. The ideal mode stability indicates that the achieved high βN equilibria violate the ideal n = 1 no-wall stability criteria. The tearing stability index, ′, computed by resistive DCON code indicates that in one case ′ is more unstable in the region where tearing mode onsets were observed in the experiment. MISK analysis explains the observed RWM stable plasma operation above the ideal stability limit through stabilization by the kinetic effects. This result supports that future experiments with a controlled rotation profile can alter the stability

FIG. 10. (a) The perturbed poloidal magnetic field for the unstable n = 1 eigenfunction with no wall. (b) The mode phase measured by the sensor arrays with respect to the phase at the midplane.

(b)

MPZU04

MPZU03

without wall (dashed lines) VALEN-3D

MPZL20

(a)

FIG. 11. (a) Measured amplitude and (b) toroidal phase of an n = 1 tearing mode that locks to the wall.

(b)

(a)

KSTAR 15279

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of RWMs to prevent disruptions of fully non-inductive, higher performance KSTAR plasmas. An RWM identification and feedback algorithm has been developed in the real-time PCS that includes magnetic sensor compensation of the field from the induced current on the passive conductors. The present analysis of equilibrium, stability, transport, and control provides the required foundation for disruption prediction and avoidance on KSTAR [5].

ACKNOWLEDGEMENTS

This research was supported by the U.S. Department of Energy under Contract No. DE-FG02-99ER54524 and DE-SC0016614.

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