A path to stable low-torque plasma operation in ITER with test blanket modules

ITER operational scenarios have been developed on DIII-D to help understand the techniques required for ITER to meet its physics and technology goals [12]. Recently, sustained operation of the ITER scenario envisioned for ITER Q  =  10 experiments has been achieved in DIII-D at low applied torque for multiple resistive relaxation times [10]. These discharges match the ITER performance metrics including a scaled (reduced by a factor of 3.7) lower single null boundary shape (shown in figure 1), normalized plasma current ${{I}_{\text{N}}}=1.41$ corresponding to q₉₅  =  3.2, ${{\beta}_{\text{N}}}=1.8$ and an energy confinement factor (H_98Y2) of 1.05. (H_98Y2 is the enhancement factor above the H-mode confinement scaling IPB98(y,2) [11].) A key challenge had been in learning how to maintain stability, as these discharges are highly susceptible to rotation collapse—a problem further exacerbated by TBM-like error fields. Since plasma reproducibility is found to generally improve with plasma density, the discharges reported here use significant fueling to maintain high line-averaged electron plasma densities near $8\times {{10}^{19}}$ ${{\text{m}}^{-3}}$, corresponding to Greenwald fractions of 0.65, which is close to the expected ITER Q  =  10 operational point [13].

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These plasmas are heated with up to 4.4 MW of NBI with beamlines pointing in both toroidal directions, which decouples the NBI heating power from the applied torque (T_NBI), allowing independent control of ${{\beta}_{\text{N}}}$ and rotation. Feedforward beam power and torque control are employed to study ${{\beta}_{\text{N}}}$ values in the range of 1.8–2.2 whenever the impact of the applied 3D fields on energy and momentum transport is documented. Feedback control of ${{\beta}_{\text{N}}}$ is used in experiments when the applied torque is varied during a discharge and constant ${{\beta}_{\text{N}}}$ is desired at a fixed torque. Since reproducibility worsens as the applied torque is decreased below 1 N m, only transient experiments are pursued at torque values below this level. (See [10] for a discussion of the relevant stability issues under investigation.)

Error fields similar to those expected from the ITER TBMs are generated in DIII-D using a TBM simulator (see [5] for details), which is a set of electromagnetic coils: two 60-turn racetrack coils surrounding one 330-turn solenoid. These coils, located on the low-field side of the torus and centered vertically at the midplane (figure 1), mimic the toroidal and poloidal magnetization of a pair of representative TBMs in one equatorial port. In ITER, all six TBM designs differ in the exact amount of ferromagnetic material, but all will target a design with less than 1.3 tons of ferritic steel [2], which is calculated to produce a local magnetic field ripple (δ) of 1.2% [5]. The standard definition of ripple is used: $\delta =\left({{B}_{\text{max}}}-{{B}_{\text{min}}}\right)/\left({{B}_{\text{max}}}+{{B}_{\text{min}}}\right)$. Since the scaling of TBM effects from DIII-D to ITER is not well established, TBM fields of up to 3% total magnetic field ripple, as calculated at the maximum radial location on the plasma boundary ($R_{\text{mid}}^{\text{out}}$), are investigated to help resolve the operational limits and for comparison against numerical simulation. The applied ripple in each experiment varies somewhat depending on the plasma shape and TBM current so it is reported throughout the manuscript when appropriate. Although the extrapolation from DIII-D results to ITER is not well understood, the maximum field strength of three times the expected ITER field ripple was motivated by particle transport simulations with the Monte Carlo code F3D-OFMC, which indicate thermal particle losses scale linearly with the number of TBM ports [14].

The recent experiments focused on assessing the capabilities of ITER-like actuators to control TBM effects. As in ITER, the DIII-D experiments utilize a row of ex-vessel mid-plane coils (the 'C-coil') for compensation of the n  =  1 harmonic of the intrinsic error field and the TBM field⁸. Compensation of higher toroidal harmonics, namely n  =  2, is achieved using two rows of six internal coils (the 'I-coil') located above and below the midplane. These coil arrays are similar to the upper and lower ITER in-vessel coils to be used for control of edge localized modes (ELMs) [13]⁹. While the poloidal (m) spectrum of the C-coil is fixed, the m-spectrum of the applied I-coil field can be adjusted via the toroidal phase difference between the upper and lower I-coil arrays ($\Delta {{\phi}_{ul}}$) in order to maximize the coupling between the applied field and the dominant plasma mode. For example, the coupling to the dominant n  =  2 plasma mode in the ITER scenario, as calculated by perturbed equilibrium codes such as IPEC [17], is maximized for an up–down symmetric coil configuration ($\Delta {{\phi}_{ul}}={{0}^{\circ}}$), also referred to in the literature as the 'even parity' configuration.

Analysis of EFC algorithms in multiple devices has shown that optimal EFC is achieved by minimizing the drive for the plasma mode that couples most strongly to the total resonant field [15–20]. Although the C-coil m-spectrum cannot be tuned to match the dominant n  =  1 plasma mode, it is expected to perform as well as the I-coil. This follows from n  =  1 proxy error field studies that have shown that the plasma is insensitive to n  =  1 error fields that are orthogonal (i.e. couple weakly) to the dominant mode, which is a kink mode [22, 30].

The error field tolerance of the ITER Q  =  10 scenario to uncorrected TBM error fields is studied at an applied torque level of 1.1 N m, which is close to the scaled ITER-equivalent applied torque of 0.8 N m [21]. When energized at 3 s, the TBM error field, which reaches a maximum of 2.86% ripple, is found to slow the plasma rotation, leading to the onset of an n  =  1 locked mode instability (figure 2). The locked mode is followed by a plasma current disruption that terminates the discharge. This result contrasts previous observations at higher applied torque and lower plasma current where only a reduced level of plasma rotation braking is observed. At low torque, the rotation profile is observed to decrease nearly self-similarly across the profile with no indication of localized braking near rational surfaces (figure 3). Although large sawtooth crashes with inversion radii up to mid-radius and large type-I ELMs are observed as the rotation decreases, these instabilities do not appear to trigger the locked mode. Instead, the onset of the n  =  1 locked mode occurs when the rotation near the q  =  2 surface decreases to half of the unperturbed (pre-TBM) rotation. A bifurcation at this rotation level arises from error field penetration associated with a locked magnetic island [23].

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A database of TBM-induced locked modes shows a consistent rotation scaling over a wide range of applied torque values (figure 4). The database includes ITER Q  =  10 discharges as described above and an ITER similar discharge at lower plasma current (${{I}_{\text{N}}}=1.1$), higher beta (${{\beta}_{\text{N}}}$  =  3) and higher applied torque (${{T}_{\text{NBI}}}=4.3$ N m). This scaling, also observed in n  =  1 locked mode experiments [22], suggests that the toroidal torque balance includes contributions from a resonant electromagnetic braking torque. Unlike resonant magnetic perturbations (RMPs), which displace magnetic field lines more in one radial direction when integrated along an initially closed field line, the magnetic field from the TBM module deflects field lines equally outwards and inwards, making it a purely non-resonant field. Therefore, the resonant magnetic field torque must be generated from perturbed plasma currents associated with the plasma response to the TBM field. Previous studies have shown that the dominant plasma mode contributing to the plasma response is the n  =  1 global kink mode [22, 30]. The plasma response leads to enhanced rotation braking at low torque with the rotation level reduced below the threshold required to trigger a 'downward' bifurcation into a 'fully reconnected' state as described by Fitzpatrick [23]. Although NTMs are present in these discharges, they do not appear to cause significant changes in the evolution of rotation or in the onset of n  =  1 locked modes.

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At the ITER ${{\beta}_{\text{N}}}$ target, the dominant effect of the TBM field is on the plasma rotation and magnetic plasma response, making these two quantities suitable metrics for identifying the optimal compensation fields. The data are obtained by varying the amplitude I₀ and toroidal phase ${{\phi}_{n}}$ of the coil current ${{\mathbf{I}}_{n}}={{I}_{0}}{{\text{e}}^{\text{i}{{\phi}_{n}}}}$ for a given toroidal harmonic (n) in order to either maximize the toroidal angular momentum (${{L}_{\phi}}$), which includes changes in the particle and momentum confinement, or minimize the magnetic plasma response (${{\mathbf{B}}^{\text{plas}}}$) [8]. Typically, the empirical optima identified by these two metrics yield similar but not identical optimal currents [16]. (Note that the current at a fixed toroidal location can be recovered using $I\left(\phi \right)=\text{Re}\left\{{{\mathbf{I}}_{n}}{{\text{e}}^{-\text{i}n\phi}}\right\}$.) This approach has been used recently for studying proxy error fields with only a single toroidal harmonic [30]. During the optimization of n  =  1 fields, the input torque is set to 2.1 N m and an estimate of the compensation field from the IPEC and PENT [31] codes is applied simultaneously with the TBM field in order to reduce the initial TBM rotation braking, and give some operational headroom at the maximum TBM coil current.

The total control coil current ($\mathbf{I}$_tot) can be decomposed into three contributions from currents representing the intrinsic error field ($\mathbf{I}$_intri), the TBM error field ($\mathbf{I}$_TBM) and the varied control current ($113\mathbf{I}$$113_{\text{cc}}^{\text{opt}}$). Assuming any residual error field generates a torque proportional to ${{L}_{\phi}}|{{\mathbf{I}}_{\text{tot}}}{{|}^{2}}$, the steady-state angular momentum balance implies

$$\begin{eqnarray}&&{{L}_{\phi}}\left({{\mathbf{I}}_{\text{cc}}}\right)=\frac{L_{\phi}^{\ast}}{1+{{\tau}_{L}}c|{{\mathbf{I}}_{\text{cc}}}-\mathbf{I}_{\text{cc}}^{\ast}{{|}^{2}}}\end{eqnarray} \tag{ 1 }$$

where ${{\tau}_{L}}$ is the angular momentum confinement time, c is the proportionality constant for the non-axisymmetric field torque, $\mathbf{I}_{\text{cc}}^{\ast}$ is the optimal control current for a given toroidal harmonic and error field source 'cc', and $L_{\phi}^{\ast}$ is the angular momentum achieved at $\mathbf{I}_{\text{cc}}^{\ast}$. Here, 'cc' is either 'TBM' when the TBM coil is energized and 'intri' otherwise. Given the errors in the density and rotation measurements, which are about 4%, the error in the measured ${{L}_{\phi}}$ is about 6%. A fit over the widest possible range of coil currents helps to compensate for this error. Equation (1) is consistent with a non-resonant magnetic field torque, and is used here as a fit function to infer the optimal currents. Due to the presence of a non-negligible intrinsic error field in DIII-D, the optimal compensation currents due to the TBM field cannot be measured directly but must be inferred from optimizations with and without the TBM coils energized with ${{\mathbf{I}}_{\text{TBM}}}={{\mathbf{I}}_{\text{tot}}}-{{\mathbf{I}}_{\text{intri}}}$.

An initial step in these experiments involves the correction of the n  =  1 intrinsic error field $\mathbf{I}_{\text{intri}}^{\ast}$. Attempts to empirically optimize the C-coil currents at low torque (${{T}_{\text{NBI}}}=2$ N m) were very challenging owing to changes in the NTM and ELM stability during coil current scans including the onset and locking of 3/2 and 2/1 NTMs and ELM-free periods, both of which pollute the dependence of ${{L}_{\phi}}$ on the control field. Therefore, the present best estimate of $\mathbf{I}_{\text{intri}}^{\ast}$ comes from a combined estimate from multiple experimental techniques.

The first technique is referred to in the DIII-D plasma control system as the 'standard algorithm', and provides the optimal coil currents for a given plasma current and toroidal field using the results from 'COMPASS scan' experiments. In these experiments, the amplitude of control fields is ramped at different toroidal phases in Ohmic plasmas in order to identify the critical current level for inducing a non-rotating locked magnetic island [9]. In the complex amplitude space for a given toroidal harmonic, the center of a circle fitted to the critical currents identifies $\mathbf{I}_{\text{intri}}^{\ast}$ since a field ramped up from this current offset would lock at the same amplitude independent of the toroidal phase of the applied field. For the targeted plasma conditions, the $\mathbf{I}_{\text{intri}}^{\ast}$ for the C-coil is 1.296 kA at 49°. It is useful to compare other empirical estimates of the optimal currents relative to this estimate by quoting the amplitude multiplier and phase shift (e.g. the standard algorithm has a multiplier of unity and phase shift of 0°).

A second technique for $\mathbf{I}_{\text{intri}}^{\ast}$ using the n  =  1 C-coil can be determined by identifying the EFC currents that minimize the magnetic plasma response. In this approach, optimal I-coil currents are identified from a database of ITER like H-mode discharges indicating a minimum in the measured n  =  1 magnetic plasma response ($\delta {{B}^{\text{plas}}}$) inside the vacuum vessel wall at the equatorial midplane on the low-field side. These I-coil currents are then mapped to the C-coil currents by minimizing the drive from the I-coil to the dominant plasma mode as predicted by IPEC. In this approach, the empirically optimized I-coil field is a proxy for the intrinsic error field. The analysis identifies a multiplier and phase shift relative to the standard algorithm of 1.6 and 5°, respectively, which is consistent with an enhancement of the intrinsic error field by the plasma in H-mode relative to the plasma response in lower pressure Ohmic plasmas.

The evolution of ${{L}_{\phi}}$ in three discharges where these two estimates were used (figure 5) shows little to no change in plasma performance. During these experiments, only the C-coil EFC was varied: two cases use the standard algorithm and one discharge used the second estimate. Although the time range for comparison was limited by differences in MHD events (e.g. rotating tearing modes), ${{L}_{\phi}}$ is similar during the early phase of the plasma current flattop, suggesting that the estimates are likely to be near the optimal currents or are equidistant from the optimal $\mathbf{I}_{\text{intri}}^{\ast}$.

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A third technique for $\mathbf{I}_{\text{intri}}^{\ast}$ comes from scanning the C-coil amplitude and phase during a discharge, monitoring ${{L}_{\phi}}$ and using equation (1) to identify $\mathbf{I}_{\text{intri}}^{\ast}$. Ideally, the scans would cover a wide range of amplitudes and toroidal phases; however, due to the aforementioned variations in the MHD events and limited experimental time, only a limited range of currents yield meaningful results. Even so, the fits show good agreement with the the previous two estimates for $\mathbf{I}_{\text{intri}}^{\ast}$ (figure 6). As speculated, the first two estimates are equidistant from the inferred value of $\mathbf{I}_{\text{intri}}^{\ast}$, which has a multiplier and phase shift relative to the standard algorithm of 1.3 and 0°, respectively. This also happens to be the average of the result from the first two techniques.

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A final estimate for $\mathbf{I}_{\text{intri}}^{\ast}$ can be obtained using a technique referred to as 'dynamic error field correction'. In this approach, active magnetic feedback (as developed for resistive wall mode control) is enabled after a stationary plasma equilibrium is achieved. A low-pass filter with a relatively long time constant (100 ms) is used to smooth an error signal derived from an n  =  1 fit to a toroidal array of poloidal field probes located at the midplane. The error signal is taken with respect to an arbitrary offset measured after the plasma current flattop. Results using the DEFC technique are limited in this target plasma; however, in one discharge where the technique was used, the coil currents initially moved away from the pre-programmed EFC currents only to return to those values later in the discharge. The trajectory is noted in figure 6. In this discharge the pre-programmed values were found by minimizing the plasma response (the second technique), which agrees well with the IPEC prediction of the EFC currents that minimize the coupling of the total field to the dominant n  =  1 mode (red star in figure 6).

Table 1 summarizes the various estimates of $\mathbf{I}_{\text{intri}}^{\ast}$. An error estimate of 22% is found between the various methods. The average value taken from the mean of the empirical methods agrees well with the IPEC prediction, which is based on an error field source model for DIII-D.

Table 1. Empirically optimized and theoretically predicted values of C-coil correction of the intrinsic n  =  1 DIII-D error field. The average value is taken over the empirical methods.

Condition	$\mathbf{I}_{\text{intri}}^{\ast}$
Standard algorithm	1.296 kA ∠49°
Zero $\delta {{B}^{\text{plas}}}$	2.060 kA ∠54°
Max. ${{L}_{\phi}}$	1.696 kA ∠49°
DEFC	2.247 kA ∠54°
Average	1.823  ±  0.430 kA ∠52  ±  3°
IPEC SVD1	2.06 kA ∠54°

Empirically optimized values for $\mathbf{I}$_tot are obtained via variations of the current in the C-coil with the TBM field applied at 2.94% ripple, and are used to identify $\mathbf{I}_{\text{TBM}}^{n=1}$. The data are obtained in the presence of 4/3 NTMs, which, at large control coil current, can slow down and lock the plasma rotation to the resistive wall leading to disruption (green traces in figure 7). With partial compensation fields applied, the average change in ${{L}_{\phi}}$ due to the TBM field is $\Delta$ ${{L}_{\phi}}=0.13\pm 0.03$ N m s. Multiple discharges are analyzed to identify an extremum ${{L}_{\phi}}$ value that recovers as much as 58% of the partially corrected TBM-induced ${{L}_{\phi}}$ degradation (figure 8). The fit residual is small, indicating that equation (1) captures the dominant variation of ${{L}_{\phi}}$.

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The empirically optimized and theoretically predicted values of ${{\mathbf{I}}_{\text{TBM}}}$ with n  =  1 are compared in figure 9 and table 2. The empirically optimized value is over four times larger than that predicted by IPEC–PENT with a toroidal phase difference of 21.1°. However, the optimal value is expected to be closer to the value noted as $\mathbf{I}_{\text{TBM}}^{\text{trial}}$ in table 2 since it was successfully used to access operation at near zero applied torque as described in section 5.1. This value was selected during the experiment based on previous results, which showed that IPEC predictions of the optimal correction accurately predict the phase, but underestimate the amplitude [8]. Since a reduction of the n  =  1 compensation field by 50% significantly increases the torque threshold for n  =  1 locked mode onset (see section 5.1), we can conclude that $\mathbf{I}_{\text{TBM}}^{\text{trial}}$ must be quite close to the optimal value. Note that $\mathbf{I}_{\text{TBM}}^{\text{trial}}$ is in good agreement with the phase predicted by IPEC–PENT but underestimates the amplitude by a factor of two.

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Table 2. Empirically optimized and theoretically predicted values of $\mathbf{I}_{\text{cc}}^{n=1}$.

Condition	$\mathbf{I}_{\text{cc}}^{n=1}$
$\mathbf{I}_{\text{TBM}}^{\text{IPEC--PENT}}$	0.328 kA  ∠−15.6°
${{\mathbf{I}}_{\text{tot}}}$	3.140 kA ∠35°
Average ${{\mathbf{I}}_{\text{intri}}}$	1.823 kA ∠52°
${{\mathbf{I}}_{\text{TBM}}}$	1.360 kA ∠5.5°
$\mathbf{I}_{\text{TBM}}^{\text{trial}}$	0.685 kA  ∠−14.4°

Together with results from a previous analysis [8], we conclude that the phase of the optimal compensation currents can be accurately predicted by IPEC–PENT analysis but that the codes consistently underestimate the required amplitude. The reason for the discrepancy found in this analysis is under further investigation. Uncertainty in the determination of the optimal compensation for both the intrinsic error field and the TBM error field could contribute. The estimated uncertainty in the amplitude of $\mathbf{I}$_TBM is marked in figure 9, but doesn't fully explain the discrepancy. An important known sensitivity that remains to be quantified is related to the sensitivity of the predicted perturbed fields to the safety factor profile, which is near unity across a large fraction of the minor radius resulting in near zero magnetic shear in the plasma core. The sawtooth instability itself may also play a role to modify the plasma response to the TBM field in a way not captured by linear models.

In these experiments, the EFC optimization based on maximizing the rotation yielded a result ($\mathbf{I}$_TBM) that differs from $\mathbf{I}_{\text{TBM}}^{\text{trial}}$ in both amplitude and phase. Since previous results have shown rotation optimization to be an accurate method for correcting fields errors, further comments explaining possible reasons for these discrepancies are warranted. First, the dominant fraction of the discrepancy is likely to be due to the fact that the rotation optimization procedure was not continued until a converged result was obtained. Due to limited experimental time and the added challenges of low-torque operation, regions of the n  =  1 coil current space near the optimal value remained unexplored (see figure 8). Further studies might have identified a result for $\mathbf{I}$_TBM in better agreement with $\mathbf{I}_{\text{TBM}}^{\text{trial}}$. As mentioned previously, the added challenges of low torque operation include the presence of large-amplitude MHD instabilities (e.g. sawtooth, tearing modes, ELMs). The results of rotation optimization can be polluted by changes in the characteristics of these instabilities. In particular, changes in tearing mode amplitudes and/or mode structures from one discharge to the next make it more difficult and expensive (in terms of number of discharges required) to assemble a sufficiently large database. Second, the torque ramp-down experiments, which showed that EFC based on $\mathbf{I}_{\text{TBM}}^{\text{trial}}$ did not restore access to the torque level found without the TBM, suggest there is also an error in $\mathbf{I}_{\text{TBM}}^{\text{trial}}$ (i.e. this value is also not the converged result from this method). Further torque ramp-down experiments might have identified currents that completely restore access to low torque. It is possible those currents could be in better agreement with converged results from the rotation optimization experiments.

High-${{\beta}_{\text{N}}}$ plasma operation provides an attractive possible path to improved performance in ITER, but is more susceptible to error fields due to decreased ideal and resistive MHD stability [27]. The impact of reduced stability has been observed in previous DIII-D experiments where the effects of TBM fields on plasma performance increases dramatically with ${{\beta}_{\text{N}}}$, suggesting that TBM fields may limit confinement in high-performance ITER scenarios. Given the strong ${{\beta}_{\text{N}}}$ dependence observed in magnetic field measurements of the n  =  1 plasma response [22], it is reasonable to speculate that the beta dependence of TBM effects is due to n  =  1 field amplification by the plasma. Previous results from TBM error field studies at modest beta values show that complete suppression of the n  =  1 plasma response to the TBM field is achievable, which suggests that n  =  1 compensation may be more effective at suppressing an enhanced response at higher pressure [8]. Further, if the n  =  1 component of the plasma response is the dominant harmonic amplified by the plasma leading to performance reductions, it should be possible to compensate for TBM effects at high beta to the level observed at lower beta using only n  =  1 compensation. Here, we demonstrate experimentally that the strong performance degradation with beta can be avoided using n  =  1 compensation alone and, furthermore, the performance recovery is associated with a reduction in the plasma response and first wall heat flux caused by the TBM field.

The experiments are conducted in lower single-null, high-performance, inductive plasmas. Due to practical constraints not encountered at modest beta, it is necessary to modify the target plasma equilibrium away from the ITER Q  =  10 target. First, the plasma current was reduced (${{I}_{\text{N}}}=1.1$) in order to increase q₉₅ to 4.4, reducing the impact of NTM stability on energy confinement. Second, to improve access and reproducibility at high beta, counter NBI was not used, leading to an increased NBI torque of up to 7.4 Nm. Finally, the strength of the TBM field at the plasma surface and values of ${{\beta}_{\text{N}}}$ that could be investigated was limited by the heat flux to the first wall due to TBM-induced fast ion losses [29]. The operation limits required a target ${{\beta}_{\text{N}}}$ of 2.7 and an outer gap of 7 cm, an increase of 1 cm, in order to reduce the measured temperature change in the graphite tiles below the  +250 °C limit, figure 10 (red crosses). This configuration corresponds to a total field ripple in front of the TBM of 2.55%.

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At ${{\beta}_{\text{N}}}$ values of 2.8–3, n  =  1 EFC is able to avoid large reductions in ${{\beta}_{\text{N}}}$ and ${{L}_{\phi}}$. Figure 11 compares two discharges with TBM fields: one with n  =  1 compensation of only the intrinsic error field and another with compensation of the intrinsic and TBM error fields. The TBM and control fields are applied for 2 s allowing the discharge to reach a stationary state and the change in plasma parameters to be measured. As seen previously, TBM effects are exacerbated at high beta (figures 11(a)–(c)), the n  =  1 plasma response to the TBM is significant (figure 11(d)) and the heat flux to the first wall tiles in front of the TBM is substantial (figure 11(e)), reaching 4.5 MW m⁻², which is nearly the maximum allowable heat flux to the 'enhanced heat flux panels' in ITER [28].

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The loss of confinement with compensated TBM fields was reduced to the level found at the ITER beta target (compensation is used also at the lower ${{\beta}_{\text{N}}}$ value). This is seen in a comparison of both the TBM-induced reduction in ${{L}_{\phi}}$ and the recovered amount using n  =  1 field compensation with in-vessel coils at two values of ${{\beta}_{\text{N}}}$, figure 12. Here, we define the reduction in any parameters as the difference in the parameter before and after the TBM field is applied normalized to the pre-TBM level. Also, the 'recovered' amount is defined as the fraction of the reduction in a parameter restored with EFC. The performance recovery increases with ${{\beta}_{\text{N}}}$ more strongly than the observed reduction in performance, so as to avoid further performance degradation at higher pressure. Since the outer gap is larger at high beta, the recovery is a more indicative of the improved performance of n  =  1 compensation than the measured reduction with EFC. The performance improvement using ex-vessel coils was also measured at high ${{\beta}_{\text{N}}}$ (but not low beta) and found to be somewhat less than with in-vessel coils (47% compared with 73%).

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When the TBM field is compensated, the n  =  1 magnetic plasma response at the midplane on the centerpost (the high field side) is also reduced by 60%. The high-field side measurements on the centerpost are used here to avoid complications from direct coupling between the TBM vacuum field and the magnetic sensors. The partial reduction of the plasma response suggests that control currents were not fully optimized and leaves open the possibility that further improvements in performance may be achievable using only n  =  1 compensation. (Recall that the n  =  1 plasma response to the TBM field was completely cancelled by the I-coil at ${{\beta}_{\text{N}}}$ of 1.8.) Even so, the observed recovery is equivalent to a near complete avoidance of the strong beta dependence of TBM effects, which reduces concerns that high performance in ITER will be problematic with TBMs installed.

The optimized n  =  1 compensation is also found to reduce the area-averaged heat load to the TBM armor tiles by 80% (figure 11(e)). The heat flux is measured by a fast 2D infrared camera installed specifically to view the TBM tiles; the area average is taken over the localized hot spot. Shortly after the TBM field is applied, the heat flux reaches 4.5 $\text{MW}~{{\text{m}}^{-2}}$ for uncorrected TBM fields. If this level of heat flux were expected from the ITER TBMs, special 'enhanced heat flux panels' capable of up to 5 MW m⁻² would be needed near the three TBM ports. Such panels are envisioned for protecting the first wall from from heat flux associated with the ITER NBI system [28]. However, with n  =  1 EFC, the heat flux in DIII-D is reduced to 0.85 $\text{MW}~{{\text{m}}^{-2}}$, which is below the rated heat flux (1 MW m⁻²) for standard first wall tiles in ITER. Extensive modeling of fast ion transport in the presence of vacuum TBM fields and comparisons with previous heat flux measurements has identified enhanced energetic particle transport as the main cause for the enhanced heat flux [29]. Further work is needed to resolve the role of the plasma response in this process.

Since n  =  1 EFC does not obviate the TBM torque, it is important to understand the margin for stable operation in the space of applied torque, TBM field and the accuracy of EFC. These dependences are studied using two different experimental methods. In the first, an uncorrected TBM field is ramped up at fixed NBI torque to identify the critical TBM current for triggering a locked mode. In the second, a fixed compensated TBM field is applied and the NBI torque is ramped down to identify the minimum accessible torque prior to onset of the locked mode. Note that the second method only addresses the issue of access to low torque; it does not demonstrate sustained stable operation at the achieved torque level. Until reproducible conditions can be achieved below 1 Nm, it is not meaningful to assess TBM effects in that regime.

Without compensation, the TBM field progressively reduces low-torque access to levels above the ITER equivalent torque (figure 15, red points). Assuming the most unfavorable extrapolation to ITER where TBM effects in DIII-D and ITER are the same [5], these results imply the ITER Q  =  10 scenario will not be accessible with uncompensated TBM fields. However, with empirically optimized n  =  1 EFC, operation even below the ITER equivalent torque is achievable (transiently) at nearly three times the ITER equivalent field ripple (green point). (Recall from section 5.1 that sustained operation at 3% ripple is possible at 1.1 Nm.) With partial compensation, stability is lost near the ITER level if the TBM compensation field is reduced by 50% (yellow points). A nearly linear scaling with TBM field is found for two subsets of the data: uncorrected and partial compensation. Taken together, these results demonstrate that compensation of n  =  1 harmonics of the TBM field is essential to access the expected values of applied torque in ITER. Furthermore, they show that predictions of the optimal compensation currents must have an error that is less than 50% in order to provide access to ITER equivalent torque values without the need for empirical optimization.

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