Understanding JET-C quiescent phases with edge harmonic magnetohydrodynamic activity and comparison with behaviour under ITER-like wall conditioning

Plasma Physics and Controlled Fusion PAPER • OPEN ACCESS Understanding JET-C quiescent phases with edge harmonic magnetohydrodynamic activity and comparison with behaviour under ITER-like wall conditioning To cite this article: D Brunetti et al 2022 Plasma Phys. Control. Fusion 64 044005 View the article online for updates and enhancements. You may also like ELM-free and inter-ELM divertor heat flux broadening induced by edge harmonics oscillation in NSTX K.F. Gan, J.-W. Ahn, T.K. Gray et al. - Observation of ELM-free H-mode in the HL-2A tokamak W.L. Zhong, X.L. Zou, X.R. Duan et al. - ECEI characterization of pedestal fluctuations in quiescent H-mode plasmas in DIII-D Guanying Yu, Raffi Nazikian, Yilun Zhu et al. - This content was downloaded from IP address 150.214.182.235 on 04/09/2024 at 15:18 Plasma Physics and Controlled Fusion Plasma Phys. Control. Fusion 64 (2022) 044005 (12pp) https://doi.org/10.1088/1361-6587/ac4d3a Understanding JET-C quiescent phases with edge harmonic magnetohydrodynamic activity and comparison with behaviour under ITER-like wall conditioning D Brunetti1,∗, C J Ham1, J P Graves2, E Lazzaro3, S Nowak3, A Mariani4, C Wahlberg5, W A Cooper6, E R Solano7, S Saarelma1, L Frassinetti8, M Fontana2,11, A Kleiner9, G Bustos Ramirez2, E Viezzer10and JET Contributors12 1UKAEA-CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB, United Kingdom 2´ Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland 3Istituto per la Scienza e Tecnologia dei Plasmi CNR, Via R. Cozzi 53, 20125 Milan, Italy 4Dipartimento di Fisica ‘G. Occhialini’, Universit` a di Milano-Bicocca, Milan, Italy 5Department of Physics and Astronomy, Uppsala University, PO Box 516, SE-751 20 Uppsala, Sweden 6Swiss Alps Fusion Energy (SAFE), CH-1864 Vers l’Eglise, Switzerland 7Laboratorio Nacional de Fusión, CIEMAT, Madrid, Spain 8Division of Fusion Plasma Physics, KTH Royal Institute of Technology, Stockholm, SE, Sweden 9Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, United States of America 10 Department of Atomic, Molecular and Nuclear Physics, University of Seville, Avda. Reina Mercedes, 41012 Seville, Spain E-mail: [email protected] Received 6 October 2021, revised 17 December 2021 Accepted for publication 20 January 2022 Published 18 February 2022 Abstract An analysis of edge localised mode-free (quiescent) H-mode discharges exhibiting edge harmonic magnetoydrodynamic activity in the JET-carbon wall machine is presented. It is observed that the otherwise quiescent pulses with multiple-nharmonic oscillations are sustained until a threshold in pedestal electron density and collisionality is crossed. The macroscopic pedestal parameters associated with the quiescent phase are compared with those of a database of JET-ELMy discharges with both carbon and ITER-like wall (ILW). This comparison provides the identification of the existence regions in the relevant pedestal and global plasma parameters for edge harmonic oscillations (EHOs) in JET plasmas. Although the ELMy 11 Present address: UKAEA-CCFE Culham Science Centre, Abingdon, Oxon OX14 3DB, United Kingdom. 12 See the author list of ‘Overview of JET results for optimising ITER operation’ by Mailloux et al to be published in Nuclear Fusion Special Issue: Overview Summary Papers from the 28th Fusion Energy Conference (Nice, France 10–15 May 2021). ∗Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1361-6587/22/044005+12$33.00 Printed in the UK 1 © 2022 Crown copyright. Reproduced with the permission of the Controller of Her Majesty’s Stationery Office. Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al database scans pedestal collisionality and βvalues typical of ET-carbon quiescent operation, shaping and current are not simultaneously compatible with EHO existence. Nevertheless, ILW operation with JET-carbon quiescent-like parameters could in principle be achieved, and improved pedestal performance could be observed in more recent JET-ILW pulses. Keywords: tokamak, JET, QH-mode, EHO, ELMs (Some figures may appear in colour only in the online journal) 1. Introduction The most promising scenarios for achieving efficient controlled thermonuclear fusion in tokamak machines are the so called high-confinement (H-mode) regimes. Such scenarios show long energy confinement times and are typically characterised by the presence of sharp and narrow plasma edge pedestals, both in mass density and temperature. Unfortunately, the associated strong radial gradients favour the appearance of short wavelength magnetohydrodynamic (MHD) perturbations called edge localised modes (ELMs) [1]. These sudden and violent events are associated with rapid energy and particle expulsions which deposit intolerable heat loads on plasma facing components. In addition to severe plasma contamination, ELMs can significantly reduce machine lifetime. Therefore, it is of crucial interest to attain high-performance scenarios without the deleterious presence of ELMs [1]. One of the most promising intrinsically ELM-free regimes is the so called quiescent H-mode. In this regime, which shares with the standard H-mode large edge pressure gradients and long energy confinement times, ELMs are avoided and replaced by continuous low-nmild MHD perturbations, and the associated peak energy and heat loads on the plasma facing materials are significantly lower compared to ELMy regimes. These edge harmonic oscillations (EHOs) are well localised within the edge region of large gradients (pedestal) and feature multiple ntoroidal harmonics with a rather long lifetime, of the order of 1 s [2]. EHOs have been observed in DIII-D, ASDEX-U, JT60 [3–6], and JET [7]. In [7] such oscillations are called Outer Modes. Since the MHD dynamics described in [3,4,7]. have the same characteristics, for the sake of clarity, hereafter we will refer to such oscillations as EHOs13. As observed in [7], EHOs have several common features with the low-ntype-I ELM precursors studied in [10]. It is observed that EHOs in JET are prone to develop in the early phase of the discharge, during the density ramp when ion and electron temperatures reach their highest values at the pedestal top. It is also observed that above a critical value of the pedestal density (∼5×1019 m−3) the quiescent phase with EHOs abruptly ends and ELMs appear. We point out that quiescent regimes in DIII-D, ASDEX-U and JT60-U experiments [3–6] usually operate with lower values of the pedestal top density compared with JET, typically three or four 13 Historically, Outer Modes refer to low-n(mainly n=1) MHD oscillations with frequencies ∼10 kHz observed typically within the outer 20% of the plasma [8,9] (broader compared to EHOs). In [9], Outer Modes refer to current driven external kinks. times smaller. Although for some discharges EHOs can reemerge after an ELM crash, the quiescent phase is not usually recovered after the first ELM is triggered. Thus, the aim of this paper is to detail and characterise the existence conditions for EHOs in JET, in order to determine the pedestal features required to guarantee the accessibility to quiescent regimes with EHOs, and potentially in machines with a metallic wall. These existence conditions are assessed by comparing global and pedestal parameters, namely electron β, collisionality, q95 and triangularity, of quiescent with EHOs (Q-EHO) shots with the ones extracted from a carbon (C) and ITER-like wall (ILW) EUROfusion pedestal database of ELMy discharges [11,12]. It is found that the operational regime of Q-EHO plasmas identified by the parameters given above does not overlap the one explored by the ELMy database. This holds in particular for ILW plasmas where the electron temperature, which plays a crucial role, is significantly smaller compared to carbon wall discharges. We finally point out that some indications of brief edge coherent activity have been observed in recent hybrid JET-ILW shots with high pedestal performance. Although these oscillations have been observed transiently, efforts are now focussed on steadily sustaining this behaviour in metal machines [13]. Thus, the paper is organised as follows: In section 2we describe the JET-C experimental set-up and the typical features of the EHOs which are observed during the quiescent phase. In section 3we analyse a database of JET discharges with a carbon and ILW, which although exhibiting quiescent compatible pedestal parameters are in ELMy regime. This is done by inspecting the associated physical global and pedestal parameters (e.g. collisionality, temperature, etc). These parameters are then compared with the ones observed in the Q-EHO JET-C pulses analysed in section 2. By assessing the differences between JET-C plasmas with EHOs and the ELMy database, we infer the conditions that have to be met to achieve quiescent operation, and in particular whether such conditions are compatible with a metallic wall. Finally, a discussion of the results and concluding remarks are given in section 4. 2. JET-C quiescent discharges with EHO activity 2.1. Experiment and analysis setup We analyse a set of four JET-C discharges showing a quiescent ELM-free phase in which coherent edge EHOs are observed. These pulses feature a hot-ion H-mode phase [7,14], obtained by reducing particle fuelling from external sources and wall with an initial operation at low plasma density and fairly high 2 Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al Table 1. Macroscopic global plasma parameters for four JET-C discharges with EHO activity. Triangularity is computed by averaging between its upper and lower values. For each pulse, βN,q95,κ, and δare averaged over time window t1−t2. Note the ≈30%reduction in the injected NBI power in #79455. Shaping, i.e. κ, and δ, and q95 take similar values across the four pulses. Shot # Bt(T) Ip(MA) NBI (MW) βNt1(s) t2(s) tELM (s) q95 κ δ 75411 2.7 2.5 15.3 1.94 14 16 15.4 3.37 1.72 0.41 78012 2.7 2.5 16.8 1.87 13.6 16 14.65 3.36 1.73 0.39 78014 2.7 2.5 16.7 1.98 13.8 16 14.23 3.38 1.73 0.41 79455 2.7 2.5 11 1.67 14 16 14.85 3.3 1.71 0.40 co-current NBI power yielding very high ion temperatures. This was specifically designed for achieving high pedestal temperatures. Bolometry and Dαemission confirm the ELMfree phase, and the EHO identification is achieved by matching the mode rotation frequency inferred from magnetic signals with the one obtained by edge electron temperature fluctuation measurements [15] (see the next subsection for further details). This provides a unique mode identification for toroidal spectral structure and spatial localisation. The requirements for the pulse selection are (i) a relatively long quiescent phase duration, and (ii) diagnostic signal clarity, i.e. all of the EHO footprints must be clearly visible on all the relevant diagnostics. The pulse numbers of the four discharge analysed in this work are listed in table 1, which also reports the vacuum toroidal field Btat the plasma geometric centre, the plasma current Ip,βN(see [3] for the definition), q95, elongation κand triangularity δ. The NBI input power is also given, as well as the time window t1−t2within which the analysis is performed. The EHO appears approximately at t1, whereas tELM indicates the time when the quiescent phase with EHOs is lost and the plasma enters the ELMy regime. At time t2the plasma is deep into the ELMy phase. Other quiescent discharges sharing very similar features with the ones reported in table 1with a likely EHO activity, have not been analysed because of the lack of clarity on some of the diagnostics signals. Error field correction coils (EFCCs) for ELM control were employed in discharges #78012 and #78014. In both pulses the coil current was ramped up and down in 100 ms, with the current flat-top of ±0.5 and ±1 kA for shots #78012 and #78014 respectively lasting from t=14.1 s to t=15.9 s (the plus/minus sign refers to 1–5/3–7 octants). No EFCCs were employed in pulses #75411 and #79455. The ICRH heating is switched on only at the very end of each pulse, so that we regard these shots as Ohmically and NBI heated. All pulses in table 1exhibit similar behaviour, in which the electron temperature increases all across the plasma core region during the early phase when the NBI is switched on, and whose power is steadily maintained for the whole discharge (cf figure 8in section 2.3). At the same time, the plasma density neis ramped up, reaching the stationary core value >7−8×1019 m−3. The value of the pedestal density rises accordingly, as shown in figure 1from high resolution Thomson scattering (HRTS) measurements. The corresponding values of ion (charge exchange) and electron (HRTS) pedestal temperatures, Tiand Terespectively, are shown in figure 2. Details on the definition of pedestal quantities, e.g. height and Figure 1. Evolution of the pedestal density for the discharges of table 1. A steady increase in nped eis observed. The dashed vertical lines in each plot indicate the appearance of the ELM after which the Q-EHO phase is lost. Note the large errorbars in the pedestal density value after the first ELM in shot #79455 (errorbars are obtained by a weighted fit of HRTS data). width, are detailed in [16]. The density rise is accompanied by an increase of the effective charge Zeff which ranges approximately from 1.8 to 2 during the quiescent phase, whereas during the ELMing stage reaches values up to 2.5. We observe that in pulse #78014, the EHO disappears at t=14.23 s despite the low pedestal density, and a sudden increase of nped e occurs after the appearance of the first ELM. The EHO loss may be caused by variations in the global temperature profile which are not captured by the local pedestal analysis (see section 2.5). As the mass density is ramped up, the toroidal rotation vtor (obtained from charge exchange measurements, cf figure 3) is observed to reduce whereas βNremains approximately constant. Note that in JET the NBI is co-current [17]. In the time window indicated in table 1, ion and electron temperatures tend to decrease, with Tiexhibiting smaller gradients in the pedestal compared with Te.Tiand vtor are found to have similar radial dependencies. We point out that during the quiescent phase the ion temperature at the pedestal top is slightly larger on average compared with Te, the former taking values 3 Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al Figure 2. Evolution of the pedestal ion (red) and electron (blue) temperatures for the discharges of table 1.Tiis obtained from charge exchange measurements, whereas Tefrom HRTS. Note that the ion temperature has a more pronounced decrease during the pulse evolution compared to Te. Figure 3. Time evolution of the toroidal (C) rotation profile for discharge #78012 from charge exchange measurements in the time window indicated in table 1(early times in red, later ones in dark blue). Error bars are not shown for the sake of visual clarity. A steady decrease of the core rotation frequency is observed. Note that the separatrix position is allowed to vary within the region delimited by the dashed vertical line. of about 2 keV whereas the latter is ∼1.4–1.5 keV at the EHO onset. The two temperatures get closer after the appearance of the first ELM. 2.2. Characterisation of MHD dynamics Very rich MHD dynamical behaviour is observed during the early NBI heating phase as clearly shown in figure 4. EHOs however behave similarly in all four shots of table 1with a lifetime of ∼0.5–1 s. In pulse #78014, after an internal (core) temperature crash at t=13.68 s, a steady EHO is sustained Figure 4. MHD mode analysis inferred from high bandwidth pick-up coils signals of the early phase of discharge #78014. After an internal temperature crash at t=13.68 s, a MHD activity with multiple harmonics up to n=7 is observed from t=13.8 s to t=14.2 s (highlighted in the dashed box). Brief coherent MHD bursts localised in the pedestal region appear before ELM crashes at 14.35, 14.45 and 14.53 s, resembling the type-I ELM precursor activity discussed in [10]. for ∼400 ms starting at t=13.8 s (cf table 1). Each toroidal harmonic with mode number nof the EHO rotates with frequency nΩped where Ωped is the rotation frequency at the pedestal top [7]. After the steady EHO phase is lost, short lived pre-ELM EHO bursts with multiple low-nharmonics appear from 14.3 to 14.5 s. We point out that similarities between EHOs (or Outer Modes) and the low-nELM precursors studied in [10] have been pointed out in [7]. The latter appear as multiple ncoherent oscillations localised at the plasma boundary, and were observed frequently in hot-ion H-mode regimes [10]. The poloidal spectral structure of these low-nELM precursors features poloidal mode numbers comparable or slightly larger than q95, and we expect EHOs to have similar characteristics. Indeed, as described in [7], the magnetic signal was found to have a strong m=4 component. Note that this is also consistent with recent findings in [18], where a thorough description of the magnetic spectrum is given. During the density ramp-up, when the electron temperature is the highest, a clear signature of multiple nharmonics all equally spaced in the frequency domain appear on the magnetic diagnostics. In order to assess the radial location of these MHD modes, and therefore identify their EHO-like nature, in analogy with [5,15] the magnetic measurements are compared with the electron cyclotron emission (ECE) signals. The EHO is uniquely identified by matching the rotation frequencies of the various harmonics measured by the two diagnostics. The ECE channel distribution and location in the major radius of the outer midplane is given in figure 5. Note that for all the shots listed above, channels 54 and 66 are usually associated with pedestal measurements (odd number channels were not available). 4 Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al Figure 5. Temperature profile of shot #75411 showing the major radius location of the ECE lines of sight. Note that in all discharges listed in table 1, the pedestal ECE emission is, with a good approximation, associated with channel 66 (highlighted in red). Channel 56 is the nearest-non pedestal channel, so that it is always inspected to check the edge mode localisation. It is important to point out that even channels only are associated with the fast ECE data acquisition. The separatrix position is denoted by the dashed vertical line. Figure 6. Time trace of the Dαouter divertor signal (a) and the ECE emission channel 66 (b) for JET discharge number #78014. The EHO lasts for approximately 400 ms from t=13.8 s to t=14.2 s. The ECE signals (colourbar in log scale) have to be compared with the magnetics shown in figure 4. A typical spectrogram of ECE near-pedestal signals (channel 66 of figure 5) is shown in figure 6. The electron temperature fluctuation with the many-nharmonic structure displayed in figure 4is clearly recognisable. It is found that the ECE signal does not propagate further beyond the pedestal shoulder. Indeed, as clearly shown in figure 7, the ECE trace of the EHO is not visible inside channel 56 which is the first available channel in the core region outside the pedestal. DIII-D and JT60-U experiments [6,19] also reported similar behaviour, which resembles the dynamics of low-nELM precursors studied in [10]. These fluctuations have been shown to be localised within the pedestal radii and not to extend radially beyond the pedestal shoulder, giving us confidence on the pedestal Figure 7. Spectrogram of the ECE emission (colourbar in log scale) for channels 54, 56, 58 and 66 (cf figure 5) for shot #78014. radial localisation of the EHO in JET, which must indeed be extremely narrow. It is worth noting that EHOs in DIII-D, ASDEX-U and JT60 have been observed in low pedestal density plasmas of the order of 1 ×1019 m−3and currents of 1 MA [3–6], whereas JET quiescent plasmas can be sustained up to fairly large values of the pedestal density (nped e,crit ∼5×1019 m−3, cf figure 1). Although JET operates at higher plasma current, this behaviour is not fully explained as local quantities such as collisionality, the electron βe,Zeff seem to be comparable across these machines [4,20]. Furthermore, we notice that EHOs are not affected by external magnetic perturbations, at least up to 1 kA of EFCC current. Indeed, the EHO dynamics observed in discharges #75411 and #79455 with no active EFCCs, is essentially equivalent to the one of pulses #78012 and #78014 in which EFCCs were applied. Also, in shots #78012 and #78014, EHOs occur well before EFCCs are applied at ∼14 s, and disappear well before the EFCC current is switched off at ∼t2. This suggests that the EHO must be driven primarily by internal, i.e. within the last closed flux surface, mechanisms. It is worth pointing out that the ELM appearance does not necessarily imply that the quiescent regime cannot be recovered. Indeed, in discharge #78012 a first quiescent phase lasts until t≈14.3 s when an ELM occurs and the EHO is lost; after this ELM event, the EHO appears again at t≈14.45 s and lasts until tELM. In pulse #79455 instead, the EHO disappears spontaneously at t≈14.64 s, whereas the quiescent state persists until t=tELM. 2.3. The role of plasma rotation We now argue that the toroidal rotation affects weakly the appearance of EHOs. This is because we observe that the toroidal rotation frequency at the pedestal top drops after the appearance of the first ELM as shown in figure 8, which also indicates that EHOs exist within a wide range of pedestal rotation frequencies. Moreover, although a connection between 5 Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al Figure 8. Toroidal rotation at the pedestal top (computed by averaging density and electron temperature pedestal positions) and NBI power for the four shots of table 1. Note that, despite the steady NBI power, a drop in the rotation pedestal value occurs at the appearance of first ELM, indicated by the dashed vertical line, after which the EHO phase is lost. toroidal (carbon) rotation shear and Q-EHO phase was established in [7], DIII-D results of [21] show that the accessibility of the quiescent phase is almost independent of the toroidal (carbon) rotation shear. It is also worth stressing that there could be a consistent difference between carbon and mainion species rotation profiles in the pedestal region, the latter exhibiting significantly weaker gradients [22–24]. As such, the rotation of the carbon impurity may not be a good proxy for inferring the main ion rotation properties. Furthermore, nonlinear MHD simulations with the JOREK code [25] found that toroidal flows have a weak effect on the destabilisation and saturation of modes which might be related to a Q-EHO phase. Interestingly, we notice that similar edge localised oscillations with a dominant n=1 component have been recently reported in Alcator C-Mod in low-collisionality and high pressure pedestal regimes [26]. No NBI was employed in the C-Mod experiments [26], supporting our claim that these edge fluctuations do not depend explicitly on plasma toroidal rotation. In conclusion, the experimental evidence in JET, also supported by the results presented in [6,21] and numerical modelling, gives us confidence that other physical effects might be more relevant for the EHO appearance. 2.4. Radial electric field during the quiescent and ELMy phases As pointed out in [21], one of the key parameters which determine the accessibility to the quiescent phase is the edge E×Bflow shear. This flow manifests itself as a plasma rotation mainly in the poloidal direction, and its strength is proportional to the radial electric field. From the radial ion force balance equation [27], allowing for plasma shaping through elongation, we have near the edge Figure 9. Radial electric field for pulses #75411 (a) and #78012 (b) during the quiescent (black, averaged over t1−tELM) and ELMy (red, averaged over tELM −t2) phases. The separatrix position varies within the region indicated by the two vertical dashed lines (same colour meaning as for Er). Erhas been calculated up to R=3.8425 m for which averaged Tidata are available. Er≈√2 1+κ2(dpi/dr eni +aκBt qΩtor)−vpolBt, where pi=niTiwith nithe ion density, ethe ion electric charge, κthe plasma elongation, aand R0the minor and major radii respectively, Ωtor =vtor/Rthe toroidal angular frequency, vpol the poloidal velocity and ra flux label (for the geometry of the beam injection and sign conventions we refer to [17,28]). Writing R=R0+rcosθ, we have d/dr =d/Rat θ=0. This allows to simplify the analysis by taking all the relevant quantities as a function of Ron the equatorial outer mid-plane. Figure 9shows Eraveraged over the quiescent and ELMy time windows as a function of the major radius. The Erwell takes values comparable to those observed in DIIID [19,29] of the order of ∼100 kV m−1, although no strong variations of Erare observed when transitioning to the ELMy phase [30]. This finding suggests that in the four discharges of table 1, the pedestal density evolution should be the main actor responsible for transition from quiescent to ELMy regime. This, indeed, is discussed in the next subsection. 2.5. Pedestal density and temperature conditions for the Q-EHO phase accessibility Thus, to further investigate what conditions favour the EHOs existence, we study the localisation of the discharges of table 1 in nped e−Tped espace. Figure 10 shows the instantaneous pedestal values of density and electron temperature during the time window t1−t2for the four shots considered. We observe that the Q-EHO phase exists in the region of low-density with temperatures ≳1 keV. Note that most of the high pressure values associated with an ELMy pedestal belong to pulse #78014, and these may be connected with the EHO-like bursts prior to ELMs shown in figure 4. During the discharge, the plasma evolves towards an ELMy regime which loses the EHOs. 6 Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al Figure 10. Scatter plot of the instantaneous pedestal values for density and electron temperature at the pedestal top for the discharges in table 1during the selected time window (we point out that the pedestal position of neis approximately the same of the one of Te). The red points refer to ELM-free phases with EHO activity. The constant electron pressure and collisionality level curves are also indicated, νped e∗is computed by averaging q95,R0,κ,Zeff over the time window t1−t2. EHOs tend to cluster in high temperature-low density regions. As shown in figures 11(a) and (b), the pedestal density increase is accompanied by a temperature decrease where the pedestal knee appears to shift inwards, at least for the electron temperature. βped e, where βe=2µ0pe/B2 tand pe=neTe, varies accordingly (cf figure 11(c)) with the Q-EHO phase sustained at βped e>0.2%. This suggests that EHOs should be observed mainly in the high pressure region of the nped e−Tped espace. The evolution of the density and temperature profiles are associated with an increase of the pedestal collisionality leading to the loss of the EHO when νped e∗≳0.3 (cf figure 11(c)), in line with the results in DIII-D and JT60-U [4,15,31]. Here νe∗ follows the definition of [32] νe∗=6.921 ×10−18 q95R0neZeff lnΛe T2 eϵ3/2, where εis an effective inverse aspect ratio defined by ϵ= a R0√1+κ2 2with R0and athe major and minor radii respectively with a/R0≈0.33, and lnΛeis the Coulomb logarithm. As pointed out in [5], plasmas with a higher percentage of impurities may require smaller pedestal densities in order to maintain the pedestal electron collisionality sufficiently small. Notice that the increase of pedestal collisionality is likely to yield a reduction of the bootstrap current, and a consequent increase of the local magnetic shear [32–35]. Hence, the collisionality threshold may be associated with a critical value of the magnetic shear below which EHOs can develop [36], in accordance with recent analytic and numerical modelling [18,37–40]. Thus, EHO dynamics in JET appear to be governed primarily by βped eand νped e∗, both identifying a threshold for the EHO Figure 11. Electron temperature (panel (a), data from ECE) and density (panel (b), from HRTS) profiles of discharge #78012 for the time window t1−tELM of table 1(early times in red, later ones in dark blue). The separatrix position varies within the region identified by the vertical dashed lines. Note that for this discharge, Tevalues from ECE are higher than the ones recorded by the HRTS diagnostic, although the radial profile remains the same. In (c), the instantaneous pedestal values of βped e=2µ0pped e/B2 tversus νped e∗of the four discharges in table 1during the Q-EHO phase are shown (these correspond to the red points of figure 10). appearance, i.e. βped e>0.2%and νped e∗<0.3 (see figure 11). Other parameters, such as q95 and the pedestal values of the magnetic shear, may play a role in the EHO triggering and their effect on the edge MHD behaviour this will be discussed in the following section. 3. JET-C and ILW ELMy database pedestal analysis The aim of this section is to analyse the pedestal features of a database of JET discharges with carbon and ILW that, although partially fulfilling the parameter requirements for Q-EHO operation, are in ELMy regime. This would help in identifying if further hidden parameters, other than νped e∗ and βped ediscussed in the previous section, determine the accessibility to the ELMs/no-ELMs phase, and assessing if Q-EHO scenarios could potentially be reproduced in metallic machines. The JET-C/ILW database under consideration consists of 1216 shots in high performance ELMing H-mode, divided into 360 shots with carbon wall and 856 shots with ILW [12]. Further details about this database can be found in [12]. The pedestal values of the associated physical quantities are averaged over a time window of 1–2 s during an inter-ELM stationary phase. Contrarily to the analysis of the previous section which focussed on the discharge evolution in the early phase when density is ramped (cf figure 1), the time window of all shots in the ELMy database is taken during the steady state flat-top. It is worth stressing that if EHOs exist in a transient phase, i.e. they are robust, they should be expected to be also observed 7 Plasma Phys. Control. Fusion 64 (2022) 044005 D Brunetti et al Figure 12. Scatter plot of JET carbon (a) and ILW (b) database discharges in the nped e−Tped eparameter space (each point corresponds to a pulse in the database). The dashed lines indicate the constant electron pressure levels, while bands of different pedestal electron collisionality are indicated by the colour associated with the discharge. Note that JET-C discharges exhibit larger pedestal Tped eand an associated smaller νped e∗with a wider span in pedestal electron pressure. Note that the pulses of the ELMy database are a small subset of the JET carbon (from pulse #73342 to #79759) and ILW (from #81768 to #92437) experiments. during a flat-top stage, if the plasma conditions required for their existence are met. In analogy with figure 10, the pedestal electron temperatures plotted versus density for the shots in the database are shown in figure 12. At first glance, ILW discharges tend to occupy the lower part of the nped e−Tped eplane having on average lower temperatures, while exploring regions of similar densities. We observe that for these pulses the ion and electron temperatures have comparable values (i.e. Ti∼Te). We point out that within this database, high electron pressure regimes above 12 kPa are not explored by ILW discharges. As a direct consequence, from an inspection of the associated pedestal electron collisionality, we clearly see that ILW discharges tend to have higher νped e∗values. Nevertheless, a reasonable number of ILW shots lie in a region of low to moderate collisionality at fairly high (low) electron temperature (density), where EHOs might be expected to exist. As a first check, it is instructive to see whether the JETC discharges in the database lie in the same region of the nped e−Tped eparameter space of the quiescent ones studied in the previous section. Hence, the nped e−Tped edata points of Figure 13. Plot of the JET-C points of figure 12(a) overlaid with the nped e−Tped epedestal values (in cyan) of discharges of table 1during the quiescent phase with EHOs. Note how the quiescent discharges tend to cluster in the region of high Teand low newith electron pressure above ∼7 kPa, although there are no EHOs for pressure larger than 14 kPa regardless of neand Te. figure 12(a) are overlaid with the ones of figure 10 in section 2. This is shown in figure 13. It is immediate to notice that quiescent discharges occupy the region of the parameter space of high temperature and low density with the electron pressure above ∼7 kPa at low collisionality (νped e∗≲0.3 in line with DIII-D results [4]). It should also be noted that in figure 13 an upper limit in pressure ∼14 kPa appears where no EHOs are observed. As pointed out in section 2.5 (cf figure 11), beyond the small collisionality requirement, these results may suggest that quiescent EHOs phases are accessed when a threshold in the pedestal pressure is crossed. In addition, by comparing figures 12 and 13, the nped −Tped eparameter space explored by JET-ILW shots seems not to overlap with the one of the JET-C Q-EHO discharges. However, we notice that JET-C ELMy plasmas are found in regions where EHOs are expected to exist, i.e. despite having similar pedestal characteristics with the quiescent ones. Thus, we argue that other parameters must play a key role in determining whether or not the quiescent phase is accessible. We point out that when interpreting EHOs as pedestal localised pressure driven MHD instabilities [37,39,41], similarly to ballooning modes and to some extent Mercier modes, it is more appropriate to compare the pedestal βvalue rather than the pressure alone. This indeed is shown in figure 14, where the pedestal values of βe, defined as in section 2.5, of the carbon and ILW database discharges are plotted against of νped e∗(cf figure 11(c)). The green points in figure 14 and in the following figures highlight the database pulses, both carbon and ILW, which have νped e∗<0.3 and βped e>0.2%, whereas the red ellipse indicates the region in the νped e∗− βped espace which is explored by the discharges of table 1of section 2. 8