European transport simulator modeling of JET-ILW baseline plasmas: predictive code validation and DTE2 predictions

To initiate fusion reactions in tokamak devices, the plasma has to be heated to a suitably high temperature using one or a combination of external heating methods. For example, in ITER neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH) will be used to increase the temperatures beyond what is achieved by ohmic heating. To be able to predict how ITER discharges will behave it is necessary to have numerical tools capturing the dynamics sufficiently realistically. Adopting these tools to study current-day discharges and compare their predictions with actual experimental results allows one to benchmark and improve models.

The European Integrated Modeling effort (EU-IM) has led to the creation of a standardized simulation platform for testing and exploiting numerical code modeling aspects of plasma dynamics in fusion machines [1, 2]. A wide variety of programs provided by many European fusion laboratories is currently available under EU-IM. One of its key achievements is the European Transport Solver (ETS) [3]. This suite of codes was designed to simulate arbitrary tokamak plasma discharges, not only highlighting the evolution of particle density and energy due to transport effects, but providing insight into fast ion dynamics resulting from ICRH and NBI, and the impact these high-energy populations have on the plasma core. An important feature of this platform is that it allows coupling independent codes each focusing on various aspects of the dynamics of the discharge while making use of a shared database of parameters. This allows one to provide answers on different levels of complexity and integration ranging from relying on simple scaling laws to making use of very sophisticated first-principle models. ETS can be run in two distinct modes: 'interpretative' analysis exploits experimentally available information to compute quantities (such as the distribution function of various plasma constituents) that are not experimentally available, allowing one to assess performance-related quantities, such as the neutron rate and further compare them to experimental measurements. This kind of analysis is carried out by taking a snap shot in time. 'Predictive' analysis goes a step further, allowing one to predict how quantities, such as ion and electron temperatures evolve as a result of the applied power and governing plasma dynamics.

In order to prepare the next JET DT experimental campaign [4], the extrapolation of fusion performance on DT plasma from DD plasma is required. In this paper, self-consistent extrapolation results obtained with ETS will be shown with a particular focus on ICRH/NBI synergy. Making these simulations is a demanding task since the coupled set of equations concerning additional heating and temperature transport have to be solved consistently, tracking the dynamics and evolution of multiple interacting populations, each evolving as a result of combined heating, Coulomb collisional interaction and transport. Each of these aspects is modeled in dedicated modules. In the present paper, the focus is on the description of wave-particle and particle–particle interaction involved in wave and neutral beam heating, and the Coulomb collisional interactions between particle populations through which externally applied energy is transferred to the main plasma species. As this was the first time that these simulations were done using ETS, adaptations of the simulator had to be made to remove bugs and inconsistencies, while upgrading the physics and improving numerics. Because a number of populations has to be monitored simultaneously on a sufficiently large number of magnetic surfaces and iterative solving is required (e.g. because modeling Coulomb interaction between non-Maxwellian distributions requires adopting the non-linear Coulomb collision operator), many thousands of calls to specific submodules are being made. As a result, these simulations are time consuming. To enable parametric scans, it is necessary to adopt simple and fast yet sufficiently realistic models instead of sophisticated tools starting from using first principles (as in [5]). ETS allows one to predict ion temperatures (by solving an ad hoc energy transport equation for each bulk ion temperature) as well as distribution functions consistent with combined wave and beam heating and does so by solving sets of coupled equations. The fact that this allows one to describe Coulomb interaction of non-Maxwellian minorities, majorities and beam populations sets it apart from other modeling, which typically accounts for one non-Maxwellian at a time only in spite of the fact that multiple populations are well away from thermal equilibrium in most if not all fusion-relevant scenarios. In contrast, DT extrapolations were done with other integrated modeling software [4, 6, 7], but with making different assumptions. For instance, CRONOS [8] relies on the fact that there is only one bulk ion temperature, which will not necessarily be the case in mixed majority DT experiments. And JINTRAC [9] uses prescribed idealised Gaussian ICRH heating profiles in order to be able to make some parametric scans [10]. Some recent work on extrapolated DT plasma scenarios and using TRANSP [11] highlighted the synergistic effects observed when simultaneously exploiting ICRH and NBI heating. This description hinges on temperatures being prescribed—making use of profiles provided by another code, such as JINTRAC—rather than predicted [12–15]. Confidence is gained in making predictions for future experiments by adopting a wide range of tools, each having advantages and drawbacks. The main advantage of the tool exploited to obtain the data in the present paper is the fact that it accounts for interactions between all ion populations.

The European transport simulator is developed by the European Integrated Modeling team [3]. The main emphasis of this group effort is to enhance the reliability as well as the capability of the suite of codes so that they can be used in routine fashion to prepare experiments, and provide theoretical insight when analyzing their results. The ongoing JET campaigns—intended to culminate in a second period of DT operation—is an ideal target to do predictive as well as interpretative work. The ETS suite is run using a 'workflow', the various components of which address sub-aspects of the physics, which are typically developed by different contributors, each specialized in their physics subdomain. In the present paper, the emphasis is on auxiliary heating and more particularly on the impact of NBI/ICRH synergy on fusion performance. Two 1D Fokker–Planck solvers for arbitrary distribution functions have recently been implemented in ETS: StixRedist [16] and FoPla [17]. The former allows one to obtain distribution functions for non-beam populations heated at any cyclotron harmonic while interacting with multiple non-Maxwellian distributions via Coulomb collisions. In addition, the latter extends the scope by computing the distribution functions for the beam populations. Whereas the first is solved very CPU efficiently, the latter requires inverting large matrices and is significantly slower. To ensure the CPU time remains acceptable, the FoPla module was parallelized [18]. The verification/validation of these modules in the heating and current drive ETS workflow in high-power JET-ILW discharges has permitted us to highlight the importance of the non-linear collision operator when solving a set of coupled Fokker–Planck equations for cases when majority species play a key role [18].

The integration of these modules including the computation of NBI/ICRH synergy is depicted in figure 1. Describing the impact of auxiliary heating requires knowledge of (i) how externally applied energy is deposited locally in the plasma, (ii) how this power is redistributed in velocity space among the various plasma constituents and (iii) how it is spatially redistributed, shaping the fast particle and bulk temperature profiles. Each of these aspects requires solving a dedicated equation and the various equations are coupled:

• (a)  
  Prior to the NBI/ion cyclotron range of frequencies (ICRF) synergy computation, the beam densities, energy sources and power densities are computed by BBNBI/ASCOT code [19] accounting for the various energy levels (full, 1/2 and 1/3 energy) of the neutral beam source.
• (b)  
  The 2D RF wave equation solver (in the present application, CYRANO [20] is typically used) provides the RF electric fields and RF power absorption profiles by the various species in the plasma, including high-energy sub-populations created by NBI.
• (c)  
  On the basis of the RF and beam deposition profiles, the Fokker–Planck solvers (either the StixReDist or the FoPla module) describe the Coulomb collisional power exchange between the various populations, in particular, the interaction of RF-heated RF minorities or beam accelerated ion populations and the bulk plasma, providing a heat source (per species) to the transport solver.
• (d)  
  The transport solver evolves the kinetic profiles as a response to the ICRH and NBI power applied using the heat source to the various species obtained in (b), and provides a new plasma target to be used in the next time iteration.

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A simplifying assumption is that guiding centers are stuck to magnetic surfaces, i.e. zero banana width approximation, allowing the solving of sets of coupled Fokker–Planck equations on each of the considered magnetic surfaces. In order to ensure a self-consistent wave/Fokker–Planck equation computation, a consistency loop is introduced. As accounting for RF-heated arbitrary distribution functions is beyond the scope of CYRANO, the distribution functions are replaced by their Maxwellian 'equivalent', which has a mean energy ⟨E⟩ given by ⟨E⟩ = 3/2NkT_eff, where T_eff is the effective temperature of the actual distribution function and k is the Boltzmann constant.

In the case of a DT plasma, the alpha power resulting from fusion reactions has to be taken into account. The alpha birth rate is deduced from the DT neutron yield. Since the alpha particle energy (several MeV) is far above that of the critical energy (several tens keV), it is a reasonable approximation to simply add the alpha power density to the electron heat source.

Based on the species densities and electronic temperature, the impurity radiation is predicted by relying on a module [8] (coming from the CRONOS software) that computes, under the ionization equilibrium hypothesis, the radiation profiles using an atomic data database. As a first step, only one impurity is taken into account representing an average contribution of all impurities present in the plasma to match the value of Z_eff measured experimentally. A more accurate simulation would be to use several impurities. Based on experimental evidence from JET baseline shots, it was assumed that the radiated power is 30% of the additional heating power, as shown in the next section. Thus, the radiation profiles are renormalized with that value.

When running the ETS in interpretative mode, the temperature profiles are not evolved predictively but quantities such as the distribution functions consistent with the experimental data and required to compute the fusion yield are found. In predictive mode, the temperature profiles are not found experimentally but computed. Hence, a suitable transport model is required to make sure the predictions are meaningful. Comparing predictions with experimental findings allows one to assess which models are best suited for simulating particular experiments, subsequently allowing one to make predictions for future experiments. ETS offers the possibility to make transport predictions accounting for a wide variety of transport models, among them anomalous plasma transport coefficients stemming from first-principle models, such as TGLF [21] and QUALIKIZ [22], but also simpler models based on Bohm/gyro-Bohm scaling [23, 24] 24. In our study—where the focus is on improving the quality of the RF heating description and where the transport model is only used to illustrate predictive capability—we only use the latter, the reason being that it is simple, fast and has proved to be reasonably meaningful for the type of discharges modeled [23]. Other JET DTE2 predictions [7, 10] use more sophisticated transport models but usually use a more simplified module for the ICRF heating physics of the various species present in the plasma. An empirical module is used, which consists of manually fixing the transport coefficient in the pedestal region in order to fit the experimental data. The neoclassical transport coefficients are computed with NEOS [25]. In the present study, the densities are taken from available experimental input (mainly D, H ion densities and electron density); only the (bulk) ions and electron temperatures are predicted. For each temperature, a dedicated transport equation is solved. Rather than solving a separate energy transport equation for the minority, the minority species temperature is prescribed; it is assumed to match the bulk ion temperature. On Fokker–Planck level, however, the minority is a key participant and cannot be neglected. The same holds true for the beams. But for transport analysis, their role is mainly to set up the proper local heat sources for the bulk species (ions as well as electrons). Finally, the current diffusion equation is solved consistently with the equilibrium computed by a fixed boundary code CHEASE [26]. This is necessary when the magnetic configuration changes are accounted for, which will be the case when predictions are made.

As mentioned, for the present study, the 'predictive' simulations were produced on the basis of the computed heating depositions and assuming a fixed fraction of the radiation loss w.r.t. the launched auxiliary power. The profiles of the temperatures, current density and equilibrium are found through solving the relevant equations. The transport in the pedestal is fixed manually so that the predicted temperatures match the experimental values of the DD reference shot at the top of the pedestal. These transport coefficients are then kept constant for the DT-extrapolated simulations. In what follows, ρ_norm = sqrt(Ψ/Ψ_b)—where Ψ is the toroidal magnetic flux and Ψ_b is the toroidal magnetic flux at the last closed surface—is used as the radial variable.

The JET baseline scenario is based on high-current (I_P >= 3 MA) ELMy H-mode plasmas with β_N ≈ 1.8 and q₉₅ ≈ 3. The current is typically fully diffused after the start of the H-mode phase, leading to a central safety factor of around q₀ ≈ 1 and long sawteeth [6]. The baseline scenario relies on the favorable scaling of the confinement with plasma current to achieve high fusion power.

The studied discharge is the JET baseline shot 92436. The main parameters of discharge 92436 are shown in figure 2. The magnetic field is B₀ = 2.88 T and the plasma current is I_P = 3 MA. The current is practically fully diffused at t = 48.5 s with safety factor values at the edge and in the core of q₉₅ = 3.2 and q₀ ≈ 1, respectively (from EFIT with polarimetry constraints), while some other quantities, such as the core density (b) and the normalized kinetic pressure β_N (d) are still evolving to reach a steady state around t = 49 s. The fact that the q₀ value drops below unity quite early is illustrated by the presence of long sawteeth in the discharge, as can be seen by the central electron temperature traces (c). The H₉₈ factor reaches about 1.1 in the flat-top, showing the good confinement obtained in this discharge. The β_N value (from pressure-constrained EFIT) is about 2.2–2.4 in the flat-top, slightly higher than the usual target typically envisaged for baseline plasmas (β_N < 2), but there is no evidence of deleterious MHD in this pulse. As will be discussed later, the predictive simulations were done from 48.5–49 s, to assess whether the models can properly describe the plasma evolution in this time interval that precedes the more steady phase of the discharge (see section 2 for the computation details).

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Although there is no N > 1 MHD activity in the modeled window, there is a sawtooth crash at t = 48.6 s. The plasma and additional heating parameters are described in table 1.

The discharge contains 1.7% of hydrogen (as measured by the visible light spectroscopy diagnostic). It was assumed that the plasma only contains a single impurity, which is nickel. The Ni concentration was imposed to fit the experimental averaged value of Z_eff = 1.4–1.5, as measured by visible spectroscopy between 48.5–49 s and as used in the TRANSP simulations published in [13]. For the prescribed magnetic field (2.88 T), fixing the frequency of the ICRF antennas at 42.5 MHz ensures the reigning wave heating mechanisms are core fundamental cyclotron heating of the H minority and second harmonic heating of the D majority and D beam population. A reference interpretative TRANSP run (92436Q01) was taken. In order to facilitate the comparison with TRANSP, all the input data and in particular the initial kinetic profiles that serve for ETS interpretative and predictive runs are taken from that simulation. The TRANSP kinetic profiles are obtained from the JET diagnostics using for T_e, the electron cyclotron emission diagnostic and the high-resolution Thomson scattering (HRTS) diagnostic, for T_i the core and edge charge exchange diagnostics, for Ne the LIDAR and HRTS diagnostics, and for the minority concentration, the visible spectroscopy (KS3). The deuterium density is deduced from the quasineutrality. The charge exchange diagnostic available at JET provides ion temperature up to ∼20 cm from the center and hence the actual core temperature is not experimentally known. In TRANSP, a choice was made to adopt a conservative estimate of the core value by truncating the ion temperature in the plasma center to the value at the innermost known position.

A first verification and validation effort on the ICRH/NBI absorption was reported on [18, 27]. A good agreement was obtained, both when comparing the predictions with TRANSP for cases within its reach (the only non-Maxwellian population either being a minority or beam population) and with experimental neutron yield data. Through this exercise, the importance of accounting for the majority self-collisions via the non-linear collision operator has also been shown. The next step is to verify and validate the predictive simulations. The results from the interpretative TRANSP run—and in particular the kinetic profiles—are used as input data. The Fokker–Planck solver FoPla can either be run only by means of modeling the velocity space evolution of the minority—in which case it adopts a philosophy similar to that used in TRANSP—or alternatively modeling the full set of coupled equations describing the evolution of the distributions of all species interacting via Coulomb collisions. In the latter case, the importance of adopting the non-linear self-collision operator becomes clear; it accounts for the actual shape of the distribution functions F_o, i.e. it does not assume F_o is Maxwellian. An iterative scheme is used to account for the non-linearity.

The current diffusion is computed, as described in section 2. The q profile found is in agreement with EFIT measurement and TRANSP computation. The results of the predictive simulation for electron and ion temperatures and density profiles at 49 s versus ρ_norm, in the case where the Fokker–Planck equations are solved for all ions, is shown in figure 3. These results were obtained after the modification of the original Bohm/gyro-Bohm model by multiplying the original diffusivities by a factor 1.3 in order to minimize the differences with respect to the experimental temperatures. This retuned version of the model is used uniformly throughout the paper, even for the D−T extrapolations discussed in sections 4 and 5. This simple tuning of the model is not intended to deliver a full validated version but rather a change aimed at avoiding too high temperatures leading to an optimistic DT fusion yield, which could also mask the main goal of this paper, i.e. the analysis of the ICRH-NBI synergy. A similar strategy was adopted in other conservative D−T extrapolation activities at JET [7, 28]. Further validation and verification activities will be carried out in the near future with TT and D−T plasmas to check whether the adjustment made is compatible with experimental findings.

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As mentioned earlier, the flat T_i near the core as well as the discontinuous break of the derivative is a TRANSP choice to adopt a conservative estimate. A good agreement of the predictive temperatures with the experimental data is observed in the region where experimental data is available. One of the advantages of predictive transport modeling is that if the correct transport model is used, the central temperature can be estimated in the absence of core ion temperature measurements. The correct temperature profile is essential for estimating the fusion rate. The agreement is good for both T_i and T_e.

The reader can refer to section 2 for the radiation computation details, which are not self-consistently described since a rigorous treatment of the impurities requires information about the impurity densities; these are poorly known at best. The left graph of figure 4 shows the experimentally observed integrated radiation. Although the radiation undergoes large variations (due to the ELMs ejecting particles and energy) the mean value of radiated power is about 10 MW, representing 30% of the incoming power. In the computations, the integrated power level due to radiation was assumed to be 30% of the incoming power throughout. The radiation profile at 49 s is not available for this shot, but at 50 s it can be seen that most of the radiation occurs in the outer layers of the plasma (right graph of figure 4). This is compatible with the radiation profiles computed in figure 4 (middle): initial and final profiles of the radiation.

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A good agreement with the experimental data is obtained for the ion temperature in the region where charge-exchange spectroscopy data are available (ρ_norm > 0.3) and the simulations predict a considerable ion temperature peaking (left graph of figure 5) in the central region. The central ion temperatures are in the right ballpark, as can be seen by the good agreement between the measured and calculated neutron rates, shown in the right graph of figure 5 (note that the plasma density is imposed in these simulations, so the neutron rate only depends on the ion temperature profile and the neutral beam deposition of each NBI energy component). The fact that the kinetic stored energy W_p = W_th + 3/4W_fast (figure 5 middle) is also well reproduced confirms the successful predictions of the kinetic temperature profiles for ions and electrons. The discrepancies observed in the first time steps of the simulation are mainly due to the ion temperature clipping imposed at the initial simulation instant due to the lack of charge-exchange measurements inside ρ_norm = 0.2 (see figure 3) followed by an overestimation of the ion temperature before the collisional relaxation processes of all the ions included in the modeling are properly taken into account. The relatively fast convergence of the simulations (100–150 ms) is related to the fast evolution of the predicted core ion temperatures with central ICRF and NBI heating, where the slowing-down time is around ∼100 ms in this case. The dynamics of the ions accelerated by ICRH also evolves in a similar timescale and thus influences the convergence rate of the simulations. However, because the (all-ion) Fokker–Planck solver used here is non-linear and uses an iterative algorithm, all the ion distribution functions accelerated by ICRH are self-consistent with each other, and the converged distributions of the fast ions are passed to the transport solver at each iterative step. It is interesting to see that the difference between the experimentally measured and predicted values decreases as the transport simulation restores the core temperature to a value that deviates from the artificially clipped one while reconstructing a peaked core profile, which is more aligned with what is physically expected (see figure 3). The step observed in the measured ion temperatures at t = 48.7 s (also seen in the neutron rate to a lesser extent) is due to a strong sawtooth crash that is not described in the current model. After t = 48.7 s, the sawtooth effect disappears from the experimental signals and at about the same time the simulations achieve converge. From there on the predicted ion temperatures, stored energy and neutron rate are in very good agreement with the experimental measurements.

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Figure 6 illustrates why it is important to account for the evolution of all distributions when modeling scenarios for which various populations are simultaneously heated. The demonstration has already been discussed in detail in the interpretative simulation in [18] with interpretative simulations and is merely mentioned again in the present paper. When the D majority Fokker–Planck equation is not solved (i.e. when only the minority power redistribution is accounted for, as TRANSP does), all power absorbed by the D ions stays in the D channel, which leads to dominant D heating and potentially constitutes an overestimate of the D power density that is used by the transport solver (figure 6 (left)). When, on the other hand, the D majority tail formation and associated Coulomb collisional redistribution are accounted for, a small fraction of the ions carrying a non-negligible part of the wave power is accelerated to high energies (far above the critical velocity) causing part of the RF power originally absorbed by the D ions now to end up in the electron channel, leading to more balanced core electron/deuterium heating (figure 6 (right)). The impact of the D RF power density on the ion temperature is rather small but not negligible (see figure 7) because the majority's temperature is mainly prescribed by the massive NBI power injection, resulting from the slowing of beam particle heating ions as well as electrons. The main role of the RF power is to influence the fast particle sub-population, which in turn influences the neutron rate (as will be discussed later in the text, a large fraction of the neutron rate is due to the presence of fast sub-populations). Keeping the same main ion temperatures while omitting the impact of the RF waves on the majority ions as well as the beams yields a 10% decrease in neutron rate (see [18]).

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Having established in the previous section that the ETS suite is capable of reproducing experimental findings up to an acceptable error bar, the present section is devoted to making predictions for the upcoming DT experimental campaign. A logical exercise when preparing for such a campaign is to extrapolate from the previous shot with a D majority the expected behavior of a DT plasma in terms of neutron yields with the maximum available NBI power. To this end, we replace the deuterium plasma with 50% deuterium and 50% tritium. Again, in the following simulations, the bulk species densities are prescribed. We keep the same magnetic configuration as in the reference shot. The temperatures and equilibrium are computed with ETS as described in section 1, consistent with the externally applied heating power and its impact on the fast and bulk populations. To ensure the bulk ion populations remain balanced, the NBI should contain 50% D and 50% T. In these simulations, alpha heating is taken into account, with the alpha particle density being inferred from the local fusion reaction rate (i.e. the alpha heating profile is homothetic of the DT neutron rate profile). Since the alpha particle energy (3.45 MeV) is far above of the critical energy (∼150–200 keV), a good approximation is to consider that all the alpha power is collisionally transferred to the electrons. Since the alpha particle concentration is small it is not treated as a separate species, only its impact on the fusion yield is accounted for.

In order to assess the impact of using tritium beams, we made two DT simulations: one with pure D-beams and the other with DT beams keeping the same ICRF heating scheme but increasing the NBI power to the optimal power based on optimal engineering aspects accounting for decreasing risk of beam trips. The optimal parameters for the D-beams case are 32 MW of heating power with a birth energy of 125 keV, whereas for the DT beams case there are 33.44 MW of total NBI power decomposed in 17.44 MW coming from T-beams and 16 MW coming from D-beams. The T-beams birth energy is fixed to 118 keV. We observed that an increase in NBI power leads to an increase in the bulk species temperatures in the plasma core and even at the top of the pedestal. The final temperatures are given in figure 8. Despite a higher NBI power in the DT beams case, the T ion temperature is a little lower (0.2 keV) than in the D-beams only case. This can be explained by T-beam penetration. As can be seen in figure 9, the T-beam penetration in the plasma core is less efficient than D-beams because the T velocity is smaller than the D velocity. This is due to its larger mass and a smaller injection energy (118 instead of 125 keV). However, it is worth stressing that the extrapolation from DD to DT performed here might neglect some effects, such as isotope effects [29], which are not included in the Bohm/gyro-Bohm model. Furthermore, the retuned version of the Bohm/gyro-Bohm model used in this paper might not be optimal for DT plasmas. Further validation and verification of the models applied in this paper will be performed in the upcoming JET DT campaign.

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The neutron rate is given by a new EU-ITM module called 'FusReac', which for arbitrary 1D isotropic distribution functions of the various species computes the reactivities using DD, DT and TT cross-sections. The FusReac module is based on the cross-sections as provided for the relevant reactions by Bosch and Hale [30] accounting for the three components of the relative velocity but assuming isotropic distribution functions; some details can be found in [17]. Table 2 provides an example.

The main contribution to fusion power is the main bulk plasma DT reactivity. In this computation, the full ion distribution functions, including the tails, are taken into account. The beam-target reactivities (T/D-beams and D/T-beams) are considerable and also contribute to the neutron rate. These fusion reactivities occur mainly in the central region of the plasma (figure 10). Table 2 shows a higher neutron rate for the pure D-beams case because of a higher beam/target neutron rates. The lower T-beam penetration induces less T population in the central core where neutron production is highest (see figure 10).

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In order to be closer to future experiments, we now repeat the previous exercise but also evolve the magnetic configuration and exploit parameters closer to those likely to be used in the actual DT experiments. A magnetic field B₀ ∼ 3.4 T was considered since this value allows the central ICRF heating of hydrogen and/or ³He minority in the high-power frequency range available at JET. The current was upscaled accordingly to keep the same normalized beta as in the reference baseline discharge 93436. So, in what follows, the current plasma is increased from 3 to 3.5 MA and the magnetic field from 2.8 to 3.28 T up to ∼3.4 T. All the simulations presented in this section use this new magnetic configuration. The safety factor obtained by solving the coupled Grad–Shafranov equation and current diffusion equation is close toreference shot 92436 for all simulations. Depending on the preferred minority heating scheme, the driver frequency and magnetic field need to be adjusted to ensure wave heating in the core.

In order to assess the so-called 'RF fusion enhancement', the total fusion power is calculated with and without the application of ICRH but keeping the same prescribed temperature. This allows one to identify the direct impact of the ICRF acceleration of the bulk and beam ion on the DT fusion power while excluding the impact of the modified bulk temperature (which indirectly results from the heating).

We remind the reader that the emphasis of the present paper is on the study of ICRH and ICRH/NBI synergy. The adopted transport model is Bohm/gyro-Bohm, available in the ETS suite of codes and thought to provide a reasonable description of the transport. The implicit assumption is that the bulk species transport mechanism does not change significantly when changing the minority concentration so that the predicted trends are correct. A detailed assessment of, for example, the impact of MHD activity and plasma turbulence is beyond the scope of this paper.

5.1. H minority with ∼1.7% concentration

In order to have a central ICRF heating deposition, the adopted antenna frequency is 51 MHz for a chosen magnetic field of 3.43 T. N is the cyclotron harmonic at which the RF heating occurs; N = 1 refers to heating at the fundamental cyclotron resonance ω = Ω while N = 2 signifies heating at ω = 2Ω.

Figure 11(a) shows the direct absorption of the wave power by the various species of which the plasma is composed. Note that the beams absorb a fraction of the wave power. We have a strong second harmonic absorption for the bulk D ions as well as the D-beams (synergistic effect). The hydrogen population absorbs a significant part of the power and the absorption is broad due to the Doppler shift effect. As the critical energy is quite low for D and H (134 and 67 keV, respectively), a significant part of the power absorbed by the ions is redistributed to the electrons by Coulomb collisions leading to a more balanced ion/electron heating. Nevertheless, we still have dominant ion heating (figure 11(b)). Fusion-born alpha particles contribute to the plasma heating: 2.3 MW of alpha heating was produced. As discussed in section 3, this power has the same profile as that of the DT fusion rate. The radiation losses occur near the edge and their shape is inferred from modeling. Their amplitude is renormalized so that the total radiated power amounts to 30% of the additional heating.

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In figure 12, we observe high central ion temperatures with deuterium temperature (central T_D = 10.8 keV) higher than the tritium temperature (central T_T = 10.3 keV). This is explained by the additional heating, which provides significantly higher heating to the deuterium ions than the tritium ions. The electron temperature (central T_e = 8.5 keV) has also increased compared to the reference shot but less than ion temperatures, leading to a higher ratio T_i over T_e.

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In table 3, accounting for the fast ion distribution due to the ICRF acceleration, we observe higher DT and beam-target reactivities than without ICRF acceleration. The fusion power is now 11.7 MW, which represents an ICRF enhancement of 16% caused by the ICRH/NBI synergy.

Table 3. DT prediction with a new magnetic configuration and ICRF H minority heating scheme. Comparison of fusion power between with and without ICRH/NBI synergy at the final time of the simulation (49 s).

(a) Fusion power with ICRH/NBI synergy
Integrated neutron rate:
D–D	0.490 × 1016
D–Dbeam	0.495 × 1016
Dbeam–Dbeam	0.294 × 1015
T–T	0.116 × 1017
T–Tbeam	0.915 × 1016
Tbeam–Tbeam	0.465 × 1015
D–T	0.166 × 1019
D–Tbeam	0.679 × 1018
Dbeam–T	0.104 × 1019
Dbeam–Tbeam	0.724 × 1017
Grand total: 0.348 × 1019 neutrons s−1
Fusion power: 9.8 MW
Alpha power:
0.204E + 01

(b) Fusion power without ICRH/NBI synergy (keeping the same
temperatures)
Integrated neutron rate:
D–D	0.734 × 1016
D–Dbeam	0.623 × 1016
Dbeam–Dbeam	0.369 × 1015
T–T	0.139 × 1017
T–Tbeam	0.944 × 1016
Tbeam–Tbeam	0.472 × 1015
D–T	0.221 × 1019
D–Tbeam	0.704 × 1018
Dbeam–T	0.113 × 1019
Dbeam–Tbeam	0.756 × 1017
Grand total: 0.416 × 1019 neutrons s−1
Fusion power: 11.7 MW

5.2.  ³He minority with ∼1.7% concentration

In most JET discharges where RF heating plays an important role, fundamental minority H heating has been used. The JET RF system is however equipped to allow the use of a ³He minority instead. Just like N = 1 H coincides with N = 2 D, N = 1 ³He coincides with N = 2 T. Hence, exploiting a ³He minority is potentially useful in plasmas containing T as one of the majority gases. The heating schemes relying on a ³He minority ICRF heating are analyzed in this section and compared to the schemes using H. In order to have absorption in the plasma center, the antenna frequency now needs to be reduced to 32.7 MHz and the magnetic field to 3.35 T. As for the H minority case, the ³He minority concentration is 1.7%.

In figure 13(a), it can be seen that most of the wave power is absorbed by the ³He minority at its fundamental cyclotron layer. There is also significant second harmonic T absorption and some modest T-beam absorption. Compared to the H minority case with D bulk and D beam RF heating, the latter absorptions are reduced. There is a more modest synergistic effect. Finally, there are few absorptions of D ions in the high-field side region. Because of the high critical velocity of ³He and T (E_crit = 195 keV), the redistributed power by collisions leads to higher ion heating than electron heating. Because of its lower mass, the D ions receive more collisional power than the T ions.

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Because of higher ion additional heating and less electron additional heating in the central core region (see figures 12 and 13) due to the effect of the RF minority scheme, the direct consequences are higher ion temperatures (central T_D = 11.2 keV, T_T = 10.6 keV) and lower electron temperature (central T_e = 8.3 keV) than in the H minority scheme case, as can be seen in figure 14.

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The fusion power obtained is 12.2 MW (table 4). Due to the ICRF ion acceleration, a boost of 18% of the fusion power is achieved (adopting the same temperatures but without the synergistic effects, fusion power of 9.98 MW was obtained).

Table 4. DT prediction with a new magnetic configuration and ICRF ³He minority heating scheme. Comparison of fusion power between with and without ICRH/NBI synergy at the final time of the simulation (49 s).

(a) Fusion power with 3He minority scheme
Integrated neutron rate:
D–D	0.515 × 1016
D–Dbeam	0.484 × 1016
Dbeam–Dbeam	0.283 × 1015
T–T	0.121 × 1017
T–Tbeam	0.904 × 1016
Tbeam–Tbeam	0.176 × 1015
D–T	0.176 × 1019
D–Tbeam	0.672 × 1018
Dbeam–T	0.101 × 1019
Dbeam–Tbeam	0.706 × 1017
Grand total: 0.354 × 1019 neutrons s−1
Fusion power: 9.98 MW
Alpha power:
0.207E + 01

(b) Fusion power without ICRH/NBI synergy (keeping the same
temperatures)
Integrated neutron rate:
D–D	0.656 × 1016
D–Dbeam	0.513 × 1016
Dbeam–Dbeam	0.295 × 1015
T–T	0.173 × 1017
T–Tbeam	0.996 × 1016
Tbeam–Tbeam	0.490 × 1015
D–T	0.247 × 1019
D–Tbeam	0.727 × 1018
Dbeam–T	0.104 × 1019
Dbeam–Tbeam	0.725 × 1017
Grand total: 0.435 × 1019 neutrons s−1
Fusion power: 12.2 MW

Tables 3 and 4 show the fusion power comparison between the ³He minority scheme and H minority scheme. For the two schemes, we obtained almost the same fusion power but by using different mechanisms. In one case, despite the dilution effect, higher ion temperatures lead to higher DT neutron rate (2.79 × 10¹⁸ neutrons s⁻¹ compared to 2.54 × 10¹⁸ neutrons s⁻¹). In the other case, the higher synergy ICRH/NBI leads to a higher beam-target neutron rate (1.73 × 10¹⁸ neutrons s⁻¹ compared to 1.66 × 10¹⁸ neutrons s⁻¹).

In order to highlight the ICRH/NBI synergistic effect on the fusion power, we tried to isolate the impact of the NBI power on the fusion power first by making a predictive simulation without ICRF and second by prescribing the temperature with the final one to compute the RF enhancement. These simulations are summarized in table 5.

Table 5. DT prediction with a new magnetic configuration. Summary of the obtained fusion powers.

	Total fusion Power	Fusion power without RF power but accounting for the final temperatures with RF power (% of total fusion power)	Fusion power without RF power (% of total fusion power)
3He minority	12.2 MW	10 MW (82%)	7.2 MW (60%)
H minority	11.7 MW	9.8 MW (87%)	7.7 MW (66%)

The majority of the fusion power comes from the NBI (around 60%, a little more for H case). Around 20% comes from the increase in temperatures and less than 20% comes from the RF majority tail formation.

One of the main questions for JET DTE2 is whether H minority or ³He minority ICRH is better for boosting the DT fusion performance for a 0.5/0.5 DT mixture plasma. Both scenarios are feasible in JET at B ≈ 3.4 T and f = 51 MHz or f = 33 MHz, respectively. Aside from the impact of the slowing-down of the minority ions (accelerated by fundamental ICRH) on the kinetic profiles of the bulk species, the direct effect of second harmonic (N = 2) acceleration of the fuel ions (D or T) and of the NBI ions (D_nbi or T_nbi) also plays a key role in the ICRH fusion enhancement and therefore needs to be included in the wave/Fokker–Planck modeling. The interplay between these effects depends strongly on the minority concentration. Remember that to model the ICRF acceleration of the bulk ions, a non-linear collisional operator is needed in the Fokker–Planck equations since the self-collisions are important in this case.

Figure 15 shows the integrated ICRH power absorbed by the various species for the N = 1 H/N = 2 D + D_NBI (3.4 T, 51 MHz) and for the N = 1 ³He/N = 2 T + T_NBI (3.35 T, 32.7 MHz) ICRF heating scenarios. At low minority concentrations, the fuel ions (thermal and NBI) absorb most of the ICRH power and will, therefore, because of for the Coulomb collisions, be accelerated away from their initial (Maxwellian) distributions and impact the fusion yield. Once the minority fractions exceed ∼1%–2%, they become the dominant absorber and their impact on the kinetic profiles and plasma dilution will have a dominant role in the RF fusion enhancement. For the cases with dominant minority ICRF absorption, the results shown here should agree better with simulations that only take into account the Fokker–Planck equations for the minority species, such as in TRANSP [11]. Hence, this result is fully aligned with what is expected. Note that the second harmonic absorption of the D + D_nbi ions at 51 MHz is more important than the T + T_nbi absorption at 33 MHz, even at very low minority concentrations. This is partly explained by the different RF electric field polarizations obtained at the two RF frequencies and also by the far off-axis fundamental D heating that takes place in the 33 MHz case, which takes part of the RF power actually intended for ³He and T (see figure 13(a)). Third harmonic T absorption at 51 MHz is not included in the model but is expected to be small under these conditions.

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The impact of H minority and ³He minority ICRH on the kinetic profiles is illustrated in figure 16, where the central temperatures calculated in the simulations for deuterium (a), tritium (b), electrons (c) and the effective minority ion tail temperatures (d) are shown as a function of the minority concentration for the two cases discussed: 51 MHz, H/D heating (solid); 33 MHz, ³He/T heating (dashed). The effect on the central temperatures is clear. The ³He heating case favors higher core ion temperatures, in particular when the minority concentration is high enough to absorb a large fraction of the ICRF power. The tritium temperature is lower than the deuterium temperature, mainly as a consequence of the larger fraction of NBI power absorbed by the latter. The electron temperature is always slightly higher in the H minority case because the collisional RF power transferred to the electrons is larger than in the ³He heating case (higher tail temperatures and lower critical energy for the H ions), but there is no indication of stronger electron heating at high hydrogen concentrations. This is related to the fact that the hydrogen tails actually become weaker when more H is injected into the plasma under these conditions (see figure 16(d)), even if more power is absorbed by this species at higher H concentrations.

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As far as the plasma stored energy and neutron production are concerned, the stronger ion heating predicted in the ³He heating case is somewhat balanced by the stronger fuel dilution caused by the presence of ³He ions. Figure 17 compares the effect of H minority (solid) versus ³He minority heating (dashed) on the D + T ion and electron stored energies (left) and on the fuel ion dilution (right). The remaining contributions for quasi-neutrality on the dilution graph come from the NBI species and impurities (Ni) considered in the simulations. For both cases, the electron stored energies are substantially smaller than the ion energies (T_i > T_e) and do not significantly change with minority concentration, illustrating the fact that the NBI bulk ion heating is the main global energy source in these plasmas. The ion energies are also comparable with H or ³He minority ICRH heating, but both decrease when the minority concentration is larger. For the H heating case, the ion temperature does not increase with H minority injection (see figure 17), so dilution is the dominant effect on the curve shown in figure 17 (left). For the ³He heating case, the enhancement of the central ion temperatures (local effect) compensates for the higher plasma dilution and the ion stored energies are comparable with the ones obtained with H minority heating, even at high concentrations. Note that even if the global energies are comparable in general, different ion temperature peaking can impact on the high-Z impurity transport [31] and thus influence plasma performance, but this is beyond the scope of the modeling presented.

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The impact of H (solid) versus ³He (dashed) minority heating on the DT fusion performance is illustrated in figure 18, subdivided as total (left), bulk–bulk (middle) and beam-target (right) contributions. The beam–beam fusion power is low (less than 0.1 MW) and therefore not shown. By bulk–bulk we refer to the fusion power produced by the collisions between the various RF-heated bulk ion species (non-Maxwellian distributions). The small symbols (dashed curves) show the DT fusion power values for cases for which P_icrh is set to zero in the simulations, but the final (predicted) bulk plasma temperatures in the presence of ICRH are maintained. That is, the bulk ion species are the pure 'heated' Maxwellians that are computed by the ETS transport solver, without accounting for the RF acceleration effect. If the ICRF heating is neglected completely in the predictive simulations, the plasma temperatures will be much lower and the total fusion power will be only about 7–8 MW (see table 5).

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The general trend is a decreasing fusion performance with increasing minority concentration. This results from a combination of the plasma dilution and diminishing direct (second harmonic) acceleration of the fuel ions. The latter is exchanged by indirect collisional heating of the ions at higher minority concentrations and is therefore mainly impacting the thermal plasma sub-populations. The ³He heating case favors bulk–bulk ion reactions because of the enhanced ion temperature values but offers less potential for beam-target enhancement, because the T and T_nbi ions absorb less ICRF power than the D + D_nbi ions under similar conditions (see figure 15). Interestingly, the pure D + D_nbi heating case (51 MHz, no H minority) shows the highest fusion power, as a combination of efficient bulk ion heating without hydrogen (see figure 16) and moderate RF acceleration of the D and D_nbi ions. At higher minority concentrations, both cases show similar neutron potential, the ³He heating case giving slightly higher power, as a consequence of enhanced bulk–bulk D- reactions (despite the larger dilution).

The direct impact of the ICRF acceleration of the bulk and beam ions on the DT fusion yield (excluding kinetic heating effects) is called 'RF fusion enhancement' and can be estimated by calculating the total fusion power with and without the application of ICRH but keeping the same (prescribed) temperatures in the simulations, as discussed earlier. Figure 19 compares the RF fusion enhancement obtained in the two cases discussed (51 MHz, H/D heating—solid; 33 MHz, ³He/T heating—dashed) as function of the minority concentration, subdivided in total, bulk–bulk and beam-target contributions. First, note that the RF enhancement in the beam-target channel (figure 19 (right)) is small compared to the bulk–bulk power channel. This is because, as opposed to the case of pure D plasmas, the NBI source energies in JET (∼120 keV) are already in the appropriate energy range for efficient DT nuclear reactions and accelerating a small sub-population of the beam ions to higher energies (via second harmonic ICRH) is not very efficient. Fundamental ICRH acceleration of the beam ions would be more appropriate, as described in [32, 33], since it drives more modest fast ion tails and also increases the population of ions in the sub-source energy window (50–120 keV).

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As shown before, when neglecting the RF acceleration effects but keeping the predicted temperatures due to RF and NBI heating (from ETS) one sees that the ³He/T heating case favors thermonuclear reactions (due to enhanced kinetic T_i profiles) while H/D heating favors beam-target reactions, both giving similar values for the total fusion power (figure 18, dashed curves). The RF enhancement of the fusion power shown in figure 19 shows a similar trend: the bulk–bulk ion contribution is dominant for the two cases, but is stronger for the ³He/T heating case since the RF power absorbed by the minority ions is mainly transferred to the bulk ions by Coulomb collisions, while for H minority heating some fraction stays in the electron heating channel. Note that the bulk–bulk fusion enhancement for the ³He/T heating gets stronger at high concentrations but the total fusion power gradually decreases (figure 18 (left)), mainly due to the plasma dilution. Interestingly, the pure N = 2 D heating case at 51 MHz (H minority concentration = 0) gives a similar RF fusion enhancement as the ³He/T cases with finite minority concentrations, but the total neutron rate is slightly higher, as can be seen in figure 18.

To illustrate the effect of the N = 2 RF acceleration of the majority ions in the absence of minority heating, figure 20 shows the energy distribution functions of the D ions (a), T ions (b), D_nbi ions (c) and T_nbi ions (d) for the 51 MHz (solid) and 33 MHz (dashed) ICRF heating cases with X[H] = X[³He] = 0. The dotted lines correspond to the non-accelerated (input) distribution functions. The energy distributions are shown at ρ_norm = 0.1, for which the respective RF power densities are comparable: p_D = 0.65 MW m⁻³, P_T = 0.5 MW m⁻³, P_Dnbi = 0.12 MW m⁻³, P_Tnbi = 0.07 MW m⁻³. Despite small differences in the local RF power densities absorbed by each species, some features are clear. The deuterium ions are more efficiently accelerated at 51 MHz than the T ions at 33 MHz, which impacts the bulk–bulk (thermonuclear) reactions. Interestingly, the D ions are hardly accelerated at 33 MHz but the tritium ions are accelerated at 51 MHz, due to efficient collisions with the heated D ions. As far as NBI-RF synergy is concerned (c) and (d), none of the beam distributions is touched when it is not RF-resonant (as expected), but the D_nbi ions are also more accelerated at 51 MHz than the T_nbi ions at 33 MHz, mainly due to the lower RF power available for the T_nbi ions at 33 MHz compared to the D_nbi ions at 51 MHz (see figure 15). As a combination of efficient RF acceleration of both the D and T ions at 51 MHz and the fact that fast D_nbi ions colliding with thermal T ions is more efficient than the other way around as far as fusion reactions are concerned [34], makes the pure N = 2 heating scheme very attractive for good fusion performance in JET-ILW DTE2. Fundamental D + D_nbi heating in DT plasmas [32] is not discussed here but is also an option for ITER's full field phase at f ∼ 40 MHz and will also be tested in JET DTE2 [34]. This scheme probably has the most potential to accelerate the deuterium bulk and beam ions to optimal energies for fusion reactions (E < 200 keV) and is expected to provide the largest RF fusion enhancement.

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The EUROfusion Integrated Modeling (EU-IM) effort and the European transport simulator (ETS) offer a convenient framework for making predictions for high performance fusion plasmas, in particular for DT reactors. In this paper, self-consistent simulations of combined RF + NBI heating schemes in which majority, minority and beam ions are simultaneously heated have been documented and the synergistic effects have been highlighted and discussed. Traditional ICRF heating models do not permit the study of Coulomb collisional interaction of various ion species simultaneously and generally forces one to consider only minority populations. Accounting for multi-population interaction is made possible here by solving coupled sets of Fokker–Planck equations for all ion species adopting the non-linear collision operator for arbitrary distribution functions, accounting for effects such as self-collisions of majority (or large minority) populations. Combining an equilibrium solver, an NBI code, a multi-species ICRH wave + Fokker–Planck solver and including transport allows one not only to evaluate the high-energy tails formed but to predict the temperature rise brought about by the combined heating. By evolving the distribution functions of all populations, a detailed study of the fusion yield can be made allowing one to assess the importance of thermal and non-thermal ion populations on the total fusion yield. The direct RF heating is described here using the CYRANO wave solver [20] while the initial neutral beam deposition is provided by ASCOT [19], the exploited Fokker–Planck modules are StixReDist [16] and FoPla [17, 18] while the transport is described using the ETS code [3, 35].

Prior to proceeding to making DT predictions, JET baseline shot 92436 was studied in detail to validate the numerical workflow described above. Experimental findings, such as the electron and ion temperature profiles, plasma stored energy and neutron rate are reproduced by selecting the ion and electron heat transport coefficients using a Bohm/gyro-Bohm model, while the particle density is imposed. One of the interesting features is that predictive modeling helps to provide crucial information that is not experimentally available. The core ion temperature and distribution functions of the various ion populations are good examples. In turn, this information allows detailed insight into physics processes. Not only the fusion rate but its composition can be predicted, identifying the importance of increasing the bulk ion temperature by the auxiliary heating schemes to boost the fusion yield harvested from reactions involving thermal populations. Comparing the obtained results with TRANSP simulations allows one to illustrate the need of tracing the Coulomb collisional evolution of the power flowing to all populations and not just that flowing to the minorities. As the D bulk and D beam are heated via second harmonic heating in shot 92436, a fraction of the fast ion tails created a slow down of the electrons and hence contribute to electron rather than ion heating.

Subsequently, a prediction of DT plasmas is made based on the transport coefficients determined in the DD validation discharge, but using the full NBI and ICRH power expected to be available in JET DTE2. The starting temperature profiles are the same as in the DD reference discharge and the simulations are repeated in small time interval steps until the final temperatures achieve convergence (0.5–0.7 s). The density profile is assumed to be constant and the same as in the DD reference discharge. The performance of pure D beams is compared to that of mixed D + T beams. A difference is already noticed at the source; T beam penetration is less efficient. Since T beams deposit more of their power in the outer layers of the plasma they tend to be somewhat less efficient in heating the core. As a result, slightly less fusion power is produced by mixed DT beams than by pure D beams fired into a 50:50 D:T plasma in JET-ILW.

Both H and ³He minorities can efficiently be heated at their fundamental cyclotron frequency in JET, suggesting—from the ICRH point of view—exploring two scenarios in DTE2, one relying on N = 1 H and N = 2 D + D_nbi heating, and one on N = 1 ³He and N = 2 T + T_nbi heating (ω = Nω_ci). Comparing the two schemes with the same minority concentration (X[H] = X[³He] = 1.7%) while ensuring the ICRH frequency is chosen to allow central heating in both cases (f_ICRH = 51 MHz for H/D and 33 MHz for ³He/T for a central magnetic field of B₀ = 3.4 T), higher core electron and lower core ion temperatures are achieved for the RF scenario involving H compared to that using ³He heating. This effect is anticipated due the lighter mass of the H minority (stronger electron collisional heating) but is also partly due to the difference in polarization and the width of the deposition profile. For 33 MW of NBI and 5 MW of ICRH, temperatures of about 8 and 11 keV are reached for electrons and ions, respectively, leading to a DT fusion power estimate of the order of P_fus = 12 MW for both cases. This estimate is in line with the results obtained in other predictive simulations for JET-DTE2 under similar conditions [4, 7], but the bulk ion temperatures are slightly on the low side. This apparent inconsistency is explained by the fact that most of the DT predictions do not take into account the RF acceleration of the bulk (majority) ions on the neutron calculation, which corresponds to ∼20% of the total fusion power predicted here, as shown by simulations done without ICRH (Maxwellian distributions) but keeping the prescribed 'heated' ion temperatures obtained in the final time point of the global transport simulation (P_fus ≈ 10 MW). The fact that the second harmonic RF acceleration of these majority ions is not included in the predictions can also lead to an overestimate of the RF power flowing into the bulk ions via Coulomb collisions (slowing-down on electrons is neglected) and hence to higher predicted kinetic ion temperatures but similar fusion yields. Moreover, differences in the impurity radiation treatment and the transport models used can also have a considerable impact of the fusion power predictions.

A minority concentration scan for the two ICRH schemes discussed above (H/D heating at 51 MHz and ³He/T heating at 33 MHz) in otherwise similar conditions was performed to identify the optimal scenario(s) for fusion enhancement with combined NBI + ICRH. As expected by simple theory, the ³He/T heating scheme does favor bulk ion heating, but the higher ion temperatures obtained when the minority concentration is larger is counter-balanced by the larger fuel dilution as far as the DT fusion power is concerned. Maximum fusion power is obtained around X[³He] ≈ 2%. For the H minority heating case, the fusion power is typically somewhat lower—except at very low X[H]—and decreases as a function of concentration, mainly due to plasma dilution and larger H minority absorption (collisional electron heating). The RF fusion power enhancement is about 2.3 MW (∼23%) for the ³He/T heating case and about 1.8 MW (∼18%) for the H/D heating case when a minority is present. In both cases, the RF enhancement is mainly related to the heating of the majority fuel ions (bulk–bulk reactions), either directly by second harmonic ICRH (dominant for the H/D case) or by a combination of the former with efficient collisions with the minority ions (dominant for the ³He/T case). The RF-NBI synergistic effects (beam-target reaction enhancement) are small in the DT cases studied (as opposed to the DD cases) and only contribute with 0.2–0.4 MW to the total fusion power (∼12 MW), being slightly higher for the H/D heating case. Interestingly, the highest DT fusion power obtained in the simulations is the pure N = 2 D + D_nbi heating scenario at B_o = 3.4 T/f = 51 MHz (with minimum H minority levels), followed by the ³He scenario at B_o = 3.35 T/f = 33 MHz with X[³He] ≈ 2%. The former is boosted by second harmonic acceleration of the D ions, efficient collisional acceleration of the T ions and slightly enhanced beam-target reactions while the latter is mainly a consequence of efficient bulk ion heating (thermonuclear reactions), as discussed above. This supports the choice of the latter as the main ICRH work-horse for the active phase of ITER (5.3 T, f ∼ 53 MHz [36]). Finally, the fusion power predictions found in this paper could be significantly improved if the following effects are accounted for: isotope effects, expected at high input power [29], transport reduction by ICRH fast ions [37] or fast alphas [38], all of them not accounted for in the gyro-Bohm model used. Therefore, the work done in this paper will be extended to more sophisticated transport models in the future.

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. The views and opinions expressed herein do not necessarily reflect those of the European Commission.