Thermal energy mitigation and toroidal peaking effects in JET disruptions Open Access

ITER¹ and SPARC² will both operate at record high energy density for tokamak experiments. High energy density operation increases the risk of machine damage from plasma disruptions. During an unmitigated disruption, thermal energy (⁠ $Wth$⁠) is released in a fast thermal quench (TQ) and deposited on plasma facing components (PFCs), especially the divertor.³ Divertor heating in the TQ could cause melt damage and impede operation of the machine.

Damage may be prevented by a disruption mitigation system (DMS). A typical DMS injects impurities into the plasma through massive gas injection (MGI), as planned for SPARC,⁴ or shattered pellet injection (SPI), as planned for ITER.⁵ Impurities radiate and disperse the plasma thermal energy more evenly across the first wall, which avoids the otherwise concentrated heating of the divertor and reduces the risk of divertor melt damage.⁶ 

The poor $frad,th$ found on JET was not replicated on ASDEX-Upgrade (AUG), where $frad,th$ was found to be $∼1$ for both low- and high-field-side MGI.⁹ Contrasting thermal mitigation quality on these two reactor-relevant machines is an obstacle for predicting mitigation quality on SPARC and ITER.

A confounding factor in JET disruption studies is the uncertainty in $frad$ due to toroidally incomplete bolometry coverage. Mitigated disruptions produce highly three-dimensional radiation, especially during the thermal quench and “pre-thermal quench” (pre-TQ), due to localized impurities and 3D MHD modes.^13–18 In previous JET $frad,th$ studies, radiation is measured at one or two toroidal locations, and then extrapolated to full volumetric radiated power $Prad$ with the assumption of toroidal symmetry. 3D effects are often acknowledged in these studies, but are not fully accounted for due to limited toroidal coverage.

One such unquantified effect is the concentrated radiation emitted in or near the MGI gas cloud or SPI injection plume during the pre-TQ. This radiation causes a peak in the toroidal distribution of radiation around the injection location, hereafter referred to as the “plume peak” or “plume peaking”. Significant plume peaking has been observed in the pre-TQ on Alcator C-Mod with MGI,^19,20 in neon SPI experiments on KSTAR,²¹ and to a lesser degree in neon SPI on AUG.²² Plume peaking also appears in NIMROD simulations of DIII-D MGI^23,24 and in JOREK simulations of JET SPI²⁵ and ITER SPI.²⁶ 

In this paper, we investigate whether plume peaking is a significant factor in the poor $frad,th$ previously observed in JET. In Sec. II, the disruption mitigation and bolometry systems on JET are described. In Sec. III, sets of experimental MGI and SPI data are described. In Sec. IV, the evidence for plume peaking on JET is presented. In Sec. V, the Emis3D radiation analysis code²⁷ is adapted to model plume peaking on JET. In Sec. VI, the effect of plume peaking on $frad,th$ measurement is demonstrated for the MGI and SPI datasets. In Sec. VII, the implications for high $Wth$ fusion reactors are discussed.

Four disruption mitigation systems have operated on JET at various periods during its lifetime. Three MGI disruption mitigation valves (“DMVs 1–3”) operated on JET starting in 2008,¹⁰ at the locations shown in Fig. 1. In 2019, the DMV1 MGI valve was removed and replaced with an SPI injector in the same toroidal location.^5,28 Disruption studies shifted from MGI to SPI in response to the selection of SPI as the disruption mitigation method on ITER, although DMVs 2 and 3 continued to be used for machine protection in unplanned disruptions until the JET end of life in 2024.

Two large foil bolometer arrays, known together as the “KB5” bolometers, are the main diagnostics for radiated power on JET.²⁹ The arrays are toroidally separated as seen in Fig. 2. One array has primarily vertical sightlines, looking downwards from the top of the machine, and is known as “KB5V;” the other has horizontal sightlines, looking inboard from the outboard side, and is known as “KB5H.” Both arrays observe a single cross section of the plasma, with particularly high spatial resolution near the divertor, where radiation is concentrated during flattop operation. The time resolution of these two arrays in disruptions is on the order of 1 ms.

JET also had four isolated foil bolometers,²⁹ known as KB1.2, KB1.3, KB1.6, and KB1.7 according to their toroidal octant locations. These bolometers were installed and then removed from operation on JET prior to 2008. The KB1s were not operational during the 2008–2019 period when many MGI disruption studies were conducted. However, the KB1s were brought back on-line in 2019 to assist with SPI studies. The KB1 bolometers all have the same cross section view of the plasma, but are toroidally separated both from each other and from the two larger arrays. They are not absolutely calibrated, so only relative comparisons between the four individual bolometers are possible. Their relatively higher noise and slower time resolution (⁠ $∼$ 100 ms) compared to the KB5 arrays also make them unreliable for fast, sub-disruption timescale radiation analysis. However, in combination with Emis3D, the KB1s provide important information on whole-disruption toroidal peaking in SPI. Emis3D helps to accommodate the limited poloidal viewing angle of the KB1s, which is otherwise a limiting factor, as noted in Ref. 12.

MGI data analyzed in this paper come from MGI campaigns conducted between 2011 and 2016. MGI set 1 data were previously reported in Ref. 8, and MGI set 2 data were previously reported in Ref. 30. Both sets include discharges from the DMV1 injector only. The DMV2 injection data presented in Sec. IV come from mitigation campaigns referenced in Refs. 8 and 30, and were likely among the presented data, although exact discharge numbers are not known.

The SPI data in this paper come from a 2019 experimental campaign on the JET tokamak focusing on disruption thermal mitigation efficiency. A scan was conducted with identical pellet parameters and varying plasma scenarios to assess the $fth$ vs $frad$ scaling, which we will refer to as the “SPI scan” set of discharges. Scans were also conducted to assess other SPI objectives, such as the minimum required impurity quantity for good thermal mitigation. All SPI shots not included in the specific $fth$ vs $frad$ “SPI scan” will be referred to as the “SPI misc” set of discharges.

Injections in the misc dataset are more varied than those in the scan dataset. The 51 discharges in the misc set include not only varied pellet and plasma parameters, but also 15 attempted dual injections, in which two pellets were injected at the same injection location from different barrels. These cases are filtered so that only discharges with $Prad$ evolution resembling a single injection are included: either simultaneous pellet arrivals, or sufficiently late second arrivals such that the pre-TQ and TQ reflect primarily the first pellet to reach the plasma. Cases where pellets arrived in sequence before the TQ and caused multiple $Prad$ peaks are not included. The misc set is included to provide a larger context to the smaller seven-discharge scan set, but its variations should be kept in mind. The scan set is the cleaner, more direct test of the $fth$ vs $frad$ trend.

As shown in Table I, these experiments span large ranges in plasma, pellet, and/or gas parameters. All data sets are plotted independently and provide some indications of how the radiation efficiency depends on the parameters varied within the set.

$Wth$ is calculated using the diamagnetic loop on JET. This provides higher time resolution than standard EFITs, which is important to capture plasma cooling between the SPI pellet firing and the pellet arriving at the plasma. The beam power is interlocked off when the pellet is fired. $Wcoupled$ is calculated by accounting for the mutual inductance between the plasma and the various conductors surrounding it, including the vacuum vessel and poloidal field coils. The algorithm used here is the same as reported in Ref. 10.

JET was equipped with divertor infrared (IR) cameras during the 2019 SPI campaign.³¹ However, as previously noted in Ref. 12, the IR cameras cannot be used to reliably infer tile temperatures and heat fluxes on mitigated disruptions due to the high background signal. An illustration is provided here. Representative divertor images from mitigated and unmitigated disruptions are shown in Fig. 3. Both discharges in the image are from $Ip=2.5MA$⁠, B₀ = 2.5 T scenarios. The mitigated discharge has 9.5 MJ total stored energy and 4.1 MJ $Wth$ prior to disruption, while the unmitigated discharge falls to 5.7 MJ total stored energy and $<0.5$ MJ $Wth$ before disruption due to the control system anticipating the disruption and attempting a soft landing. Concentrated IR regions near strike points are clearly visible in the unmitigated disruption despite low pre-disruption $Wth$⁠, but are not identifiable in the mitigated disruption despite high $Wth$⁠. The mitigated disruption IR image is representative of most SPI discharges referenced in this paper. In unmitigated disruptions, heat fluxes from the TQ are visibly concentrated at strike points. In mitigated disruptions, IR brightness increases evenly across the divertor in the TQ, likely due to heating and reflected IR light from the radiation flash. There is no clear and separable signature of a conducted heat load in these cases. The high radiation flash loading and lack of identifiable conducted heat load are consistent with good thermal mitigation and $frad,th$ close to 1 in mitigated disruptions. However, good mitigation is not the only possible explanation for the missing conducted heat load. Heat loads could, for instance, be conducted to the wall outside of the IR camera views due to large perturbations of the strike point locations or scrape-off layer topology.

Plume peaking can be observed on JET in a small number of mitigated disruptions where the plasma thermal fraction $fth$ is high, and there is a direct bolometer view near the injection location. DMV2 disruption experiments provide the most direct evidence of plume peaking in MGI due to the proximity of the KB5V bolometer array. SPI plume peaking can also be detected using the relatively nearby KB1 bolometer channel. This section. will focus on plume peaking observed from these sources. The two remaining MGI valves, as well as machine protection discharges from DMV2, are discussed in  Appendix A.

During a pre-TQ induced by DMV2 MGI, the KB5V array measures much higher brightness than the KB5H. In discharges from a DMV2 mitigation study, $Prad,V$ is higher than $Prad,H$ throughout the pre-TQ (Fig. 4). Summed over the entire pre-TQ, $Wrad,pre,V>Wrad,pre,H$ by around 7× on average (Fig. 5). The peaking ratio is highest just after injection and decreases approaching the thermal quench. When separated into an “early pre-TQ” (⁠ $>2$ ms before the TQ) and “late pre-TQ” (⁠ $<2$ ms before the TQ), $Wrad,early,V>Wrad,early,H$ by around 9 or 10× for high- $fth$ discharges and even more for low $fth$ discharges, while $Wrad,late,V>Wrad,late,H$ by a smaller factor of around 3.5×. These signals are the most direct evidence of plume peaking from JET bolometry.

Plume peaking can also be observed in SPI due to a relatively nearby KB1 bolometer. The SPI injection port was $23°$ toroidally separated from KB1.2, and at least $67°$ distant from the other three channels. In high $fth$ discharges from a 2019 SPI study, the KB1.2 channel sees higher brightness than the other three channels, often by a factor of $∼$ 2 (Fig. 6). Low $fth$ discharges typically do not see peaking of this magnitude (Fig. 7). This peaking was previously reported in Refs. 11, 12, and 29, and was attributed to peaking before the current quench (CQ). That hypothesis is expanded upon as follows:

While the ratios between KB1 bolometers show peaking at some point during the disruption, this is not direct evidence of exclusively pre-TQ peaking. Because of their slow time resolution, the KB1s do not easily distinguish between the pre-TQ, TQ, and CQ stages of the disruption; they measure only cumulative peaking over the entire disruption, and the observed peaking could conceivably be primarily in the TQ or CQ. However, the early CQ typically has good axisymmetry, as seen in Fig. 4.

The late CQ is similarly unlikely to cause of the observed KB1 asymmetries. While the late CQ is sometimes asymmetric due to vertical displacement or other effects, total $Prad$ is likely too low in this stage to dominate the KB1 measurement, and there is no obvious reason for this asymmetry to consistently peak at the same toroidal location or to vary with pre-disruption $fth$⁠, as the KB1 measurement does.

TQ asymmetries would be more likely to cause the asymmetry seen in the KB1s than CQ asymmetries. However, a recent SPI investigation on JET by Piron et al. using the KB5 bolometer arrays in combination with TQ direction from the error field correction coils found that the TQ is actually less peaked if $fth$ is high;³² the opposite of the trend seen in the KB1s. These apparently opposite trends may be reconciled if the observed KB1 peaking is dominated by heavy peaking in the pre-TQ, similar to the plume peaking seen in neon SPI on KSTAR.²¹ The study by Piron et al. examines only peaking at the height of the TQ, which has very high $Prad$⁠, but its relative brevity and lower peaking compared to the pre-TQ could cause pre-TQ effects to dominate the whole-disruption KB1 measurement. An alternate hypothesis in which TQ peaking is a significant contribution to the KB1 measurement asymmetry is addressed in Sec. VI.

In combination, the DMV2 and SPI bolometry data suggest significant plume peaking in both MGI and SPI on JET, particularly in the case of high $fth$⁠. Plume peaking observations on JET are not significantly challenged by radiation frequency sensitivity, as they may be on other machines. Observations of plume peaking in C-Mod and KSTAR were primarily made with AXUV photodiode detectors. Photodiodes are desirable for their fast time resolution, but sometimes have frequency sensitivity variation, including a reduced sensitivity to the vacuum ultraviolet frequencies that dominate most mitigated disruptions.¹² Resistive foil bolometers have flat frequency sensitivity, and the resistive bolometers on JET corroborate the AXUV-based observations from other machines.

Disruption radiation is analyzed with Emis3D²⁷ to better account for the 3D nature of pre-TQ radiation. $Prad$ and $Wrad$ are typically measured on JET using weighted averages of bolometer channels in the KB5 arrays. More sophisticated 2D tomography approaches are also available to reconstruct radiation cross sections, including Lagrangian optimization,³³ neural networks,³⁴ and maximum likelihood methods.³⁵ These methods are typically used at times when the plasma is approximately toroidally symmetric, including flattop operation and the current quench. However, pre-TQ radiation and impurity distributions are known to be highly three-dimensional. 2D tomographic approaches do not fully capture the 3D radiation structures at the relevant times for plume peaking. Full 3D variations on these methods are also challenged by the low toroidal resolution of available JET bolometry, with fast bolometry data available at only the two toroidal locations of the KB5 arrays.

Emis3D addresses the low toroidal resolution difficulty with a “guess-and-check” forward modeling approach, using reduced $χ2$ goodness-of-fit testing to identify the best-fit radiation structure from a user-controlled library of possible structures. In the case of the pre-TQ, helical field-line centered structures are often found to be the best fits. Constraints in the radiation structure definitions overcome the otherwise under-determined problem of 3D modeling with low toroidal resolution. Emis3D does not reconstruct radiation structures at the same level of detail as the above-mentioned 2D methods, but it does capture the 3D nature of the pre-TQ. See Ref. 27 for a more detailed description of the Emis3D algorithm.

In this analysis, we follow the radiation structure algorithm described in Ref. 27 with a variation on the toroidal distribution of fitted radiation structures. Pre-TQ radiation is modeled by field-line-centered helical structures, with a bivariate Gaussian cross section. Helical pre-TQ radiation structures following magnetic field lines are consistently observed in mitigation, both in simulation and experiment.^{4,18,23,36,37} Radiation sources are susceptible to various drifts, including grad-B drifts,^38,39 ExB drifts or other poloidal flows,⁶ and even ablation rocket effects⁴⁰ in the case of pellet injection. Poloidal motion of radiation structures is captured in Emis3D by the reduced $χ2$ fitting process, as the radiation structure is fitted independently at each timestep to match the bolometry data as it evolves. Higher-order drift effects such as 3D distortion of the radiation structure may not be captured, although helical structures on JET typically appear in fast camera images to retain their shape well in the pre-TQ despite drifts, as seen in Ref. 37.

The asymmetric Gaussian toroidal distribution of helical radiation structures in Ref. 27 is used here as a reference case. The asymmetric Gaussian toroidal distribution captures the broader toroidal behavior of the radiation structure constrained by the KB5 bolometers, but does not capture plume peaking directly in front of the injector, and is referred to as the non-plume-peaked radiation model. A simple, top hat-shaped feature is added to the reference toroidal distribution to investigate the effect of plume peaking, as described in Fig. 8.

The flat “top hat” peaking model is used to make direct and simple comparisons to the bolometry data in Figs. 5 and 7, and is not intended to represent the true shape of the plume. The plume is likely closer approximated by a smoother distribution like a Lorentzian. However, this study addresses a broad range of injection parameters, with high variation both between injectors and between discharges from the same injector, and the low toroidal bolometry resolution is insufficient to determine plume parameters on individual discharges. Injection characteristics can also vary significantly between devices and between simulation and experiment. While plume characterization studies^41–43 help inform expectations of plume behavior, applying their scalings without direct experimental JET data introduces additional degrees of freedom that we cannot constrain. Appropriately tailoring plume models for each injection in this study would test the limits of disruption diagnostics on JET even more than we attempt in this study. We instead address the more limited question of how $frad,th$ scales with the magnitude of the plume, and use the simplified top hat model to determine reasonable bounds for this effect.

For DMV1 MGI, the height of the plume is set to the scaling factors identified in Fig. 5, with 10× higher radiation in the plume than that observed at the horizontal bolo at each timestep in the early pre-TQ, and 3.5× higher in the late pre-TQ. DMV1 MGI is selected for Emis3D analysis because the toroidal fitting step of the Emis3D algorithm is best suited to injections in octant 1, and in particular, may be challenged by the injection plume directly in front of the KB5V array in DMV2 injections; and for its ease of comparison to SPI injections at the same toroidal location. The relatively similar toroidal distances between the DMV2 and DMV1 MGI valves and the KB5H array assist with scaling plume height to the KB5H array, although the possibility of asymmetries in toroidal impurity spread from the injection location, such as the magnetic nozzle effect noted in Refs. 24, 44, and 45 are acknowledged. No plume peaking is applied to the TQ, defined for this purpose as the timestep of peak radiation to a time resolution of 0.5 ms, or to the CQ.

For SPI, the height of the plume is set with the same scaling factors as MGI for $fth>0.2$⁠, and no plume is included for $fth<0.2$⁠, to most closely match the KB1 experimental data, as shown in Fig. 9. By comparing the plume-peaked model to the non-peaked reference case, we can identify and estimate the previously unexplored effect that plume peaking has on thermal mitigation efficacy.

Another change from Ref. 27 is the toroidally self-similar radiation structures used to model the thermal and current quenches. In Ref. 27, the radiation structures at these times are based on BOLT 2D Lagrangian optimized reconstructions. BOLT reconstructions are designed for axisymmetric plasmas. They include assumptions that radiation spreads poloidally along magnetic surfaces, and these magnetic surfaces are taken from the pre-disruptive magnetic geometry. The plasma's location and its magnetic geometry change significantly in the current quench, in particular often moving inboard [referred to elsewhere as a plasma movement event (PME)⁴⁵], possibly due to the loss of plasma pressure. BOLT reconstructions based on pre-disruptive magnetic geometry may be unable to capture this motion correctly. In this study, we instead model TQ and CQ radiation as elongated, toroidally self-similar, bivariate Gaussian-shaped radiation structures, referred to as “elongated rings” or “e-rings.” These structures are less sophisticated than BOLTs, and typically produce worse $χ2$ goodness-of-fit to the experimental bolometry data, which would typically indicate a less precise fit. However, e-rings are not tied to pre-disruptive magnetic geometry, and are more likely to correctly represent bulk motion of plasma radiation during the TQ and CQ, and its effect on KB1 signals and $frad,th$⁠. See Ref. 27 of Sec. V for discussion of BOLTs in Emis3D.

Plume peaking in the thermal or current quench is not included in this study. Injection plume effects are unlikely to persist through the TQ into the CQ, and while TQ radiation is known to be highly three dimensional, it is not well captured by the same field-line centered radiation models as the pre-TQ, due to fast evolving MHD activity and impurity transport. In this study, the simple step-function toroidal radiation distribution described in Ref. 27 is used for both TQ and CQ radiation structures. TQ and CQ radiation structures and peaking are not varied on any given shot, and are held the same for all of the pre-TQ variations specified in Fig. 8, in order to isolate the specific effect of pre-TQ plume peaking.

Plume peaking-aware analysis increases the measured $frad,th$ in both MGI and SPI mitigated disruptions on JET relative to plume peaking ignorant approaches. In SPI, significant plume peaking is only observed at high $fth$⁠, raising $Wrad$ only at high $fth$ and raising the resulting $frad,th$ (Fig. 10). In DMV1 MGI, peaked radiation is present at both high and low $fth$⁠, but total pre-TQ radiation is lower at low $fth$⁠, so $Wrad$ is raised more significantly at high $fth$ again, resulting in a higher $frad,th$ measurement (Fig. 11).

$frad,th$ varies significantly with the toroidal width of the radiation plume feature, so various plume width cases are presented as approximate lower and upper bounds on the space of $frad,th$⁠.

The “wide” case corresponds to a plume toroidally spanning $135°$ centered on the injection location, reaching from the SPI barrel in octant 1 to the KB1.3 bolometer, numbered after its location in octant 3. Because the plume feature does not appear to reach the KB1.3 bolometer in SPI discharges, the plume can be no greater than this width, and this case bounds the SPI plume width from above. This case is also used as an approximate upper bound for DMV1 MGI injections, as the $135°$ width centered at DMV1 is just short of the KB5V array, which the DMV1 MGI plume does not reach.

The “narrow” case corresponds to a plume toroidally spanning $45°$ centered on the injection location, just reaching from the SPI barrel to the KB1.2 bolometer in octant 2. Because the plume feature does reach the KB1.2 bolometer in SPI discharges, the plume can be no narrower than this, and this case bounds the plume width from below in the case of SPI. In the case of MGI, where KB1 data are not available, the “no peaking” case is used as the lower bound.

The “moderate” case corresponds to a plume of $90°$⁠, halfway between the wide and narrow cases, and is neither a lower nor an upper bound but serves as an additional point of interest for both MGI and SPI.

$frad,th$ is estimated simply as $frad,th=1+m$⁠, where m is the slope of the line of least squares fit for a given set of disruptions $frad$⁠. Higher-order fitting is impeded by the large scatter between shots in both MGI and SPI. MGI analysis shows some increase in $frad,th$ over plumeless analysis, but not full mitigation. SPI analysis shows a significant increase in $frad,th$ over plumeless analysis, and a moderate width plume shows full mitigation (⁠ $frad,th∼100%$⁠). The use of the simplified top hat model may particularly under-represent the plume magnitude in the narrow width case, as a more smoothly peaked plume shape with similar brightness at the KB1.2 toroidal location would imply higher radiation near the injector and overall greater $Wrad$⁠.

The wide plume case for SPI results in both total $frad$ and $frad,th$ well in excess of 100%, and is therefore likely an inaccurate plume model. $frad>1$ on individual discharges may be attributed to the large uncertainties typical of disruption bolometry and $Prad$ reconstruction, but overall $frad,th>1$ is inconsistent with energy conservation. Plumes of narrow to moderate width are more consistent with both the KB1 bolometry data and the energy conservation requirement.

Thermal mitigation on JET with either SPI or MGI appears to be significantly more effective than previously predicted, as shown in Table II. Neon SPI achieves full thermal mitigation if the injection plume is moderately wide. Lower limits of $frad,th=84%$ and 92% are reported for two sets of SPI disruptions under the narrowest plume width assumptions. MGI does not appear to reach full thermal mitigation, but better mitigation is observed when including injection plume radiation in the measurement, with upper limits of $frad,th=65%$ and 85% for two sets of disruptions, compared to $frad,th=28%$ and 42%, respectively, with no plume model.

The “unpeaked” cases do not include a plume model, but do account for 3D helical radiation structures in the pre-TQ. These cases show higher $frad,th$ in SPI than initially suggested by Ref. 11 where $frad,th$ appears to be $<50%$ for the larger set of shots in particular (mostly the same list as SPI set 2). Sweeney¹¹ and Sheikh et al.¹² both explored corrections to these initial findings using an early version of Emis3D, in which the entire pre-TQ and TQ stages of each discharge were fitted to a single radiation structure. Their results indicated that fully accounting for the 3D structure might improve $frad,th$⁠. The further developed Emis3D analysis in this paper may corroborate their work, demonstrating higher $frad,th$ with helical pre-TQ analysis. However, we also demonstrate that thermal radiation is not fully accounted for just by capturing the helical structure of the pre-TQ, as injection plume radiation contributes significantly and was not previously included.

The described $frad,th$ ranges represent best estimates based on available bolometry data. They are limited by the large variation in radiation structures and bolometry measurements between disruptions, even among identically prepared plasmas, as seen in Ref. 27. Additional sources of uncertainty include, but are not limited to:

1. Abstraction of the plume's toroidal extent to a top hat model.

2. The simplifying assumption that the plume width is constant with $fth$ and constant in time.

3. Bolometry time resolution limitations.

4. The coarse binning of plume peaking ratios into early and late pre-TQ.

5. Use of plume peaking ratios derived from MGI discharges to estimate peaking in SPI, which could have different time evolution (time-resolved bolometry at the SPI location is not available to capture SPI peaking ratios).

6. Restriction of plume radiation analysis to the pre-TQ, excluding any plume peaking in the TQ.

(6) is the simplest way in which the peaking seen in the KB1s agrees with the findings of Piron et al., as discussed in Sec. IV. If (6) is incorrect, and peaking extends into the TQ, then the peaking ratios applied in our analysis for the pre-TQ are likely too high, and peaking in the TQ is too low. The net result would be a shift in the timing of plume radiation from the pre-TQ to the TQ, but still overall higher thermal radiation than without a plume model. Similarly, (1)–(5) could all significantly affect $Wrad,th$⁠, but are unlikely to change the qualitative result of increased $frad,th$ when including injection plume radiation.

The plume peaking observed in this paper suggests significant thermal radiation in the pre-TQ in mitigated disruptions. Significant pre-TQ thermal energy loss runs counter to the common conception that nearly all thermal energy is lost in the TQ, and the fraction of thermal energy lost in the pre-TQ may be of interest. Thermal radiation in the pre-TQ, as a fraction of total pre-disruption thermal energy, is reported in Table III, averaged over each set of discharges. Low $fth$ SPI discharges are presented separately from their sets, as the plume peaking cases apply only to the high $fth$ discharges. The pre-TQ thermal energy loss fraction appears particularly high in low $fth$ discharges, for SPI especially and to a lesser extent in MGI as well. This may be influenced by small fractions of magnetic energy lost in the pre-TQ and TQ, which is negligible when $fth$ is high, but not when it is low. Note also that pre-TQ and TQ are defined in this paper relative to the time of highest $Prad$⁠, which may vary slightly from values derived from core confinement diagnostics.

Effective thermal mitigation on JET is a positive indicator for successful thermal mitigation on ITER and SPARC. In particular, the ITER mitigation criterion of $frad,th≥90%$ with SPI appears to be closely approached or achieved on JET when accounting for plume peaking. The SPARC criterion of $frad,th≥90%$ with MGI is approached in some cases, but is not achieved with moderate plume width assumptions. Full thermal mitigation with MGI has previously been reported on AUG.⁹ 

The disagreement between full thermal mitigation in AUG MGI and incomplete thermal mitigation in JET MGI is not fully eliminated by the JET $frad,th$ reported here. The cause of the remaining discrepancy is an open question. Greater distance between the MGI valves and the plasma boundary on JET, as well as the $∼$ 2× larger major radius, have been suggested as possibly causing a less abrupt, more protracted gas delivery, reducing the quantity of impurity assimilated before the thermal quench. Additional gaps in radiation modeling and analysis are also possible.

Plume peaking presents a possible increased risk of fast heating or flash melting of plasma-facing components near MGI and SPI injection locations. Flash melting of first wall tiles is of less concern on ITER after the material design change from beryllium to tungsten,^46,47 but exposed steel or diagnostic components may still be vulnerable. Flash melting is similarly a concern for diagnostic components on SPARC. The risk may be reduced by injecting simultaneously at multiple toroidal locations, as planned for SPARC and previously explored with MGI in Ref. 20. The SPARC design includes MGI systems at six evenly distributed toroidal angles.⁴⁸ ITER has three midplane and three off-midplane SPI systems planned across four toroidal angles,⁴⁹ which could in principle be used simultaneously, as explored in Refs. 18 and 26.

This work has been carried out within the framework of the EUROfusion consortium, partially funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200—EUROfusion). The Swiss contribution to this work has been funded by the Swiss State Secretariat for Education, Research and Innovation (SERI). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union, the European Commission, or SERI. Neither the European Union nor the European Commission nor SERI can be held responsible for them.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award No. DE-SC0014264. The views and opinions expressed herein do not necessarily reflect those of the Department of Energy.

The JET SPI project is a collaborative effort of EURATOM, the ITER organization, and the U.S. Department of Energy. It received funding from the ITER organization. The views and opinions expressed herein do not necessarily reflect those of the ITER organization.

The authors have no conflicts to disclose.

B. Stein-Lubrano: Conceptualization (equal); Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). R. Sweeney: Conceptualization (equal); Investigation (equal); Supervision (equal); Writing – review & editing (equal). J. Lovell: Investigation (supporting). L. Baylor: Investigation (supporting). D. Bonfiglio: Investigation (supporting). P. Carvalho: Investigation (supporting). R. Granetz: Supervision (equal). S. Jachmich: Investigation (supporting). E. Joffrin: Project administration (equal). M. Lehnen: Investigation (supporting). C. Maggi: Project administration (equal). E. Marmar: Supervision (equal). P. Puglia: Investigation (supporting). J. Rice: Supervision (equal). U. Sheikh: Investigation (supporting). D. Shiraki: Investigation (supporting). S. Silburn: Investigation (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Plume peaking is not as easily observed in either DMV1 or DMV3 disruption experiments due to more distant bolometry, as well as typically lower gas injection quantities in the case of DMV3. The KB1 bolometers were not operational in the 2008–2019 period of MGI studies, and DMV1 is not close to either large bolometer array. The DMV3 valve is toroidally separated $34°$ from the KB5H array, which is three times more distant than the DMV2 is from KB5V, but could be spanned by a wider plume. In discharges from a DMV3 mitigation study, we generally do not see clear evidence of plume peaking; in fact, $Prad,V$ is generally higher than $Prad,H$ in the pre-TQ (Fig. 12). However, these injections have very low gas injection quantities of typically $<=1bar−L$⁠, an order of magnitude lower than the quantities of the DMV2 and DMV1 injections considered elsewhere in this paper. In the few identified shots with higher gas injection quantity of $>1bar−L$⁠, $Prad,H$ is greater than $Prad,V$ in the pre-TQ, but the low ratio and total power in these cases does not provide a clear match to the high peaking seen in DMV2.

Some DMV2 machine protection injections may also show pre-TQ peaking in the KB5 bolometer arrays, but peaking is not consistently evident in the nearby KB1 bolometer (for post-2019 discharges). The large arrays are not typically calibrated for disruption radiation loads in unplanned disruptions, and tend to saturate, flatline, or otherwise make comparison to the CQ difficult. In addition, $fth$ often falls during disruption precursors before the MGI is triggered, which may explain why significant peaking is not often seen in the KB1s for these discharges. Plume peaking appears to be most easily observed in planned DMS experiments into healthy plasmas, where $fth$ can be high just before injection, and bolometer sensitivities are set to handle high disruption brightnesses.

A representation of the experimental and synthetic bolometer channel brightnesses fitted in Emis3D is included in Fig. 13 as a visual aid. Note that Emis3D synthetic radiation structures are broad to capture the correct overall radiation shape, rather than tailored structures to precisely match each channel.