Evidence for Alfvén eigenmodes driven by alpha particles in D-³He fusion experiments on JET

Dedicated fast-ion experiments in mixed D-³He plasmas with n(³He)/n_e ≈ 20%–25% were recently performed on JET [11]. In these studies, deuterium ions from neutral beam injection (NBI) with characteristic pitch, λ = v_||/v ≈ +0.62 (v_|| is the ion velocity along the confining magnetic field B) and E_NBI ≈ 100 keV were accelerated to high energies with waves in the ion cyclotron range of frequencies (ICRF), using the three-ion D-(D_NBI)-³He scenario [12–14]. Co-passing NBI-injected fast ions with v_|| > 0 reached energies up to ∼2 MeV, as confirmed by several fast-ion diagnostics, including gamma-ray and neutron measurements. As a result, a relatively high D–D neutron rate ∼1 × 10¹⁶ s⁻¹ was reached in those D-³He L-mode plasmas at moderate input heating power. Simultaneously with the enhanced neutron production, the population of energetic deuterons gave rise to fusion-born alpha particles, originating from the aneutronic reaction D + ³He → α (3.6 MeV) + p (14.7 MeV). The production rate of D-³He alpha particles was ∼2 × 10¹⁶ s⁻¹ (based on interpretive TRANSP modeling [15]), which is about twice as large as the D–D neutron rate. The toroidal magnetic field on the magnetic axis B₀ = 3.7 T, plasma current I_p = 2.5 MA (I_p and B are oriented in the same direction in JET), ICRF settings (RF frequency 32.2–33.0 MHz, dipole antenna phasing), the ³He concentration, and the central electron density n_e0 ≈ 6 × 10¹⁹ m⁻³ were chosen for efficient generation and good confinement of energetic deuterons and alpha particles in the JET plasma core.

Figure 1(a) shows an overview of JET pulse #95679 (P_NBI ≈ 6.9 MW, P_RF ≈ 5.8 MW, n(³He)/n_e ≈ 22%). ICRF generates a centrally peaked large population of energetic deuterons that results in a strong increase of the central electron temperature and in the D–D neutron rate, raising from T_e0 ≈ 3.6 keV and ∼5 × 10¹⁴ s⁻¹ during the NBI-only phase to T_e0 ≈ 7.6 keV and ∼1 × 10¹⁶ s⁻¹ in the combined ICRF + NBI phase. During this phase, fusion-born alpha particles were produced at a rate ∼2 × 10¹⁶ s⁻¹, as follows from TRANSP. This corresponds to ∼60 kW D-³He fusion power, which is four times larger than the maximum D-³He fusion power (∼15 kW) reached in JET-ILW ICRF + NBI experiments with 3rd harmonic ICRF heating of D-NBI ions [16]. The sawtooth dynamics in this pulse was rather complex and the duration of the sawtooth-free phases Δt_saw varied between 210 ms and 730 ms. A rich family of Alfvén eigenmodes (AEs) was destabilized by fast ions, including the toroidicity- (TAEs, f ≈ 200–260 kHz) and the ellipticity-induced modes (EAEs, f ≈ 540–600 kHz), as well as the reversed-shear Alfvén eigenmodes (RSAEs) during the long-period sawtooth-free phases (see figure 4(b) in [11]). Note that the injected fast NBI ions were sub-Alfvénic (v_NBI/v_A ≈ 0.4; v_||,NBI/v_A ≈ 0.25) and no AEs were destabilized in the NBI-only phase of #95679.

Zoom In Zoom Out Reset image size

In this paper, we consider specifically Alfvén instabilities in the EAE frequency range and focus on the modes observed after the monster sawtooth crash at t ≈ 11.035 s (Δt_saw = 730 ms). Figure 1(b) illustrates the destabilization of modes in the ion-diamagnetic direction (n > 0, starting from t ≈ 11.08 s), typical for plasmas with a radially peaked population of fast ions such as the ICRF-accelerated deuterons in this experiment. Similar to earlier experiments with ICRF on JT-60U [17], EAEs are located at the q = 1 surface (q is the magnetic safety factor). This was inferred from correlation reflectometer measurements (providing the radial mode localization, R ≲ 3.25 m) and sawtooth inversion radius (R_inv) analysis. In this pulse, we find that R_inv varied between 3.16 m and 3.25 m, when Δt_saw increased from 250 ms to 730 ms. Thus, shortly after a sawtooth crash favorable conditions for the destabilization of EAEs with n > 0 are present: the q = 1 surface is located close to the plasma core, where centrally peaked population of energetic D ions is generated by ICRF. The q-profile evolves during the sawtooth cycle, impacting the evolution of different types of AEs: in particular, the disappearance of EAEs nearly coincides with the appearance of RSAEs. Note that the efficient destabilization of EAEs in this series of fast-ion experiments in D-³He plasmas was also due to the high magnetic field chosen for this experiment (B₀ = 3.7 T). Indeed, under these conditions the parallel velocity of the injected fast NBI ions was smaller than v_A/2, thereby leading to a negligible EAE damping.

Surprisingly, simultaneously with n > 0 EAEs, the n = −1 EAE was observed starting at t ≈ 11.14 s (see figure 1(b)). This was unexpected as the radial-gradient mechanism associated with a radially peaked fast-D population can effectively destabilize modes with n > 0, but provides damping for modes with n < 0. Furthermore, the global AE (GAE) with n = 0 was also destabilized after the monster sawtooth crash. As neither of these two modes are currently considered for ITER, it is important to gain insight in the physics behind these JET observations.

The redistribution of fast ions during the sawtooth crash in tokamaks is complex. Present-day insights indicate that the fast-ion redistribution is pitch-angle or energy dependent, or both, e.g. [18–20]. Yet a widely accepted theoretical model that is consistent with all experimental observations is so far eluding [21].

Energetic D-ions give birth to both D–D neutrons and D-³He alpha particles. A significant sawtooth-induced redistribution of both energetic deuterons and alphas was observed. The dynamics of fast deuterons during the sawtooth crash was monitored by the neutron camera at JET, which has a temporal resolution of ∼10 ms. This diagnostic has 19 lines-of-sight, allowing to reconstruct the 2D spatial profile of the neutrons and thus energetic D-ions. Figures 2(a)–(c) show the reconstructed neutron emission profile shortly before and after the monster crash at t ≈ 11.035 s, illustrating the substantial redistribution of fast-D ions. Figure 2(d) further corroborates this observation: a reduced neutron emissivity in the central channel #5 of the neutron camera and an increased emissivity in channel #6 further off-axis after the crash. By the time the n = −1 EAE mode is destabilized, energetic deuterons recover their spatially peaked distribution (cf figure 2(c)) and their radial gradient provides damping for the n = −1 mode.

Zoom In Zoom Out Reset image size

The presence of high-energy alpha particles was independently confirmed by the gamma-ray and fast-ion loss detector (FILD) measurements. The tomographic reconstruction of the 17 MeV gamma-ray emission (from a weak secondary channel of the D-³He fusion reaction [11, 22]) shows that alpha particles were also localized in the central region of the plasma (see figure 5 in [23]), where EAEs were generated. However, this diagnostic has insufficient temporal resolution to follow the details of the alpha dynamics during the sawtooth crash. In contrast, the FILD system at JET provides fast signals (Δt ≈ 0.5 μs) of energetic ions escaping the plasma [24]. Figure 3(a) shows a snapshot of lost energetic ions with a Larmor radius ρ_L ⩾ 10 cm (E_α ⩾ 4.0 MeV) and a pitch-angle in the range ∼55°–60° shortly after the sawtooth crash (t = 11.042 s). The reconstructed orbits shown in figure 3(b) correspond to lost alphas originating from the plasma core. As shown in figure 3(c), after the sawtooth crash the loss rate of alpha-particles is increased by ∼60% with a relaxation time of ∼200 ms.

Zoom In Zoom Out Reset image size

Note that alphas are not only redistributed by the sawtooth crash, but also their birth profile is affected by the sawtooth-modified distribution of D-ions. Together with the different dependence of the D–D and D-³He reaction cross-sections on the energy of fast deuterons [25], this can lead to alpha distributions with rather non-standard features.

Figures 4(a) and (b) show the computed absolute values of the strength of various resonances for the observed n = −1 EAE at f ≈ 555 kHz, assuming fast D-ions and alpha particles as driver of the mode. The plotted quantity is the standard deviation of the particle energy, interacting with the EAE with typical fixed mode amplitude δB/B = 1 × 10⁻⁵ over 400 wave periods, as computed with the HAGIS code [26]. A uniform pitch-distribution of test particles (from λ = −1 to λ = +1) was used. As expected, the wave-particle interaction occurs along the resonance lines ω = nω_φ − pω_θ , where ω and n are the AE frequency and the toroidal mode number; ω_φ and ω_θ are the toroidal and poloidal orbital frequencies; p is an integer [7].

Zoom In Zoom Out Reset image size

The spatial structure of the n = −1 EAE was computed by the MISHKA code [27] and is shown in figure 4(c). The relevant EAE gap is produced at the crossing between the poloidal mode numbers m = 0 and m = 2. The error bars are mainly determined by uncertainties in the safety factor in the central region of the plasma. A monotonic q-profile with a variable value of q₀ was considered in this calculation. With q₀ ≈ 0.95, both the computed mode frequency and mode localization matched well with the measurements. Figure 4(c) also shows the reconstructed FILD orbits, clearly illustrating the significant overlap between the n = −1 EAE mode structure and the region where alpha particles are generated in the plasma.

The resonance maps displayed in figures 4(a) and (b) allow to identify the characteristics of fast ions that resonantly exchange energy with the mode, but they do not distinguish resonances contributing to the mode drive and mode damping. The sign of the resulting energy exchange depends on the details of the fast-ion distribution and the integrals over the distribution function gradients along the resonance lines. As discussed above, the centrally peaked fast-D population provides damping for n < 0 modes. Furthermore, as follows from figure 4(a), the resonant exchange of energy for the mode is only possible for energetic deuterons with λ_|| < 0, which are virtually absent in this fast-ion experiment, where ICRF accelerates co-passing NBI-injected ions. These two arguments imply that the generated fast deuterons are inefficient to destabilize the n = −1 EAE.

In contrast, the distribution function of alpha particles naturally spans the full range of pitch values, thus fulfilling a necessary condition for the destabilization of the n = −1 EAE (figure 4(b)). Yet the presence of such ions alone is not sufficient for the existence of modes with negative toroidal mode numbers. Having a self-consistent modeling of the mode growth rate would be ideal, but it requires a detailed knowledge of the alpha distribution function f_α = f_α(E, λ, r) and its modification during the sawtooth crash, which is particularly complex in these JET experiments. In the absence of a realistic alpha distribution when the n = −1 EAE was observed, we cannot provide credible simulations of the mode stability. Instead, in what follows we present conjectures for the origin of the modes, consistent with experimental observations.

Note that non-standard distributions of energetic alpha particles induced by sawtooth crashes were earlier reported in NBI-only D–T experiments on the tokamak TFTR. As discussed in [28], sawtooth crashes resulted in a large drop in the core alpha density and the appearance of radially hollow alpha profiles (note that n < 0 AEs were not reported in [24]). A similar depletion of alphas in the plasma core could also play a role in these JET experiments, as hinted at by the reconstructed FILD orbits (figure 3(b)). Indeed, the orbit-modelling shows that the detected alphas have energies E_α > 4.0 MeV and pitch between λ ≈ −0.5 and λ ≈ −0.36 in the plasma core, thereby fulfilling a necessary resonance condition for the n = −1 mode, shown in figure 4(b). Alphas with lower energies that resonate with the n = −1 EAE are also redistributed during the sawtooth crash. However, as these particles have smaller orbits, they do not reach the FILD detector.

Anisotropy of the pitch-angle distribution of fast ions is another source of free energy that can potentially destabilize modes with n < 0 [29]. The fast-ion anisotropy term, contributing to the energy transfer, can be expressed as δγ ∝ (1 − λ²)/(2λE)∂f/∂λ. Thus, this mechanism can contribute to the mode drive by energetic ions with λ < 0, if their distribution fulfills the condition ∂f/∂λ < 0. Note the anisotropy drive was reported to be significant only when the mode frequency is close to one of the critical frequencies, ω_nl (see the definitions in [30]). The computed frequencies ω_nl (l = 1–3) are significantly below the experimentally measured n = −1 EAE frequency.

A population of fast ions with the inverted energy distribution ∂f/∂E > 0, often referred to as a bump-on-tail, can also contribute to the destabilization of Alfvénic instabilities. This mechanism cannot be at work for the steady-state slowing-down distribution of alphas as it decreases monotonically with energy. Generating a bump-on-tail and thereby impacting the AE stability is possible by modulating the fast-ion source on a time scale shorter than the characteristic fast-ion slowing-down time. This has been successfully demonstrated in recent DIII-D experiments using NBI modulation [31]. In the JET experiments reported here the sawtooth-induced redistribution of fast D-ions provides an intrinsic mechanism for the modification and modulation of the D-³He fusion source of alphas. The importance of this novel mechanism has not yet been assessed for ITER.

Another unexpected interesting observation is the destabilization of the n = 0 GAE in the EAE frequency range at t ≈ 11.13 s, cf figure 1(b). This mode consists of two dominant poloidal harmonics (m = ±1) and is also localized in the central region of the plasma. For n = 0 modes, the spatial fast-ion gradient does not contribute to the mode drive/damping. Thus, either the anisotropy of the distribution function with respect to the pitch angle [31] or the presence of a positive energy gradient [32], or a combination of both drives these modes unstable. Further detailed mode drive analysis requires a realistic alpha distribution produced by the sawtooth crash. Note that both n = −1 and n = 0 modes were observed in other pulses of this series of experiments, as well as in previous JET experiments with 3rd harmonic ICRF heating of D ions in D-³He plasmas [33].

The reported JET experiments in D-³He plasmas with energetic deuterons and alpha particles clearly demonstrate the non-linear interplay between fast-ion plasma heating, sawtooth stabilization and crashes, and fast-ion-driven AEs. Such synergies will become increasingly more important in ITER and future burning plasma experiments with a large population of fusion-born alpha particles. While the stability of AE modes has been quite extensively analyzed late in the sawtooth cycle [5], a detailed analysis of AEs shortly after the crash has received much less attention. These JET results show that non-standard fast-ion distributions can be generated during the sawtooth crash, in turn, leading to the destabilization of AE modes that are currently not considered for ITER. As AE instabilities are potentially detrimental for the performance and stable operation of ITER, the mere observation of these unexpected modes on JET is an important message for the plasma physics community. We also note a close link between the sawtooth period and the intensity of EAEs in these JET experiments. In particular, EAEs were prominently present in JET pulses with short-period sawteeth.

Our results highlight the need for dedicated modelling activities to further improve knowledge on the complex interplay between the sawtooth-induced redistribution of fast ions and AEs in fusion plasmas. The paper also underlines the particular merit of D-³He plasmas for fusion research, allowing a better understanding of several important aspects for burning reactor plasmas, prior and complementary to future full-scale D–T experiments.

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 and 2019–2020 under Grant agreement No. 633053 and from the RCUK Energy Programme (Grant No. EP/T012250/1). To obtain further information on the data and models underlying this paper please contact PublicationsManager@ukaea.uk. The views and opinions expressed herein do not necessarily reflect those of the European Commission.