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.
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 = pωci (p = 1,2, …), in the vicinity of which the RF power can be efficiently absorbed by ions.
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 ω ≈ ωci.
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.
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 ΔTe0/ΔPICRH > 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 (ΔWp/ΔPICRH = 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, pγ)11B and 9Be(3He, nγ)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.
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) + n frot ≈ 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.
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.
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.
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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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.