Abstract

We describe a new technique for the efficient generation of high-energy ions with electromagnetic ion cyclotron waves in multi-ion plasmas. The discussed ‘three-ion’ scenarios are especially suited for strong wave absorption by a very low number of resonant ions. To observe this effect, the plasma composition has to be properly adjusted, as prescribed by theory. We demonstrate the potential of the method on the world-largest plasma magnetic confinement device, JET (Joint European Torus, Culham, UK), and the high-magnetic-field tokamak Alcator C-Mod (Cambridge, USA). The obtained results demonstrate efficient acceleration of 3He ions to high energies in dedicated hydrogen–deuterium mixtures. Simultaneously, effective plasma heating is observed, as a result of the slowing-down of the fast 3He ions. The developed technique is not only limited to laboratory plasmas, but can also be applied to explain observations of energetic ions in space-plasma environments, in particular, 3He-rich solar flares.

Main

In magnetized plasmas, charged particles gyrate around the magnetic field lines with their characteristic cyclotron frequencies ωcs = qsB/ms, where qs is the particle’s charge, ms is the particle’s mass, and B is the local magnitude of the magnetic field. A variety of strong wave–particle interactions is possible when the wave frequency is close to the particle’s cyclotron frequency or its harmonics1,2,3. Ion cyclotron resonance heating (ICRH) is a powerful tool used in toroidal magnetic fusion research. In recent decades, several efficient ICRH scenarios were identified theoretically and verified experimentally2,3,4. In brief, this technique relies on external excitation of fast magnetosonic waves in the plasma, using specially designed ICRH antennas located at the edge of the device (see Fig. 1a). Antennas consist of a series of metallic straps that carry radio-frequency (RF) currents at a given frequency delivered by an external generator. The radially varying toroidal magnetic field then determines the location of the ion cyclotron layers ω = ci (p = 1,2, …), in the vicinity of which the RF power can be efficiently absorbed by ions.

Figure 1: A new technique for fast-ion generation in magnetized multi-ion plasmas.
Figure 1

The goal of our study is to validate that, in properly chosen multi-ion plasmas, electromagnetic ion cyclotron waves can be effectively absorbed by a very low number of resonant ions at ωωci. This technique opens the possibility of high-efficiency generation of energetic ions in magnetized plasmas. a, Inside view of the world-largest magnetic confinement fusion device, Joint European Torus, showing different ion cyclotron resonance heating (ICRH) antennas at the edge. The insert shows an example of the computed RF electric field pattern in a cross-section of the JET plasma. b, ‘Three-ion’ scenarios require resonant ions with a (Z/A) ratio in between that of the two main ions, essentially following the ‘sandwich’ principle (Z/A)2 < (Z/A)3 < (Z/A)1. The figure shows the fraction of RF power absorbed by 3He minority ions for the D–(3He)–H three-ion scenario as a function of H and 3He concentrations. The computations were made by the TOMCAT code for the parameters of the JET experiments discussed in this paper (B0 = 3.2 T, f = 32.5 MHz, ne0 = 4 × 1019 m−3, T0 = 4 keV, k(ant) = 3.4 m−1). The zones within the dashed lines correspond to a single-pass absorption larger than 50%. The code predicts wave absorption by a tiny amount of 3He ions (0.1–0.2%) in H–D plasmas with H concentrations in the range 70–80%, in agreement with equation (2).

The electric field of the excited fast waves can be decomposed as a sum of the left-hand polarized component E+, rotating in the sense of ions, and the oppositely rotating right-hand component E. Wave absorption by non-energetic ions is evidently facilitated by the presence of a sufficiently large E+ near the ion cyclotron resonance. To illustrate this, we note that fundamental cyclotron heating in single-ion plasmas is ineffective since E+ almost vanishes at ωωci.

The choice of plasma composition, namely the number of ion species and their relative concentrations, allows one to control the radial dependence of the ratio E+/E. In two-ion plasmas composed of one main ion species and a few per cent of minority ions with qi/mi different from that for the main ions, RF power absorption at the minority ion cyclotron frequency is strongly enhanced5,6. These minority heating scenarios benefit from the enhanced E+ in the vicinity of the ion–ion hybrid (IIH) cutoff-resonance pair, located close to the minority cyclotron resonance2. If the IIH layer is not present in the plasma, as is the case at very low minority concentrations in two-ion plasmas, the RF power absorption by minorities is very limited. On the other hand, at minority concentrations significantly above the optimal value of a few per cent, the IIH pair is located too far away from the minority cyclotron layer, thus further reducing their absorption efficiency. Instead, such plasmas are typically used for localized electron heating through mode conversion (see ref. 7 for more details).

There is, however, an elegant way to use mixture plasmas to channel RF power to ions: simply add a third ion species with a cyclotron resonance layer close to the IIH cutoff-resonance pair. Under these conditions, a new IIH pair appears in close proximity to the cyclotron resonance of the third ion species, even if their concentration is extremely low! For this heating scheme to work, the Z/A value of the resonant ions should be ‘sandwiched’ between that of the two main plasma ions where Zi and Ai are the charge state and the atomic mass of ion species i. We use indices ‘1’ and ‘2’ for the main ions with the largest and lowest cyclotron frequencies, respectively, and index ‘3’ for the absorbing minority. Depositing nearly all RF power to a very small number of minority ions is maximized in plasmas with main ion concentrations8,9 where Xi = ni/ne. Heating minority ions at higher concentrations is equally possible; plasma mixtures with X1 X1 are more optimal in this case10. The method can also be extended to plasmas containing more than three ion species by slightly adapting the plasma composition. For proof-of-principle demonstration, we select a plasma mixture composed of two hydrogen isotopes, H ions with (Z/A) = 1 and the heavier D ions with (Z/A) = 1/2, and 3He ions with their unique (Z/A) = 2/3 as a resonant absorber. Equation (2) predicts that 3He ions should efficiently absorb RF power in H–D (or H–4He) plasmas if the hydrogen concentration is 67%. This is supported by modelling with the TOMCAT code11, using plasma parameters relevant for the JET experiments described below. Figure 1b shows dominant RF power absorption by a small amount of 3He ions, down to concentrations X[3He] ≈ 0.1–0.2%. Plasma heating with the three-ion D–(3He)–H scenario at higher X[3He] ≈ 0.5–1% is equally possible. We note that the recipe for the plasma composition given by equation (2) is valid for fast magnetosonic waves, excited at the low magnetic field side and propagating towards regions with increasing B, as in most of present-day fusion machines.

Efficient plasma heating with three-ion ICRH scenarios

A series of dedicated experiments were performed on the Alcator C-Mod tokamak12 (MIT, Cambridge, USA; major radius R0 ≈ 0.67 m, minor radius apl ≈ 0.23 m) and on the world-largest magnetic fusion device JET (Joint European Torus, Culham, UK; R0 ≈ 3 m, apl ≈ 1 m). The goal of these studies was to demonstrate that indeed a small amount of 3He ions can efficiently absorb RF power in H–D mixtures. The Alcator C-Mod experiments were run at high central electron densities ne0 ≈ (2–3) × 1020 m−3 and very high toroidal magnetic field B0 = 7.8 T at a plasma current Ip = 1.2 MA. In the JET experiments, ne0 ≈ 4 × 1019 m−3 and B0 = 3.2 T, Ip = 2.0 MA were used. Accordingly, ICRH frequencies f = ω/2π = 78.0–80.0 MHz (Alcator C-Mod) and f = 32.2–33.0 MHz (JET) were chosen to locate the 3He cyclotron resonance in the plasma centre in both devices. The Alcator C-Mod plasmas were heated with 4–5 MW of ICRH power only. In JET plasmas, 3.2 MW of neutral beam injection (NBI) was added prior to applying 4 MW of ICRH.

Figure 2 shows the time evolution of the central electron temperature Te0 and plasma stored energy Wp in response to the applied ICRH on Alcator C-Mod and on JET. These results confirm our earlier predictions (Fig. 1b) for the efficiency of 3He absorption at concentrations of a few per mille (‰) in H–D plasmas. The optimal 3He concentration for this scenario in C-Mod plasmas was approximately X[3He] ≈ 0.5%. In JET, even lower 3He concentrations 0.2% were successfully applied.

Figure 2: Illustration of the performance of the D–(3He)–H three-ion ICRH scenario on Alcator C-Mod and JET tokamaks.
Figure 2

a, Alcator C-Mod three-ion heating pulse (#1160901009, X[3He] ≈ 0.5%, red) and (3He)–D pulse (#1160823003, X[3He] ≈ 5–7%, black). b, JET three-ion heating pulses #90753 (X[H] ≈ 68–74%, X[3He] ≈ 0.2–0.4%, blue) and #90758 (X[H] ≈ 80–82%, X[3He] ≈ 0.1–0.3%, red). Whereas a few % of 3He is needed for minority heating in H or D majority plasmas, strong wave absorption in H–D plasmas is achieved with about ten times less 3He.

In JET experiments, the edge isotopic ratio H/(H + D) was varied between 0.73 and 0.92 and the 3He concentration between 0.1% and 1.5% to assess the sensitivity of ICRH on the detailed plasma composition. The core hydrogen concentration was estimated from the measured edge H/(H + D) ratio as X[H] ≈ 0.9 × H/(H + D), accounting for the presence of impurities in the plasma and additional D core fuelling from the D-NBI system. We find efficient plasma heating for a fairly broad range of the isotopic ratio (see also Supplementary Figs 5 and 6). In particular, central plasma heating with ΔTe0PICRH > 0.5 keV MW−1 was observed for H/(H + D) ≈ 0.78–0.91 mixtures at 3He concentrations below 0.5%.

Figure 2a also includes the evolution of Te0 and Wp for 3He minority heating in the Alcator C-Mod D plasma with X[3He] ≈ 5–7% (pulse 1160823003). Compared to this (3He)–D scenario, the three-ion heating scenario in C-Mod showed a larger increase in the plasma stored energy (ΔWpPICRH = 22 kJ MW−1 versus 14 kJ MW−1).

A direct comparison of the heating performance of the three-ion discharges was not possible for the JET discharges discussed here. However, it can be assessed comparing the measured thermal plasma energy to that derived from a so-called scaling law. These scaling laws predict the energy confinement value for a given plasma experiment as a function of specific engineering parameters (Ip, B0, ne, …; ref. 13) and result from a statistical analysis of data collected from multiple tokamaks worldwide. Here, we use the well-established ITERL96-P and IPB98(y,2) scalings for the energy confinement time τE (equations (24) and (20) in ref. 13) for L-mode and H-mode tokamak plasmas. τE is the characteristic time during which the plasma maintains its energy if the heating power is suddenly switched off1. Under stationary conditions it is given by the ratio of the stored plasma energy divided by the total heating power. Supplementary Figs 1–4 show the results obtained for L-mode JET discharges heated with different ICRH minority scenarios, including the ratios τE/τE, scaling. From the definition of τE given above, it follows immediately that τE/τE, scaling is equal to the ratio of the corresponding stored energies. For the three-ion heating pulse #90758 (Fig. 2b), we obtain τE/τIPB98(y,2) ≈ 0.85–0.88 and τE/τITERL96−P ≈ 1.43–1.48. This compares very well to τE/τE, scaling values for the excellent (H)–D minority heating scenario in JET plasmas (Supplementary Fig. 1).

Efficient generation of high-energy ions

Energetic ions play a crucial role in fusion plasmas14. Indeed, the success of magnetic fusion relies upon good confinement of fast alpha particles (4He ions with birth energies 3.5 MeV). This is required to sustain high plasma temperatures and for economical operation of a fusion reactor1. However, these energetic 4He ions can also trigger instabilities that degrade the plasma performance. To mimic the behaviour of fusion-born alphas, but without actually using D–T plasmas, ICRH has been extensively used in the past.

For fundamental ion cyclotron absorption the acquired ion energies scale with the absorbed RF power per particle15. Since three-ion scenarios allow minimizing the number of resonant particles down to ‰ levels, ions with rather high energies can be generated. For plasma densities and ICRH power levels available in the JET and C-Mod experiments, self-consistent power deposition computations with the codes AORSA16, PION17 and SCENIC18 predicted acceleration of 3He ions to energies of a few MeV.

Figure 2b shows fast repetitive drops in Te0 (so-called ‘sawtooth’ oscillations) with a period of 0.2 s during the NBI-only phase of JET pulses #90753 and #90758 (t = 7–8 s). Extended sawtooth periods up to 1.0 s are seen when ICRH is applied on top of NBI. Similarly, in the three-ion Alcator C-Mod discharge in Fig. 2a, the sawtooth period increases from 0.13 s during the 2 MW ICRH phase to 0.23 s during the 4 MW phase. The observation of long-period sawteeth is a first indication of the creation of energetic ions by ICRH, as the presence of fast ions in a plasma is well known to have a stabilizing effect on sawteeth19,20.

An independent confirmation of accelerating 3He ions to high energies is provided by gamma-ray emission spectroscopy on JET21,22. Figure 3a shows the gamma-ray spectrum for pulse #90753 during t = 8–14 s (PICRH = 4.4 MW), recorded with the LaBr3 spectrometer23. The observed lines originate from 9Be(3He, )11B and 9Be(3He, )11C nuclear reactions between fast 3He ions and beryllium (9Be) impurities. These impurities are intrinsically present in JET plasmas with the ITER-like wall. The reported plasmas were contaminated with 0.5% 9Be, as estimated by charge exchange measurements.

Figure 3: Gamma-ray emission from 3He  +  9Be nuclear reactions, proving the presence of energetic ICRH-accelerated 3He ions.
Figure 3

a, Gamma-ray spectra measured in JET pulse #90753 (three-ion scenario, X[3He] ≈ 0.2 –0.4%, red) and in pulse #91323 ((3He)–H scenario, X[3He] ≈ 1 –2%, blue). The error bars represent the square root of the number of counts in each channel of the spectrum and arise from the underlying Poisson statistics of the gamma-ray detection process. b,c, The JET plasma cross-section and 19 lines-of-sight of the neutron/gamma camera. The reconstructed high-energy gamma-ray emission (Eγ = 4.5–9.0 MeV) visualizes the population of the confined energetic 3He ions (E[3He] > 1–2 MeV). Pulses #90752 (b) and #90753 (c) had a nearly identical plasma composition (X[H] ≈ 70–75%, X[3He] ≈ 0.2–0.4%) and RF heating power (PICRH = 4.3–4.4 MW), except for the ICRH antenna phasing. A factor-of-two increase in the γ-ray emissivity was observed in pulse #90753, in which 2 MW of RF power was coupled to the plasma with +π/2 phasing (see text for more details).

The observation of the Eγ ≈ 4.44 MeV line implies immediately the presence of confined fast 3He ions with energies >0.9 MeV (ref. 21). Alpha particles, born in concurrent 3He–D fusion reactions, also contribute to the gamma-emission at this energy through 4He + 9Be reactions. Figure 3a also shows a number of characteristic gamma lines at Eγ > 4.44 MeV, originating from transitions between higher excited states of 11B and 11C nuclei (products of 3He  +  9Be reactions). The excitation efficiency for such high-energy levels increases by a factor of ten when the energy of the projectile 3He ions increases from 1 MeV to 2 MeV (ref. 24). For comparison, we also display the γ-spectrum recorded in JET pulse #91323, in which 3He ions (≈1–2%) were heated as a minority with up to 7.6 MW of ICRH in an almost pure H plasma (see Supplementary Fig. 3). Figure 3a clearly shows higher gamma-count rates for the three-ion pulse #90753 (X[3He] ≈ 0.2–0.4%), although a factor of two less ICRH power was injected into the plasma.

In JET, we further enhanced the efficiency for fast-ion generation by changing the configuration of ICRH antennas from dipole to  +π/2 phasing. The phasing defines the dominant k and the spectrum of emitted waves, where k is the wavenumber parallel to B. The +π/2 phasing launches waves predominantly in the direction of the plasma current with typical values |k(ant)| ≈ 3.4 m−1, which is two times smaller than for dipole phasing (|k(ant)| ≈ 6.7 m−1). Since the width of the absorption zone scales with |k|, reducing it has the advantage of increasing the absorbed RF power per ion. Furthermore, the +π/2 phasing allows one to exploit the RF-induced pinch effect, beneficial to localize the energetic ions towards the plasma core25.

The result is clearly visible in Fig. 3b, c, showing the two-dimensional tomographic reconstruction of the Eγ = 4.5–9.0 MeV gamma-ray emission21 for two comparable three-ion heating pulses #90752 and #90753. Both had a similar edge H/(H + D) ratio, varying from 0.84 at the beginning of the pulse to 0.75 at the end (X[H] ≈ 68–76%), and X[3He] ≈ 0.2–0.4%. In pulse #90752 (Fig. 3b), all ICRH power was applied using dipole phasing, while in pulse #90753 (Fig. 3c) about half of the ICRH power (2.1 MW) was launched with +π/2 phasing. Energetic 3He ions are more centrally localized and the number of gamma-ray counts increases by a factor of two in pulse #90753. The period of the sawtooth oscillations also increases from 0.54 s to 0.78 s.

We also observed excitation of Alfvén eigenmodes (AE) in JET plasmas with frequencies ≈320–340 kHz in pulses, where PICRH ≥ 2 MW was delivered with +π/2 phasing. These instabilities are excited if a sufficiently large number of energetic ions with velocities comparable to the Alfvén velocity is present in the plasma. Figure 4a shows the AE dynamics for JET pulse #90758 (previously shown in Fig. 2b), with a sequential excitation of modes with mode numbers from n = 8 to n = 5 during a long-period sawtooth. The MHD code MISHKA26 yields eigenfrequencies fAE(0) ≈ 285–295 kHz for n = 5–7 modes in the plasma frame. Even closer correspondence to the observations is obtained when plasma rotation due to NBI (frot ≈ 5 kHz measured at R ≈ 3.25 m) is taken into account (fAE(lab) = fAE(0) + nfrot ≈ 320 kHz). Further analysis of the conditions for energetic ions to interact with the n = 5 AE mode yields 3He ions with energies ≈1.5–2.5 MeV.

Figure 4: Excitation of Alfvénic eigenmodes in magnetic fluctuation spectrograms, another proof of the presence of ICRH-accelerated fast ions.
Figure 4

a, JET pulse #90758. b, Alcator C-Mod pulse #1160901023. The evolution of the central electron temperature Te0 is also plotted in the bottom part of the figures.

A similar AE activity was also detected in the Alcator C-Mod experiments during a sawtooth cycle with a period extended up to 40 ms (PICRH = 5 MW). As shown in Fig. 4b, AEs at frequencies fAE ≈ 1,270–1,300 kHz (n ≈ 12) were observed 30 ms after the sawteeth crash. Interestingly, the normalized frequency ratio fAE/fA(0) ≈ 0.56–0.61 is similar for the AE modes observed on both devices. Here, fA(0) = vA(0)/2πR0, with vA(0) the on-axis Alfvén velocity. This further highlights the similarity of the three-ion heating experiments on the two devices.

How many ‘three-ion’ scenarios exist?

These novel scenarios allow great flexibility in the choice of the three ion components. Table 1 summarizes the (Z/A) values for fusion-relevant ion species. The isotopes of hydrogen have Z/A = 1 (protons), 1/2 (D ions) and 1/3 (T ions). Fusion plasmas can also contain 4He and light impurity species, released in plasma–wall interactions. In the core of high-temperature plasmas, those ions (4He, 12C, 16O, and so on) are typically fully ionized with Z/A = 1/2, just as the D ions. We also note the isotope 3He, which has a unique Z/A = 2/3. Other ion species such as 9Be4+, 7Li3+, 22Ne10+, and so on have a Z/A ratio in the range 0.43 and 0.45, and bring extra possibilities. Among these, beryllium is of particular importance. Plasmas in JET and the future tokamak ITER naturally contain a small amount of 9Be impurities. Since (Z/A)T < (Z/A)9Be < (Z/A)D, 9Be ions can efficiently absorb RF power and transfer most of their energy to D and T ions during their collisional slowing-down, a feature particularly attractive for a fusion reactor10. As another example of the three-ion technique, we mention the observed parasitic off-axis absorption of ICRH power by 7Li impurities in D–T plasmas of the Tokamak Fusion Test Reactor27. Low-temperature plasmas offer an even larger variety of scenarios since light ion species are not necessarily fully ionized.

Table 1: (Z/A) ratio for different ion species in fusion plasmas.

Relevance for space plasmas

As discussed above, ion species with Z/A = 1/2 are nearly identical to D ions from the wave propagation point of view. Therefore, helium ions (Z = 2, A = 4) can replace D. According to equation (2) and Fig. 2b, hydrogen plasmas additionally including 10–17% of 4He ions are optimal for effective RF power absorption by a small amount of 3He ions.

The presented experimental results provide also an additional insight into the understanding of the 3He-rich solar flares28,29,30, known for the past four decades. These events are characterized by an anomalously large abundance ratio 3He/4He 1 in the energy range 1 MeV/nucleon, compared with a typical value of 3He/4He 5 × 10−4 in the solar corona. The proposed theoretical models to explain anomalous 3He-enrichment generally rely on selective energy absorption by these ions via wave interaction mechanisms making use of the unique charge-to-mass ratio of 3He.

Fisk suggested pre-heating of 3He ions via electrostatic ion cyclotron waves in H–4He plasmas, followed by a second-stage acceleration process28. Crucial in his model for the wave absorption by 3He ions is also having a plasma mixture, consisting of H and 4He ions. On the other hand, Reames highlights in his review (ref. 30) that the 3He-rich events are associated with streaming 10–100 keV electrons. He suggests that such electron beams might be a source for electromagnetic ion cyclotron waves. The advantage of this explanation is that electromagnetic waves can directly accelerate ions to MeV energies, without the need of a secondary process, which is a serious simplification compared to the theory by Fisk. Roth and Temerin developed a single-stage model for the resonant acceleration of 3He ions to high energies, utilizing electromagnetic ion cyclotron waves in H plasmas31. Their study resembles closely the (3He)–H minority heating in tokamaks. Figure 3a, showing the γ-ray spectrum for JET pulse #91323, confirms generation of MeV-range3He ions with this scenario in a fusion hydrogen plasma.

Figure 3a also illustrates that a significantly larger number of high-energy 3He ions was generated using the D–(3He)–H three-ion scenario under similar conditions. Thus, we hypothesize that resonant absorption of electromagnetic waves by a small amount of 3He ions in H–4He plasmas (that is, effectively the three-ion 4He–(3He)–H scenario) can be another effective mechanism for 3He acceleration in space plasmas. This proposal then combines in one scenario the advantages of the theories of Fisk and Temerin–Roth. We recall that in JET experiments efficient RF power absorption by 3He ions was observed in H–D plasmas with X[H] ≈ 68%–82% (see Fig. 2b and Supplementary Figs 5 and 6). Equivalent H–4He mixtures with the same H concentrations should have a n4He/nH ratio in the range between 0.11 and 0.24.

Figure 5a summarizes the 4He/H and 3He/4He ratios for a number of observed 3He-rich solar flares, taken from Table 1 and Fig. 2 of ref. 32. Remarkably, our estimates are consistent with the data points at n4He/nH ≈ 0.1–0.3. This becomes even clearer if the same dataset is plotted as a function of the estimated hydrogen concentration X[H] ≈ 1/(1 + 2n4He/nH) and using the measured number of energetic 3He ions normalized to the number of protons, n3He/nH as an indicator for the efficiency of 3He acceleration. Figure 5b shows a large 3He enhancement for events with X[H] ≈ 70–75%, thus providing additional support for our hypothesis.

Figure 5: Three-ion ICRH scenarios also explain some of the observations of energetic ions in space environments, in particular, 3He-rich solar flares.
Figure 5

a4He/H and 3He/4He ratios for 3He-rich solar flares. Data taken from Table 1 and Fig. 2 of ref. 32, including the original error bars. The data cloud within the red line corresponds to a n4He/nH ratio very similar to our theoretical predictions for a hypothetical three-ion 4He–(3He)–H scenario at work in space plasmas (see text for more details). b, The ratio n3He/nH = (n3He/n4He) × (n4He/nH), measured in the MeV-energy range, versus H concentration estimated from X[H] ≈ 1/(1 + 2n4He/nH) for the same dataset (ref. 32). A large 3He enhancement for the events at X[H] ≈ 70–75% is seen. The error bars for n3He/nH are directly taken from Table 1 of ref. 32. The error bars for the estimated H concentration are computed using the relation between X[H] and n4He/nH, and taking the maximum and minimum values of n4He/nH for a particular 3He-rich event.

Data availability.

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This paper is dedicated to the late P. E. M. Vandenplas, founder and first director of LPP-ERM/KMS, in recognition of his lifelong outstanding commitment to fusion research, in particular to ICRH. The support from the JET and Alcator C-Mod Teams is warmly acknowledged. We are grateful to A. Cardinali, C. Castaldo, R. Dumont, J. Eriksson, T. Fülöp, C. Giroud, C. Hellesen, S. Menmuir and M. Schneider for fruitful discussions. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement no. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. This work was also supported by the US DoE, Office of Science, Office of Fusion Energy Sciences, SciDAC Center for Simulation of Wave Plasma Interactions under DE-FC02-01ER54648 and the User Facility Alcator C-Mod under DE-FC02-99ER54512. The Alcator C-Mod Team author list is reproduced from ref. 12. The JET Contributors author list is reproduced from ref. 33.

Author information

Affiliations

  1. Laboratory for Plasma Physics, LPP-ERM/KMS, TEC Partner, 1000 Brussels, Belgium

    • Ye. O. Kazakov
    • , J. Ongena
    • , E. Lerche
    • , D. Van Eester
    • , K. Crombé
    •  & M. Van Schoor
  2. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • J. C. Wright
    • , S. J. Wukitch
    • , Y. Lin
    • , T. Golfinopoulos
    • , A. E. Hubbard
    •  & M. Porkolab
  3. Culham Centre for Fusion Energy (CCFE), Culham Science Centre, Abingdon OX14 3DB, UK

    • E. Lerche
    • , V. G. Kiptily
    • , Y. Baranov
    • , R. Felton
    • , M. Fitzgerald
    • , Ph. Jacquet
    • , S. E. Sharapov
    •  & D. Valcarcel
  4. Barcelona Supercomputing Center (BSC), 08034 Barcelona, Spain

    • M. J. Mantsinen
    •  & D. Gallart
  5. ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain

    • M. J. Mantsinen
  6. National Institute for Laser, Plasma and Radiation Physics, 077126 Bucharest, Romania

    • T. Craciunescu
  7. Dipartimento di Fisica, Università di Milano-Bicocca, 20126 Milan, Italy

    • M. Nocente
  8. Istituto di Fisica del Plasma, CNR, 20125 Milan, Italy

    • M. Nocente
    •  & L. Giacomelli
  9. Instituto de Plasmas e Fusão Nuclear, IST, Universdade de Lisboa, 1049-001 Lisboa, Portugal

    • F. Nabais
    •  & M. F. F. Nave
  10. Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Krakow, Poland

    • J. Bielecki
  11. Max-Planck-Institut für Plasmaphysik, 85748 Garching, Germany

    • R. Bilato
    •  & V. Bobkov
  12. Department of Applied Physics, Ghent University, 9000 Gent, Belgium

    • K. Crombé
  13. Institute of Plasma Physics and Laser Microfusion, 01-497 Warsaw, Poland

    • A. Czarnecka
  14. EPFL, Swiss Plasma Center (SPC), 1015 Lausanne, Switzerland

    • J. M. Faustin
    •  & H. Weisen
  15. KTH Royal Institute of Technology, 114 28 Stockholm, Sweden

    • T. Johnson
  16. European Commission, 1049 Brussels, Belgium

    • M. Lennholm
  17. JET Exploitation Unit, Culham Science Centre, Abingdon OX14 3DB, UK

    • M. Lennholm
  18. CEA, IRFM, 13108 Saint-Paul-Lez-Durance, France

    • T. Loarer
  19. Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    • E. S. Marmar
    • , S. G. Baek
    • , H. Barnard
    • , P. Bonoli
    • , D. Brunner
    • , G. Dekow
    • , P. Ennever
    • , I. Faust
    • , C. Fiore
    • , Chi Gao
    • , T. Golfinopoulos
    • , M. Greenwald
    • , Z. S. Hartwig
    • , A. E. Hubbard
    • , J. W. Hughes
    • , I. H. Hutchinson
    • , J. Irby
    • , B. LaBombard
    • , Yijun Lin
    • , R. Mumgaard
    • , R. R. Parker
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    • , J. E. Rice
    • , S. Shiraiwa
    • , B. Sorbom
    • , D. Terry
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    • , D. Whyte
    • , S. M. Wolfe
    • , G. M. Wright
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    • , S. J. Wukitch
    •  & P. Xu
  20. General Atomics, San Diego, California, USA

    • J. Candy
    •  & P. Snyder
  21. Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA

    • J. Canik
  22. Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA

    • R. M. Churchill
    • , L. Delgado-Aparicio
    • , A. Diallo
    • , E. Edlund
    •  & S. Scott
  23. Center for Energy Research, University of California San Diego, San Diego, California, USA

    • I. Cziegler
    •  & C. Holland
  24. Department of Physics, University of York, York, USA

    • B. Lipschultz
    •  & M. L. Reinke
  25. Plasma Operations Directorate, ITER Organization, St. Paul lez Durance, France

    • A. Loarte
  26. TCV Tokamak Physics, Centre de Recherches en Physique des Plasmas, Lausanne, Switzerland.

    • C. Theiler
  27. Aalto University, PO Box 14100, FIN-00076 Aalto, Finland

    • O. Asunta
    • , M. Groth
    • , A. Järvinen
    • , J. Karhunen
    • , T. Koskela
    • , T. Kurki-Suonio
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    • , M. I. K. Santala
    • , S. K. Sipilä
    • , J. Uljanovs
    •  & J. Varje
  28. Aix Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille, France

    • D. Galassi
  29. Aix-Marseille Université, CNRS, IUSTI UMR 7343, 13013 Marseille, France

    • J.-L. Gardarein
  30. Aix-Marseille Université, CNRS, PIIM, UMR 7345, 13013 Marseille, France

    • Y. Camenen
    • , M. Koubiti
    • , P. Manas
    •  & Y. Marandet
  31. Arizona State University, Tempe, USA

    • C. Luna
  32. Barcelona Supercomputing Center, Barcelona, Spain

    • S. Futatani
    • , D. Gallart
    • , M. Mantsinen
    •  & A. Rakha
  33. CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB, UK

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  34. CEA, IRFM, F-13108 Saint Paul Lez Durance, France

    • J. H. Ahn
    • , H. Arnichand
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    • , S. Vartanian
    •  & T. Vu
  35. Center for Energy Research, University of California at San Diego, La Jolla, California 92093, USA

    • R. P. Doerner
  36. Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud, 160, Rio de Janeiro CEP 22290- 180, Brazil

    • R. Galvão
  37. Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy

    • F. Maviglia
    •  & F. Orsitto
  38. Consorzio RFX, corso Stati Uniti 4, 35127 Padova, Italy

    • A. Alfier
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    •  & E. Zilli
  39. Daegu University, Jillyang, Gyeongsan, Gyeongbuk 712-174, Republic of Korea

    • O. J. Kwon
  40. Departamento de Física, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain

    • J. R. Martín-Solís
  41. Department of Applied Physics UG (Ghent University), St-Pietersnieuwstraat 41 B-9000 Ghent, Belgium

    • K. Crombé
    • , G. Hornung
    • , A. Shabbir
    •  & G. Telesca
  42. Department of Earth and Space Sciences, Chalmers University of Technology, SE-41296 Gothenburg, Sweden

    • F. Eriksson
    • , H. Nordman
    • , P. Strand
    • , D. Tegnered
    •  & D. Yadikin
  43. Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d’Armi 09123 Cagliari, Italy

    • B. Cannas
    • , A. Fanni
    • , A. Pau
    • , Pisano
    •  & G. Sias
  44. Department of Experimental Physics, Faculty of Mathematics, Physics and Informatics Comenius University Mlynska dolina F2, 84248 Bratislava, Slovak Republic

    • O. Bogar
    • , S. Matejcik
    • , J. Orszagh
    • , P. Papp
    •  & F. S. Zaitsev
  45. Department of Materials Science, Warsaw University of Technology, PL-01-152 Warsaw, Poland

    • E. Fortuna-Zalesna
    •  & J. Grzonka
  46. Department of Nuclear and Quantum Engineering, KAIST, Daejeon 34141, Korea

    • C. Jeong
    •  & S. Kwak
  47. Department of Physics and Applied Physics, University of Strathclyde, Glasgow G4 ONG, UK

    • S. S. Henderson
    • , M. O’Mullane
    •  & H. P. Summers
  48. Department of Physics and Astronomy, Uppsala University, SE-75120 Uppsala, Sweden

    • E. Andersson Sundén
    • , F. Binda
    • , M. Cecconello
    • , S. Conroy
    • , N. Dzysiuk
    • , G. Ericsson
    • , J. Eriksson
    • , C. Hellesen
    • , A. Hjalmarsson
    • , G. Possnert
    • , H. Sjöstrand
    • , M. Skiba
    •  & M. Weiszflog
  49. Department of Physics, Chalmers University of Technology, SE-41296 Gothenburg, Sweden

    • J. Weiland
  50. Department of Physics, Imperial College London, SW7 2AZ, UK

    • M. Bacharis
  51. Department of Physics, SCI, KTH, SE-10691 Stockholm, Sweden

    • E. Rachlew
  52. Department of Physics, University of Basel, Switzerland

    • L. Marot
    •  & L. Moser
  53. Department of Physics, University of Oxford, OX1 2JD, UK

    • M. Barnes
    • , E. G. Highcock
    •  & F. Parra Diaz
  54. Department of Physics, University of Warwick, Coventry, CV4 7AL, UK

    • S. C. Chapman
    •  & N. W. Watkins
  55. Department of Pure and Applied Physics, Queens University, Belfast BT7 1NN, UK

    • K. M. Aggarwal
    •  & I. Coffey
  56. Dipartimento di Ingegneria Elettrica Elettronica e Informatica-Università degli Studi di Catania, 95125 Catania, Italy

    • P. Arena
    • , A. Buscarino
    • , C. Corradino
    • , L. Fortuna
    • , M. Frasca
    •  & S. Palazzo
  57. Dipartimento di Ingegneria Industriale, University of Trento, Italy

    • A. Bisoffi
  58. Dublin City University (DCU), Ireland

    • H. J. Leggate
    • , D. Schwörer
    • , A. Somers
    •  & M. M. Turner
  59. Ecole Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland

    • P. Blanchard
    • , S. Coda
    • , B. P. Duval
    • , A. Fasoli
    • , J. M. Faustin
    • , J. P. Graves
    • , S. Lanthaler
    • , Y. Martin
    • , F. Nespoli
    • , T. Nicolas
    • , H. Patten
    • , D. Pfefferlé
    • , O. Sauter
    • , D. Testa
    •  & H. Weisen
  60. EUROfusion Programme Management Unit, Boltzmannstr. 2, 85748 Garching, Germany

    • L. Barrera Orte
    • , T. Donné
    • , T. Franke
    • , K. Gál
    • , C. Guérard
    • , M. L. Mayoral
    • , D. McDonald
    • , J. Regaña
    • , M. Reinhart
    • , M. Turnyanskiy
    •  & I. Voitsekhovitch
  61. EUROfusion Programme Management Unit, Culham Science Centre, Culham OX14 3DB, UK

    • N. Bekris
    • , D. Borba
    • , J. Figueiredo
    • , D. Fuller
    • , S. Hacquin
    • , S. Jachmich
    • , H. T. Kim
    • , X. Litaudon
    • , J. Lönnroth
    • , A. Murari
    • , C. Perez von Thun
    •  & E. R. Solano
  62. European Commission, B-1049 Brussels, Belgium

    • L. G. Eriksson
    • , L. D. Horton
    • , M. Lennholm
    • , C. Lowry
    • , A. Peackoc
    •  & A. C. C. Sips
  63. Fluid and Plasma Dynamics, ULB - Campus Plaine - CP 231 Boulevard du Triomphe, 1050 Bruxelles, Belgium

    • S. Moradi
  64. FOM Institute DIFFER, Eindhoven, The Netherlands

    • J. Citrin
    • , N. den Harder
    • , G. M. D. Hogeweij
    • , F. Jaulmes
    • , A. Shumack
    • , M. Tsalas
    •  & G. J. van Rooij
  65. Forschungszentrum Jülich GmbH, Institut für Energie- und Klimaforschung - Plasmaphysik, 52425 Jülich, Germany

    • S. Abduallev
    • , M. Beckers
    • , D. Borodin
    • , I. Borodkina
    • , S. Brezinsek
    • , J. W. Coenen
    • , P. Denner
    • , T. Dittmar
    • , P. Drews
    • , H. G. Esser
    • , M. Freisinger
    • , Y. Gao
    • , F. Hasenbeck
    • , A. Huber
    • , V. Huber
    • , A. Kirschner
    • , M. Köppen
    • , H. R. Koslowski
    • , H. T. Lambertz
    • , L. Li
    • , Y. Liang
    • , J. Linke
    • , Ch. Linsmeier
    • , O. Marchuk
    • , Y. Martynova
    • , Ph. Mertens
    • , C. Perez von Thun
    • , V. Philipps
    • , G. Pintsuk
    • , M. Rack
    • , F. Reimold
    • , D. Reiser
    • , J. Romazanov
    • , U. Samm
    • , T. Schlummer
    • , G. Sergienko
    • , E. Wang
    • , N. Wang
    • , S. Wiesen
    •  & W. Yanling
  66. Fourth State Research, 503 Lockhart Dr, Austin, Texas, USA

    • R. Bravanec
  67. Fusion for Energy Joint Undertaking, Josep Pl. 2, Torres Diagonal Litoral B3, 08019 Barcelona, Spain

    • S. Arshad
    • , D. Leichtle
    • , A. Neto
    • , G. Saibene
    • , F. Sartori
    •  & R. Sartori
  68. Fusion Plasma Physics, EES, KTH, SE-10044 Stockholm, Sweden

    • H. Bergsåker
    • , I. Bykov
    • , L. Frassinetti
    • , A. Garcia-Carrasco
    • , T. Hellsten
    • , T. Johnson
    • , S. Menmuir
    • , P. Petersson
    • , M. Rubel
    • , E. Stefanikova
    • , P. Ström
    • , E. Tholerus
    • , P. Vallejos Olivares
    • , A. Weckmann
    •  & Y. Zhou
  69. General Atomics, PO Box 85608, San Diego, California 92186-5608, California, USA

    • P. Gohil
    • , T. Luce
    • , S. Mordijck
    •  & C. Paz Soldan
  70. HRS Fusion, West Orange New Jersey, USA

    • H. R. Strauss
  71. IFP-CNR, via R. Cozzi 53, 20125 Milano, Italy

    • E. Alessi
    • , G. Gervasini
    • , L. Giacomelli
    • , L. Laguardia
    • , E. Lazzaro
    • , P. Mantica
    • , C. Marchetto
    • , A. Muraro
    • , C. Sozzi
    • , M. Tardocchi
    • , A. Uccello
    •  & N. Vianello
  72. Institute for Plasma Research, Bhat, Gandhinagar - 382 428 Gujarat, India

    • M. Abhangi
    • , J. Buch
    • , D. Chandra
    • , P. Dutta
    • , P. V. Edappala
    • , M. Ghate
    • , A. Kundu
    • , B. Magesh
    • , R. Makwana
    • , S. Panja
    • , S. Pathak
    • , V. Prajapati
    • , R. Prakash
    • , S. Ranjan
    • , K. Rathod
    • , P. Santa
    • , A. Sinha
    • , M. Stephen
    •  & K. Vasava
  73. Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Kraków, Poland

    • J. Bielecki
    •  & J. Dankowski
  74. Institute of Physics, Opole University, Oleska 48, 45-052 Opole, Poland

    • I. Książek
    •  & E. Pawelec
  75. Institute of Plasma Physics and Laser Microfusion, Hery 23, 01-497 Warsaw, Poland

    • M. Chernyshova
    • , A. Czarnecka
    • , K. Gałązka
    • , I. Ivanova-Stanik
    • , S. Jednoróg
    • , E. Kowalska-Strzęciwilk
    • , N. Krawczyk
    • , E. Łaszyńska
    • , K. Slabkowska
    • , M. Szawlowski
    •  & R. Zagorski
  76. Institute of Plasma Physics AS CR, Za Slovankou 1782/3, 182 00 Praha 8, Czech Republic

    • P. Bílková
    • , P. Cahyna
    • , R. Dejarnac
    • , I. Ďuran
    • , O. Ficker
    • , V. Fuchs
    • , J. Horáček
    • , M. Imríšek
    • , T. Markovič
    • , J. Mlynář
    • , R. Paprok
    • , M. Peterka
    • , V. Petržilka
    • , M. Tomeš
    •  & P. Vondráček
  77. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China

    • B. Ding
    • , X. Gao
    •  & Y. Liu
  78. Instituto de Física - Universidade de São Paulo Rua do Matão Travessa R Nr.187 CEP 05508- 090 Cidade Universitária, São Paulo, Brasil

    • A. Pires dos Reis
    • , P. Puglia
    • , L. Ruchko
    •  & W. W. Pires de Sa
  79. Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, Portugal

    • P. Abreu
    • , E. Alves
    • , D. Baião
    • , A. Batista
    • , J. Bernardo
    • , J. P. S. Bizarro
    • , D. Borba
    • , B. B. Carvalho
    • , I. Carvalho
    • , P. Carvalho
    • , N. Catarino
    • , R. Coelho
    • , S. Cortes
    • , N. Cruz
    • , L. Fazendeiro
    • , A. Fernades
    • , H. Fernandes
    • , J. Ferreira
    • , A. Figueiredo
    • , J. Figueiredo
    • , L. Gil
    • , R. Gomes
    • , B. Gonçalves
    • , C. Guillemaut
    • , R. Henriques
    • , A. Malaquias
    • , M. E. Manso
    • , L. Meneses
    • , F. Nabais
    • , M. F. F. Nave
    • , I. Nedzelski
    • , I. Nunes
    • , R. Pereira
    • , V. Plyusnin
    • , S. D. A. Reyes Cortes
    • , P. Rodrigues
    • , F. Salzedas
    • , B. Santos
    • , A. Silva
    • , C. Silva
    • , J. Sousa
    •  & J. Vicente
  80. Ioffe Physico-Technical Institute, 26 Politekhnicheskaya, St Petersburg 194021, Russian Federation

    • D. Gin
    • , E. Khilkevich
    • , A. Shevelev
    •  & N. Teplova
  81. ITER Organization, Route de Vinon, CS 90 046, 13067 Saint Paul Lez Durance, France

    • P. Aleynikov
    • , R. Barnsley
    • , M. Bassan
    • , B. Bauvir
    • , L. Bertalot
    • , E. Bruno
    • , W. Davis
    • , M. De Bock
    • , G. De Temmerman
    • , P. de Vries
    • , F. Di Maio
    • , Ph. Duckworth
    • , M. Henderson
    • , G. T. A. Huijsmans
    • , M. Lehnen
    • , F. Leipold
    • , G. Liu
    • , A. Loarte
    • , Ph. Maquet
    • , S. Maruyama
    • , R. Michling
    • , C. Penot
    • , R. Pitts
    • , R. Roccella
    • , A. Sirinelli
    • , P. Thomas
    • , E. Veshchev
    • , M. Walsh
    •  & C. Watts
  82. Karlsruhe Institute of Technology, PO Box 3640, D-76021 Karlsruhe, Germany

    • B. Bazylev
    • , F. Bonelli
    • , C. Day
    • , U. Fischer
    • , T. Giegerich
    • , A. Klix
    • , S. Peschanyi
    •  & S. Varoutis
  83. Laboratorio Nacional de Fusión, CIEMAT, Madrid, Spain

    • A. Baciero
    • , I. Calvo
    • , A. de Castro
    • , E. de la Cal
    • , E. de la Luna
    • , J. L. de Pablos
    • , J. M. Fontdecaba
    • , C. Hidalgo
    • , J. López-Razola
    • , U. Losada
    • , A. Martín de Aguilera
    • , F. Medina
    • , R. Moreno
    • , A. Pereira
    • , G. Rattá
    • , E. R. Solano
    •  & J. Vega
  84. Laboratory for Plasma Physics Koninklijke Militaire School - Ecole Royale Militaire Renaissancelaan 30 Avenue de la Renaissance B-1000, Brussels, Belgium

    • P. Dumortier
    • , F. Durodié
    • , S. Jachmich
    • , Y. Kazakov
    • , A. Krivska
    • , E. Lerche
    • , A. Lyssoivan
    • , A. Messiaen
    • , J. Ongena
    • , R. Ragona
    • , I. Stepanov
    • , M. Tripsky
    • , D. Van Eester
    • , G. Verdoolaege
    •  & T. Wauters
  85. Lithuanian energy institute, Breslaujos g. 3, LT-44403 Kaunas, Lithuania

    • G. Stankūnas
  86. Magnetic Sensor Laboratory, Lviv Polytechnic National University, Lviv, Ukraine

    • I. Bolshakova
  87. Maritime University of Szczecin, Waly Chrobrego 1-2, 70-500 Szczecin, Poland

    • B. Bieg
  88. Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany

    • C. Angioni
    • , M. Balden
    • , É. Belonohy
    • , M. Bernert
    • , V. Bobkov
    • , J. Boom
    • , A. Burckhart
    • , D. Carralero
    • , A. Chankin
    • , D. Coster
    • , S. Devaux
    • , A. Di Siena
    • , R. D’Inca
    • , H. Doerk
    • , A. Drenik
    • , M. Dunne
    • , R. Dux
    • , Th. Eich
    • , M. Faitsch
    • , S. Fietz
    • , K. Gál
    • , B. Geiger
    • , S. Glöggler
    • , H. Greuner
    • , J. Hobirk
    • , A. Kallenbach
    • , A. Kappatou
    • , K. Krieger
    • , P. T. Lang
    • , H. Maier
    • , M. Mayer
    • , G. Meisl
    • , F. Mink
    • , R. Neu
    • , M. Oberkofler
    • , S. Potzel
    • , Th. Pütterich
    • , C. J. Rapson
    • , M. Reich
    • , V. Rohde
    • , K. Schmid
    • , M. Sertoli
    • , B. Sieglin
    • , E. Viezzer
    • , M. Wischmeier
    •  & W. Zhang
  89. Max-Planck-Institut für Plasmaphysik, Teilinsitut Greifswald, D-17491 Greifswald, Germany

    • M. Beurskens
    • , P. Drewelow
    •  & J. Svensson
  90. MIT Plasma Science and Fusion Centre, Cambridge, Massachusetts 02139, Massachusetts, USA

    • V. Aslanyan
    • , A. Hubbard
    • , J. C. Wright
    •  & S. Wukitch
  91. National Centre for Nuclear Research (NCBJ), 05-400 Otwock-Świerk, Poland

    • A. Brosławski
    • , M. Gosk
    • , R. Kwiatkowski
    • , S. Mianowski
    • , J. Rzadkiewicz
    • , Ł. Świderski
    •  & I. Zychor
  92. National Fusion Research Institute(NFRI) 169-148 Gwahak-ro, Yuseong-gu, Daejeon 305-806, Republic of Korea

    • S. Lee
    •  & M. Park
  93. National Institute for Fusion Science, Oroshi, Toki, Gifu 509-5292, Japan

    • M. Tokitani
  94. National Institute for Fusion Science, Toki 509-5292, Japan

    • N. Ashikawa
  95. National Institutes for Quantum and Radiological Science and Technology, Naka, Ibaraki 311- 0193, Japan

    • N. Aiba
    • , H. H. Utoh
    • , N. Imazawa
    • , K. K. Hoshino
    • , K. Kamiya
    • , T. Kobuchi
    • , Y. Miyoshi
    • , N. N. Asakura
    • , T. Nakano
    • , M. T. Ogawa
    • , T. T. Suzuki
    • , H. Tojo
    •  & H. Urano
  96. National Technical University of Athens, Iroon Politechniou 9, 157 73 Zografou Athens, Greece

    • K. Hizanidis
    • , V. Kazantzidis
    • , Y. Kominis
    •  & A. Lazaros
  97. NCSR “Demokritos” 153 10, Agia Paraskevi Attikis, Greece

    • K. Mergia
    • , I. Stamatelatos
    • , P. Tsavalas
    •  & T. Vasilopoulou
  98. NRC Kurchatov Institute, 1 Kurchatov Square, Moscow 123182, Russian Federation

    • A. Alkseev
    • , A. Kukushkin
    •  & V. S. Neverov
  99. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6169, Tennessee, USA

    • L. Baylor
    • , T. Biewer
    • , E. Delabie
    • , R. Grove
    • , D. Hillis
    • , M. Kaufman
    • , C. Klepper
    • , S. Meitner
    • , S. Mosher
    • , M. Parsons
    • , M. Reinke
    •  & J. Risner
  100. PELIN LLC, 27a, Gzhatskaya Ulitsa, Saint Petersburg 195220, Russian Federation

    • A. Lukin
    •  & I. Vinyar
  101. Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy

    • F. Subba
    •  & R. Zanino
  102. Princeton Plasma Physics Laboratory, James Forrestal Campus, Princeton, New Jersey 08543, New Jersey, USA

    • R. Budny
    • , E. Cecil
    • , C. S. Chang
    • , D. Darrow
    • , W. Davis
    • , R. Goulding
    • , B. Grierson
    • , R. Hager
    • , M. Okabayashi
    • , S. D. Scott
    • , J. Strachan
    •  & W. Tang
  103. Purdue University, 610 Purdue Mall, West Lafayette, Indiana 47907, USA

    • G. Miloshevsky
  104. SCK-CEN, Nuclear Research Centre, 2400 Mol, Belgium

    • W. Broeckx
    • , K. Dylst
    • , A. Goussarov
    • , W. Leysen
    • , I. Uytdenhouwen
    •  & W. Van Renterghem
  105. Second University of Napoli, Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy

    • A. Formisano
    • , M. Mattei
    •  & F. Pizzo
  106. Seoul National University, Shilim-Dong, Gwanak-Gu, Republic of Korea

    • H. S. Kim
    • , Y. S. Na
    •  & M. G. Yoo
  107. Slovenian Fusion Association (SFA), Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

    • A. Cufar
    • , A. Drenik
    • , I. Kodeli
    • , B. Kos
    • , I. Lengar
    •  & L. Snoj
  108. Space and Plasma Physics, EES, KTH SE-100 44 Stockholm, Sweden

    • S. Ratynskaia
    •  & P. Tolias
  109. Technical University of Denmark, Department of Physics, Bldg 309, DK-2800 Kgs Lyngby, Denmark

    • A. S. Jacobsen
    • , F. Leipold
    • , V. Naulin
    • , A. H. Nielsen
    • , J. J. Rasmussen
    • , M. Salewski
    •  & A. S. Thrysøe
  110. The “Horia Hulubei” National Institute for Physics and Nuclear Engineering, Magurele- Bucharest, Romania

    • M. Enachescu
    • , A. Petre
    •  & C. Stan-Sion
  111. The National Institute for Cryogenics and Isotopic Technology, Ramnicu Valcea, Romania

    • M. Anghel
    • , M. Curuia
    •  & S. Soare
  112. The National Institute for Laser, Plasma and Radiation Physics, Magurele-Bucharest, Romania

    • T. Craciunescu
    • , P. Dinca
    • , D. Falie
    • , M. Gherendi
    • , I. Jepu
    • , C. P. Lungu
    • , M. Lungu
    • , O. G. Pompilian
    • , C. Porosnicu
    • , C. Ruset
    • , F. Spineanu
    • , I. Tiseanu
    • , M. Vlad
    •  & V. Zoita
  113. The National Institute for Optoelectronics, Magurele-Bucharest, Romania

    • V. Braic
  114. Troitsk Insitute of Innovating and Thermonuclear Research (TRINITI), Troitsk 142190, Moscow Region, Russian Federation

    • V. Amosov
    • , A. Krasilnikov
    • , V. Krasilnikov
    • , N. Marcenko
    • , S. Meshchaninov
    • , G. Nemtsev
    •  & R. Rodionov
  115. Uni of Electronic Science & Tech of China, China

    • J. Wu
    •  & L. Yao
  116. Unità Tecnica Fusione - ENEA C. R. Frascati - via E. Fermi 45, 00044 Frascati (Roma), Italy

    • L. Amicucci
    • , M. Angelone
    • , P. Batistoni
    • , F. Belli
    • , A. Botrugno
    • , P. Buratti
    • , G. Calabrò
    • , A. Cardinali
    • , C. Castaldo
    • , F. Causa
    • , S. Ceccuzzi
    • , R. Cesario
    • , V. Cocilovo
    • , F. Crisanti
    • , C. Di Troia
    • , B. Esposito
    • , D. Flammini
    • , N. Fonnesu
    • , D. Frigione
    • , E. Giovannozzi
    • , M. Marinucci
    • , D. Marocco
    • , C. Mazzotta
    • , F. Moro
    • , D. Pacella
    • , M. Pillon
    • , M. T. Porfiri
    • , G. Pucella
    • , G. Ramogida
    • , G. Ravera
    • , M. Riva
    • , F. Romanelli
    • , A. Santucci
    • , S. Villari
    • , B. Viola
    •  & M. Zerbini
  117. Universidad Complutense de Madrid, Madrid, Spain

    • A. Manzanares
  118. Universidad de Sevilla, Sevilla, Spain

    • J. Galdon-Quiroga
    • , M. García-Muñoz
    •  & E. Viezzer
  119. Universidad Nacional de Educación a Distancia, Madrid, Spain

    • D. Alegre
    • , S. Dormido-Canto
    •  & F. J. Martínez
  120. Universidad Politécnica de Madrid, Grupo I2A2 Madrid, Spain

    • S. Esquembri
    • , J. M. López
    •  & M. Ruiz
  121. Università di Roma Tor Vergata, Via del Politecnico 1, Roma, Italy

    • P. Gaudio
    • , M. Gelfusa
    • , M. Lungaroni
    • , A. Malizia
    • , M. Marinelli
    • , E. Peluso
    • , G. Prestopino
    • , S. Talebzadeh
    • , C. Verona
    •  & G. Verona Rinati
  122. University College Cork (UCC), Ireland

    • S. Knott
    •  & P. J. McCarthy
  123. University Milano-Bicocca, piazza della Scienza 3, 20126 Milano, Italy

    • N. Bonanomi
    • , G. Croci
    • , G. Gorini
    • , M. Nocente
    • , M. Rebai
    •  & D. Rigamonti
  124. University of Basilicata, Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy

    • R. Fresa
  125. University of California, 1111 Franklin St., Oakland, California 94607, USA

    • D. Nishijima
  126. University of Cassino, Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy

    • F. Villone
  127. University of Helsinki, PO Box 43, FI-00014 University of Helsinki, Finland

    • T. Ahlgren
    • , C. Björkas
    • , K. Heinola
    • , A. Lahtinen
    • , A. Lasa
    • , K. Nordlund
    •  & E. Safi
  128. University of Innsbruck, Fusion@Österreichische Akademie der Wissenschaften (ÖAW), Austria

    • V. Goloborod’ko
    • , K. Schöpf
    • , D. Tskhakaya jun
    •  & V. Yavorskij
  129. University of Latvia, 19 Raina Blvd., Riga, LV 1586, Latvia

    • L. Avotina
    • , D. Conka
    • , M. Halitovs
    • , J. Jansons
    • , G. Kizane
    • , J. Lapins
    • , A. Lescinskis
    • , E. Pajuste
    • , A. Vitins
    •  & A. Zarins
  130. University of Lorraine, CNRS, UMR7198, YIJL, Nancy, France

    • S. Devaux
  131. University of Napoli “Federico II”, Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy

    • R. Albanese
    • , G. Ambrosino
    • , V. Coccorese
    • , G. De Tommasi
    • , V. P. Lo Schiavo
    • , S. Minucci
    • , A. Pironti
    •  & G. Rubinacci
  132. University of Napoli Parthenope, Consorzio CREATE, Via Claudio 21, 80125 Napoli, Italy

    • R. Ambrosino
    •  & M. Ariola
  133. University of Texas at Austin, Institute for Fusion Studies, Austin, Texas 78712, Texas, USA

    • B. Breizman
    •  & D. R. Hatch
  134. University of Toyama, Toyama 930-8555, Japan

    • Y. Hatano
  135. University of Tuscia, DEIM, Via del Paradiso 47, 01100 Viterbo, Italy

    • M. Incelli
    •  & M. Moneti
  136. University of York, Heslington, York YO10 5DD, UK

    • J. Beal
    • , C. Bowman
    • , L. Horvath
    • , J. Leddy
    • , M. Leyland
    • , B. Lipschultz
    • , A. Lunniss
    • , M. Reinke
    • , M. Smithies
    • , H. R. Wilson
    •  & A. Wynn
  137. Vienna University of Technology, Fusion@Österreichische Akademie der Wissenschaften (ÖAW), Austria

    • F. Köchl
  138. VTT Technical Research Centre of Finland, PO Box 1000, FIN-02044 VTT, Finland

    • L. Aho-Mantila
    • , M. Airila
    • , A. Hakola
    • , S. Koivuranta
    • , J. Likonen
    • , S.-P. Pehkonen
    • , A. Salmi
    • , P. Sirén
    •  & T. Tala
  139. Wigner Research Centre for Physics, PO B. 49, H - 1525 Budapest, Hungary.

    • G. Bodnár
    • , G. Cseh
    • , D. Dunai
    • , G. Kocsis
    • , G. Petravich
    • , D. Réfy
    • , T. Szabolics
    • , B. Tál
    •  & S. Zoletnik

Consortia

  1. The Alcator C-Mod Team

  2. JET Contributors

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Contributions

All authors have contributed to the publication, being variously involved in the design of the experiments, in running the diagnostics, acquiring data and finally analysing the processed data.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Ye. O. Kazakov.

Supplementary information

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About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphys4167

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