First observation of RMP ELM mitigation on MAST Upgrade

Summary

This paper reports on the initial experimental attempts to control Edge Localised Modes (ELMs) on the MAST Upgrade spherical tokamak using Resonant Magnetic Perturbations (RMPs). In low-beta discharges, applying n=1 3D magnetic fields successfully demonstrated ELM mitigation with an ELM frequency increase of over 20-fold, accompanied by a locked mode that did not terminate the plasma. Application of n=2 fields did not achieve mitigation due to the significant presence of an intrinsic n=2 error field, providing key insight into error field correction and phase optimization for future spherical tokamak operations.

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UKAEA-CCFE-PR(24)213 CCFE CULHAM CENTRE FOR FUSION ENERGY UK Atomic Energy Authority

D A Ryan, A Kirk, S Munaretto, W Suttrop, L Piron, M Willensdorfer, T Markovic, S Saarelma, C Ham, E Viezzer

First observation of RMP ELM mitigation on MAST Upgrade

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Title Page

First observation of RMP ELM mitigation on MAST Upgrade

D A Ryan, A Kirk, S Munaretto, W Suttrop, L Piron, M Willensdorfer, T Markovic, S Saarelma, C Ham, E Viezzer

This is a preprint of a paper submitted for publication in Plasma Physics and Controlled Fusion

Abstract and Authors

First observation of RMP ELM mitigation on MAST Upgrade

D A Ryan1, A Kirk1, S Munaretto2, W Suttrop3, L Piron4, M Willensdorfer3, T Markovic5, A J Thornton1, S Saarelma1, C Ham1, E Viezzer6, the MAST Upgrade team7 and the EUROfusion Tokamak Exploitation Team8

1 UK Atomic Energy Authority, Culham Campus, Abingdon, Oxfordshire, UK 2 Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451, USA 3 Max Planck Institute for Plasma Physics, Garching, Germany 4 Dept. of Physics and Astronomy, University of Padova, Padova, Italy 5 Institute of Plasma Physics CAS, Za Slovankou 1782/3, 182 00, Prague, Czech Republic 6 Department of Atomic, Molecular and Nuclear Physics, University of Seville, Avda. Reina Mercedes, 41012 Seville, Spain 7 see the authorlist of [1] 8 see the authorlist of “Overview of the EUROfusion Tokamak Exploitation programme in support of ITER and DEMO” by E. Joffrin, Nuclear Fusion, 2024, 10.1088/1741-4326/ad2be4

Abstract. The first experimental attempts at controlling Edge Localised Modes (ELMs) via the application of resonant magnetic perturbations (RMPs) on the MAST Upgrade tokamak are reported. Using the linear MHD model MARS-F, the phase shift between the upper and lower coil rows ΔΦ was optimised for toroidal mode number n=1 and n=2 fields, to provide forward guidance to experiments. In low βN discharges, the application of n=1 3D fields caused the ELM frequency fELM to increase by over a factor 20 relative to the reference, and also induced a locked mode, which did not cause a plasma termination nor an H-L back transition. However when βN was raised, this induced locked mode caused plasma termination which precluded mitigation access. Initially, applying a numerically optimised n=2 field had no effect. However applying a rigid toroidal shift to this field caused a locked mode disruption, demonstrating the presence of a substantial n=2 error field. The n=2 locked mode coil current threshold ILM was measured with varying ΔΦ, and the ΔΦ dependence found to be shifted by 60 degrees from linear MHD predictions, with the influence of the n=2 error field identified as the most likely cause of the deviation. However, mitigation with n=2 fields was not established.

1. Introduction

Modern tokamaks when operating in high confinement mode (H-mode), typically exhibit a periodic explosive MHD instability referred to as an Edge Localised Mode (ELM)[2, 3]. While usually harmless in current devices, they are predicted to cause unacceptable degradation of plasma facing component lifetimes in ITER and reactor scale devices[4], posing a risk to the ITER scientific mission and the development of commercial magnetically confined fusion more generally. Several techniques have been proposed to mitigate this risk, of which the application of Resonant Magnetic Perturbations (RMPs) is among the most developed. RMP ELM mitigation refers to a regime in which the applied RMP causes an increase in the ELM frequency, in order to decrease the individual ELM size[5]. RMP ELM suppression refers to a regime in which the application of RMPs causes the ELMs to disappear entirely, with their heat and particle flux being replaced by a continuous transport mechanism resulting in greatly reduced peak heat fluxes on plasma facing components[6]. Many RMP ELM control experiments were performed on MAST over its lifetime demonstrating reliable ELM mitigation[5, 7, 8, 9], but full ELM suppression was not achieved in MAST. Indeed although ELM suppression is routinely achieved in single null conventional aspect ratio tokamaks[6, 10, 11, 12], suppression has yet to be achieved either in double null configuration, or in any tight aspect ratio tokamak. This adds uncertainty to extrapolations of RMP ELM control schemes to larger machines, in particular reactor scale spherical tokamaks. This motivates an experimental and modelling effort to demonstrate optimised ELM mitigation, and eventually full suppression, on the successor device to MAST: MAST Upgrade. The strategy adopted for these first experiments is to first achieve a reliable mitigation scenario, then use this scenario to validate linear MHD predictions of the optimal coil phase, as in [13]. Once the optimal applied field configuration is conclusively established, it is intended to then focus on varying suppression relevant plasma parameters to locate and access an ELM suppressed regime. This paper reports on the first experiments of this effort. In section 2, the RMP coilset of MAST Upgrade is described and compared with that of MAST. In section 3, the modelling based prediction of the optimal configurations for toroidal mode number n=1 and n=2 fields is described. In section 4, experiments are reported in which n=1 and n=2 fields are applied to Type I ELMing MAST Upgrade plasmas, and the effects on density, ELM frequency, pedestal profiles, and plasma rotation are measured. In section 5, the results are summarized, and the outlook for future experiments is discussed.

2. MAST Upgrade RMP coils

The MAST Upgrade RMP coilset consists of 4 upper and 8 lower coils. The coilset is able to produce n=1 and n=2 fields with both rows, and n=4 with the lower row only (although it is feasible to generate a mixed mode spectrum of n=0 and n=4 by applying currents of the same polarity to all coils in the upper row). In contrast with the previous MAST coilset described in [5], n=3 and n=6 fields are no longer available, due to the removal of 6 coils to avoid obstructing the off axis neutral beam and diagnostic sightlines of the X-point and divertor entrance. The coil construction is the same as used on MAST, the coils being 54cm by 22cm window coils of 4 turns, however the locations in the poloidal plane are slightly different than on MAST, now being slightly closer to the midplane and larger major radius, as plotted in Figure 2d. On MAST Upgrade as on MAST, the currents are provided by 4 independent single quadrant power supplies, however the maximum current has been increased from 1.4kA (=5.6kAt) on MAST[5] to 2.0kA (=8kAt) on MAST Upgrade. The MAST Upgrade coilset is sketched in Figure 1, alongside a CAD drawing of one of the RMP window coils.

Figure 2a and 2b plot the vacuum resonant field components for n=1 and n=2 fields respectively, for MAST and MAST Upgrade RMP coils and with typical MAST and MAST Upgrade equilibria. The vacuum resonant fields are computed using the ERGOS code[14], the MAST implementation of which is explained in[5]. In both cases the input currents are set to the maximum achievable: 5.6kAt for MAST and 8kAt for MAST Upgrade. For configurations generated by both the upper and lower coilsets (n=1,2,3 for MAST, n=1,2 for MAST Upgrade) the plotted field is the sum of fields due to the upper and lower coilsets, with the phase difference arranged to maximise the vacuum resonant component closest to the plasma edge. The plots show that the smaller number of coils of the MAST Upgrade coilset relative to MAST is sufficiently compensated by the increased maximum coil current, such that the vacuum field is comparable between the two machines. As shown in Figure 11 of [15], in previous MAST RMP experiments the threshold in vacuum field strength beyond which ELM mitigation was achieved in MAST CDN (connected double null) experiments, was approximately b_res^r = 5 Gauss (where b_res^r is the radial field component normalised to the toroidal field, as used in [15, 16]). Referring to Figure 2b, the MAST Upgrade coilset would exceed this threshold at the maximum current of 8kAt, but with only a small margin. An important caveat however, is that the threshold of 5 Gauss was measured with an n=3 applied field, and it has been previously observed that the vacuum penetration threshold varies with the n number [16]. The vacuum mitigation threshold is not available specifically for n=2 fields in the MAST archive. On MAST Upgrade n=2 is the highest n number which the coilset can generate with both the upper and lower rows. To achieve an n=2 field which comfortably exceeds the previously observed mitigation thresholds, it is necessary for the error field correction coils to be arranged into an n=2 configuration and added constructively to the RMP field. Figure 2b plots the resultant field, demonstrating it is of comparable strength to that used to achieve mitigation on MAST, and therefore should be able to exceed the mitigation threshold.

MAST Upgrade has greatly increased shaping flexibility relative to MAST, such that on MAST Upgrade the gap between the coils and plasma ΔRcoil can be made smaller than was typical for MAST CDN plasmas. The effective vacuum field, and therefore the extent of mitigation, are sensitive to ΔRcoil[16]. Figure 2d shows a plot of a plasma boundary from a MAST RMP ELM control experiment in CDN (previously reported in [15]), overlaid on the boundary of a typical MAST Upgrade ELM control experiment. It demonstrates that the typical coil-plasma gap in the MAST Upgrade case is 25% lower than in MAST. Figure 2c plots the n=4 fields from the lower row of the MAST and MAST Upgrade RMP coilsets, as well as the n=6 field from the lower row of the MAST coilset. The figure demonstrates that for higher n number fields which have a stronger spatial gradient, the vacuum resonant field of the MAST Upgrade coilset exceeds that of MAST, due to the reduction in ΔRcoil and higher maximum coil current.

3. Prediction of optimal coil phase

For coilsets consisting of two (or more) toroidal rows of coils, the poloidal spectrum of the applied field may be tuned by varying the phase offset between the toroidal waveform in the lower coil row relative to the upper, here called ΔΦ = Φlower − Φupper where Φlower and Φupper are the phases of the toroidal current waveforms in the lower and upper coilsets respectively. It has been established previously[9, 13] that the extent of ELM mitigation and accessibility of suppression access windows are sensitive to ΔΦ, and that their dependence on ΔΦ may be predicted by accounting for the plasma response to the applied vacuum field[17, 18], most typically achieved using a linear MHD code such as MARS-F[19] or VMEC[20]. Therefore in the planning of these experiments, prior knowledge of the dependence of the plasma response on ΔΦ was required. How the ‘optimal’ phase is best defined is dependent on the context, most notably, the toroidal mode number n. For n=2, we follow the approach used on ASDEX Upgrade (using n=2)[13] and MAST (using n=3)[9], which found that the mitigated ELM frequency is maximised when ΔΦ is chosen to maximise the outermost resonant component of the magnetic perturbation, as computed including the plasma response. This metric |b_res^1| is defined as |b_m^1| for which m = nq, q being the outermost surface of the equilibrium, and |b^1| = |(b · ∇ψ)/(B_eq · ∇φ) * (q / (R_0^2 B_0))|. For n=1 fields, coupling to core modes is more likely due to the lower spatial gradients of the applied field, which can lead to mode locking and plasma termination. Therefore for n=1 we follow the approach of KSTAR[21], in which n=1 suppression was accessed by careful tuning of ΔΦ so as to maximise the edge resonance of the applied field δbedge, while keeping the core interaction δbcore below a critical level which would precipitate a locked mode disruption. As the RMP coil current Icoil is ramped up, a phase of ELM mitigation (or suppression in the case of KSTAR) will be accessible if the access threshold Imit is below the threshold ILM at which a locked mode is triggered. The coupling of the RMP to marginally stable MHD modes in the edge and core (ie, δbedge and δbcore) can reduce the Imit and ILM thresholds respectively, and the extent to which the RMP couples to core and edge modes is sensitive to the RMP phasing ΔΦ. The values of Imit and ILM cannot yet be predicted a-priori, but it is now well established by studies on KSTAR[21], ASDEX Upgrade[13] and MAST[9], that the dependencies of δbedge and δbcore on ΔΦ can be predicted by linear MHD codes. Therefore, to maximise the likelihood of an ELM controlled phase being accessible (ie, Imit < ILM), ΔΦ should be chosen to maximise the ratio of edge coupling to core coupling δbedge/δbcore. It has been shown previously that the computed plasma edge displacement at the midplane ξM and X-point ξX are strongly correlated with δbcore and δbedge respectively[22]. So for the case of n=1, ΔΦopt is defined as the phase which maximises the ratio of the X-point displacement to midplane displacement ξX/ξM as computed with linear MHD code MARS-F. This metric has previously been studied in a series of RMP experiments on MAST[23], and it was found to be a good predictor of the occurrence of density pump out.

The equilibrium and kinetic profiles for discharge 47052 at 530ms were used as input to the MARS-F code for ΔΦopt prediction. In divertor plasmas the q profile tends to infinity at the plasma edge. To treat this numerically, the q profile is truncated at some finite value, which determines the precise value of q which qualifies as the ‘outermost’ resonant surface. It has been shown however that the ΔΦopt predictions made by such analyses are robust to the level edge truncation[24]. In this instance, the value of the safety factor at the plasma edge was set as qa=11.98, so the outermost resonant surfaces for n=1 and n=2 were at q=11 and 11.5 respectively. The plasma response of these equilibria to the fields applied by the upper and lower coilsets were computed separately, and the optimal phase extracted in post process. Figure 3a) plots |b_res^1| for an n=2 applied field as a function of ΔΦ, which shows an optimum of 236 degrees, which is taken as ΔΦopt for the n=2 case. Figure 3e,f) plot ξX, ξM and ξX/ξM as a function of ΔΦ for an n=1 field, demonstrating the optimal ratio of ξX/ξM (used as a proxy for δbedge/δbcore) to be 75 degrees, which is therefore taken as ΔΦopt for the n=1 case.

4. MAST Upgrade RMP Experiments

4.1. Effect of n=2 RMPs

Discharge 48670 was a 3.4MW NBI heated type I ELMing plasma scenario with plasma current Ip=750kA, edge safety factor q95=6.0, and normalised βN =3.1, in double null conventional divertor configuration. In the subsequent discharge 48671, an n=2 RMP was applied at maximum coil current. The experimental value of ΔΦ was set to 225 degrees (the ΔΦ value closest to the optimum achievable with a square toroidal waveform), following forward modelling detailed in section 3. Since it was expected (based on the results plotted in Figure 2) that the applied field may not be able to exceed the mitigation threshold with the RMP coils alone, the error field correction coils were configured into n=2, to add constructively to the RMP field. As described in section 2, the vacuum resonant components of the combined field are stronger than those employed on MAST, and comfortably exceed the previously observed n=3 mitigation threshold. The main results of the experiment are plotted in Figure 4. Despite the large amplitude of the field, it does not appear to have had a measurable effect on the ELM frequency or density, indicating no sign of ELM mitigation or density pump-out. Although the rotation speed does saturate at a modestly lower value, strong rotation braking is not observed, suggesting the field does not couple strongly to core modes. The kinetic pedestal profiles, plotted at 670ms, appear to be unchanged by the application of the field.

Prior investigations of the error fields present in MAST Upgrade[25] demonstrated that the error fields produced by the P4 and P5 coils are dominantly n=1 and n=2 in nature. The n=1 component is passively compensated by careful positioning of the P4 and P5 coils, with tilts and offsets added during construction to counteract the inherent n=1 field of the coils[25]. Compass scan experiments performed in the first campaign of MAST Upgrade[26] showed that these efforts have reduced the n=1 error field to a very low level. However, the n=2 field could not be compensated in this way, and so it is expected that the dominant error field is now n=2. This naturally raises the hypothesis that the ineffectiveness of the very large n=2 applied field used in experiments plotted in Figure 4 is due to a counter oriented n=2 error field.

4.2. Rotated n=2 field

To test the hypothesis outlined above, the polarities in all coils were reversed, having the effect of applying a 90 degree toroidal rigid shift to the applied field. This field was applied to discharge 49147, a similar plasma scenario as previously. The resulting data traces are plotted in Figure 5 (left hand plots). The discharge matches the RMP-off reference until 610ms, when the locking of a rotating mode precipitates a large density crash. This result verifies the hypothesis, since in the absence of a significant n=2 EF, a rigid toroidal shift of the field would have no effect. It is interesting to note, that although the applied field is of n=2 and it is certainly this field which causes the rotation braking, the eventual saturated locked mode has n=1 structure. An analysis of low n mode stability on MAST Upgrade which may explain these dynamics is left for future work. Figure 5 also shows no mitigated phase prior to the density crash, indicating that as the coil current was ramped up, the disruption threshold ILM was reached before the mitigation threshold Imit. We can therefore infer that ILM < Imit for this coil configuration.

To interpret the above result, a model of the n=2 component of the intrinsic error field on MAST Upgrade was constructed, using previous measurements of the error fields due to individual PF coils (as detailed in [25]), combined with the coils’ as-installed geometries. At present only the vacuum error field due to the P4 and P5 coils is included in the model. Figure 6 plots the vacuum resonant components of the error field due to the P4 and P5 coils (magenta), powered with typical flattop currents of -2.5kA and -5.9kA respectively (note these are feed currents, each of these coils has 23 turns so these correspond to -57.5kAt and -135kAt respectively). Plotted in black are the vacuum resonant components of an n=2 applied RMP field with ΔΦ=180. The blue and green markers on the figure plot the sum of the intrinsic error field and RMP, respectively with and without the 90 degree rigid rotation of the RMP field. The rigidly rotated case (blue markers) corresponds closely to the field resulting in the locked mode termination plotted in the left hand plots of Figure 5, and shows that the vacuum resonant components including the error field are over 2.5 times larger than the non-rotated case (green markers), which produced no measurable effect as plotted in Figure 4.

The observation that ILM < Imit indicates that the coil phase optimisation should also seek to minimise the core interaction, and so ξX/ξM should be used as the optimisation metric for n=2 rather than |b_res^1|, as was done for n=1. Referring to fig 3c), this yields a revised predicted optimal phase for n=2 of ΔΦopt=160. However, consideration of the error field casts doubt on this prediction. Up/down asymmetries in the error field will cause it to have its own effective up-down phasing, which when added to the applied field, will alter the dependencies of ξM and ξX on the ΔΦ of the applied field. So for rigorous prediction of ΔΦopt, the P4 and P5 error field model must be expanded to include the plasma response to the vacuum error field, which is left to a future work. Although it is expected that the P4 and P5 error fields will be dominant, the error field model would also benefit from including the other poloidal field coils, which is also left for future work.

4.3. Empirical ΔΦ scan with n=2

Having found that our approach to ΔΦopt prediction was ineffective due to the lack of a complete model of the n=2 error field, the experimental strategy was altered to search for the optimal coil phase empirically. The coil current Icoil was ramped at 6 values of ΔΦ, in an effort to measure Imit and ILM, and quantify their phase dependence. Of these 6 values, 4 resulted in locked mode disruptions very similar to that plotted in the left hand plots of Figure 5, while 2 resulted in no effect as in the right hand plots of Figure 5. None resulted in a mitigated phase; for all 6 values of ΔΦ, Imit is above either ILM or Imax.

However, we can still use these experimental measurements of ILM(ΔΦ) as a proxy measurement of the ΔΦ dependence of the RMP core coupling, to provide some guidance for the coil optimisation schemes of future experiments. For illustrative purposes, Figure 7 shows a sketch (red dashed) of the ΔΦ dependence of the core perturbation δbcore (for which we use ξM as a proxy in ΔΦopt prediction) due to 1kAt of coil current. To trigger a locked mode, δbcore must be scaled by an applied current such that δbcore(1kA) × Icoil (red solid) exceeds some threshold T (red dot dashed). Therefore the experimental measurable ILM(ΔΦ) should have a dependence ∝ T/δbcore(ΔΦ) (solid blue in Figure 7). Fitting the measured ILM(ΔΦ) to a function f = T/δbcore yields the value ΔΦ which maximises the core response. This was predicted in Figure 3b) as 330 degrees, whereas the fit to measurements yields a measured value of 270 degrees. We may infer that the influence of the error field has shifted the core dependence by -60 degrees from predicted. It should be noted that there are too few points in this fit for rigorous error analysis, so the numerical result should be treated as indicative only. Further experiments are planned which will ramp Icoil for more values of ΔΦ, in order to test this prediction and to refine the measurement of ILM(ΔΦ). Ideally more points of ΔΦ should be added between ΔΦ = 180 and ΔΦ = 90, where the rate of change of ILM(ΔΦ) is expected to be highest and so most useful for a fitting function. It should also be noted that the fitting function ‘slope’ appears higher than the data suggests. The fitting function assumes only two sources of perturbation: the upper RMP row and a lower row, the lower of which is a factor 1.41 larger in amplitude due to the larger number of coils in the lower row. This is what determines the ‘shallowness’ of the function f = T/δbcore. Adding a third source due to the error field would alter this aspect of the fitting function, but this is left to a future work in which the error field should be rigorously characterised. It is envisaged that these and future measurements of ILM(ΔΦ) may be used to develop and validate a model of the n=2 error field on MAST Upgrade. Since n=2 is the largest component of the error field on MAST Upgrade, it is thought that actively correcting it may alleviate performance limiting instabilities and permit access to higher βN regimes.

4.4. Effect of n=1 RMPs

RMPs in the n=1 configuration with a phase of ΔΦ=180, were applied to a 2.7MW NBI heated type 1 ELMing plasma scenario with Ip=750kA, q95=6.0, βN =2.0. Figure 8 shows the reference case overplotted with two cases with RMPs applied, one with a slow ramp and the other with a rapid ramp. Due to the low natural ELM frequency in the reference case, the scenario exhibits an uncontrolled density ramp which is only terminated when the density accumulation pushes the plasma out of H mode at 830ms. The MHD spectrograms and core rotation demonstrate that with the RMPs applied, a global MHD mode is strongly braked by the applied field and shortly locks to the vessel. At this point, a sustained density pump out is triggered, and the ELM frequency exhibits a sustained increase, demonstrating ELM mitigation. The ELM frequency increases from around 10Hz in the reference 45388, to between 200-400Hz in the mitigated phases of 45453 and 45457, a more than 20 fold increase. Thomson scattering profiles from the mitigated phases demonstrate that the electron temperature pedestal is not measurably degraded, consistent with ELM mitigated phases on MAST[15]. The density profiles are also plotted for the mitigated phases and a representative time point of the reference shot (timepoints shown as vertical lines in the plot of the line integrated density), although the uncontrolled density rise of the reference discharges makes it difficult to draw inferences from the comparison.

It is interesting to note that in the case where the field is applied rapidly at full strength, there is a delay of over 300ms before mitigation is accessed. This contrasts to typical observations on MAST, in which mitigation would be accessed promptly after the applied field exceeded the mitigation threshold[16]. The cause of the delay in the MAST Upgrade case appears to be the time it takes for the applied field to first cause a total collapse of the global plasma rotation. Rapid plasma rotation is known to have a screening effect on static applied fields[27], so it may be that for the field to exceed the mitigation threshold in this case, first the rotation must be braked to facilitate field penetration. This is suboptimal, since the plasma rotation crash causes the onset of a locked mode. In an attempt to disentangle the locked mode from the ELM mitigation, the applied RMP was removed and reapplied with a notched waveform, as demonstrated in Figure 9. Initially the 6 kHz mode is decelerated and locks, which is followed immediately by an ELM mitigated phase. When the applied field is removed, the mitigation is immediately lost, the mode unlocks and accelerates, and the density begins to recover towards the reference. This demonstrates that the locked mode induced by the applied field can be healed, but at the cost of losing ELM mitigation.

4.5. Optimised field applied at increased βN

Following the experiments described in section 4.4 a higher performance scenario was developed, with 3.3MW of NBI heating, Ip=750kA, q95=6.3, βN =2.8. Other than a slightly lower elongation (κ =1.94 rather than 2.1 for the low βN reference), the high βN case is closely similar to the low βN case shown in Figure 8. A slowly ramping n=1 RMP was applied, and in an attempt to avoid the previously observed core mode locking, the coil phase was changed to ΔΦ=90, close to the predicted optimum of ΔΦopt=75. The reference discharge and effects of the applied field are plotted in Figure 10. As in the lower βN experiments shown in Figure 8, the RMP caused a braking of toroidal rotation, resulting in a low order MHD mode to lock to the wall. Unlike in the low βN case however, in which the plasma survived the mode locking, in these high βN cases the mode locking caused a plasma termination. It is suspected that this is because in higher βN the increased drive of the low n mode which causes the locked mode, may cause it to have a larger saturated state. This causes the locked mode to precipitate a disruption before mitigation is accessed. The coil phase is optimised to avoid this outcome, but this measure is apparently insufficient.

5. Summary and Conclusions

A series of experiments were conducted beginning an effort to mitigate and ultimately suppress ELMs via the application of RMPs on MAST Upgrade. Since the coilset is reduced on MAST Upgrade relative to MAST from 18 coils to 12, the highest toroidal mode number which permits tuning of the poloidal spectrum by phase adjustment is now n=2, rather than n=3 as on MAST. Nonetheless, ELM mitigation in low βN by an n=1 RMP was demonstrated, although the mitigated phase was accompanied by a locked mode, which when βN was increased resulted in plasma termination prior to mitigation access. As detailed in section 3, the RMP coil phase was numerically optimised to maximise ξX/ξM, so as to minimise the ratio of Imit/ILM, and this coil phase was applied in the experiment. Since the n=1 error field has been passively minimised to a low level, it is less likely that the ΔΦopt prediction is incorrect for the n=1 case, than for the n=2 case which is known to have a substantial error field. The presence of a mixed mode spectrum by the superposition of the n=1 applied field with the n=2 error field and n=3 sidebands of the applied field, may also complicate the predictive modelling, and incorporating these factors is left to future work. Therefore, future experiments should seek to experimentally validate the ΔΦopt prediction made for n=1 fields on MAST Upgrade. If the ΔΦopt prediction is proven to be accurate however, then this experiment demonstrates that ELM mitigation via n=1 RMP fields is likely to not be viable for this plasma scenario in MAST Upgrade. In this case, future experiments should instead focus on n=2 and perhaps n=4 applied fields, which have a higher ratio of edge to core coupling and are therefore more likely to exceed the ELM mitigation threshold before the mode locking threshold. It is speculated here that careful tuning of the q profile may provide an alternate path to achieving mitigation. The plasma response to applied perturbations may augment or suppress resonant components of the total field, in particular the amplification of marginally stable MHD modes may drive nearby resonant components by poloidal harmonic coupling[24]. If the q profile were tuned such that the core modes were more deeply stable and the edge modes less deeply stable, this may increase the ratio of the edge to core coupling and thereby increase ξX/ξM. Investigating this suggestion with linear MHD modelling may be the subject of a future work.

Applying n=2 RMPs with numerically optimised phasing initially resulted in no measurable effect. Rigidly shifting the applied field toroidally resulted in a locked mode and density crash, demonstrating the presence of a substantial n=2 error field. This error field was not accounted for in optimal phase predictions, which is identified as a key modelling deficiency. Models of the vacuum error fields of the P4 and P5 coils are subsequently produced. It is shown that the vacuum error field adds constructively to vacuum field which is toroidally rotated, but destructively for the non-rotated field, which is consistent with the observation of no effect of the non-rotated field, and a strong effect of the rotated field. In this work the field being optimised to guide experiments was the sum of only two sources: the upper and lower RMP coil rows. The results of this paper suggest that the field being optimised should be considered as the sum of 4 sources: the upper and lower RMP coils, the intrinsic error field, and the error field correction coils. It is hoped that with the RMP coils and the error field correction coils arranged optimally with the intrinsic error field, a combined field may be produced with a larger ratio of edge to core resonance, than was possible by considering only the field from the RMP coils. Referring to the KSTAR n=1 experiments[21], we may expect RMP ELM control at low n to be accessible only within a narrow window of ΔΦ, hence our reliance on predictive modelling to determine ΔΦopt. Since the error field was assessed to be thwarting the numerical predictions of optimal phase, the strategy was adjusted to optimising the phase ΔΦ empirically. The locked mode coil current threshold ILM was measured for 6 values of ΔΦ. The ΔΦ dependence of the experimental ILM was estimated to be shifted from the numerical predictions by 60 degrees. In future experiments the ΔΦ scan should be repeated at greater resolution in ΔΦ and repeated for opposite absolute phase of the field, to reduce the uncertainty in the ILM(ΔΦ) dependence, to provide data for the validation of the n=2 error field model, and to empirically determine if there exists an achievable n=2 coil configuration on MAST Upgrade for which ILM exceeds Imit. It may also be possible to directly measure the magnetic perturbation of the plasma response to validate model predictions, as described in [17]. In contrast with the lack of n=2 RMP ELM mitigation observed so far on MAST Upgrade, MAST with its larger coilset could routinely demonstrate ELM mitigation using n=3,4 and 6. It is suspected that this may be attributed to the higher n numbers which were available. With higher spatial gradients, higher n numbers have an inherently stronger coupling to the plasma edge than the core, and so are less likely to trigger locked modes, an effect compounded by the improved stability of higher n core modes relative to low n core modes. That the MAST Upgrade error field is dominantly n=2, further adds to the challenge of using n=2 RMPs for ELM control. Nonetheless, it is hoped that by rigorously including the error field in future calculations of the phase dependence of the plasma response to applied n=2 RMPs, n=2 ELM mitigation may yet be achieved and studied on MAST Upgrade.

Acknowledgements and References

Acknowledgements

This material is based upon work supported by the US Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award DE-AC02-09CH11466. This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200-EUROfusion). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. This work has been funded by the EPSRC Energy Programme [grant number EP/W006839/1]. To obtain further information on the data and models underlying this paper please contact [email protected]

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