Analysis of ICRF Heating Schemes in ITER Non-Active Plasmas Using PION+ETS Integrated Modeling

Abstract

The PION code has been integrated into the European Transport Solver (ETS) transport workflow, and we present the first application to model Ion Cyclotron Resonance Frequency (ICRF) heating scenarios in the next-step fusion reactor ITER. We present results of predictive, self-consistent and time-dependent simulations where the resonant ion concentration is varied to study its effects on the performance, with a special emphasis on the resulting bulk ion heating and thermal ion temperature. We focus on two ICRF heating schemes, i.e., fundamental H minority heating in a ⁴He plasma at 2.65 T/7.5 MA and a three-ion ICRF scheme consisting of fundamental ³He heating in a H-⁴He plasma at 3.3 T/ 8.8 MA. The H minority heating scenario is found to result in strong absorption by resonant H ions as compared to competing absorption mechanisms and dominant background electron heating for H concentrations up to 10%. The highest H absorption of ∼80% of the applied ICRF power and highest ion temperature of ∼15 keV are obtained with an H concentration of 10%. For the three-ion scheme in 85%:15% H:⁴He plasma, PION+ETS predicts ³He absorption in the range of 21–65% for ³He concentrations in the range of 0.01–0.20%, with the highest ³He absorption at a ³He concentration of 0.20%.

1. Introduction

Auxiliary heating systems are essential for the plasma in ITER to reach the necessary temperature for fusion to take place. According to the ITER Research Plan in 2018 [1], these systems will be comprised of Ion Cyclotron Resonance Frequency (ICRF) heating, Electron Cyclotron Resonance Heating (ECRH), and Neutral Beam Injection (NBI). The operations at ITER will follow a staged approach, the details of which are currently under review [2]. The 2018 Plan proposed starting with two Pre-Fusion Power Operation (PFPO I and II) phases, where the auxiliary heating systems would be tested on non-active hydrogen (H) and helium (He) plasmas, and continuing with the Fusion Power Operation (FPO) phase, where a transition would be made to deuterium (D), tritium (T), and deuterium–tritium (DT) plasmas at full plasma current and in a toroidal field.

In this paper, we study ICRF heating in ITER non-active plasmas with $q_{95}=3$ at half field and current (2.65 T/7.5 MA), where $q_{95}$ is the value of the safety factor at the radial location where 95% of the magnetic flux is contained within that surface. This heating method uses fast magnetosonic waves that are launched by external antennas, propagated in the plasma and are absorbed by different plasma species. The wave–particle resonance with plasma ions, $\omega =k_{\Vert }{v}_{\Vert }+l{\omega }_c$, takes place when the wave frequency $\omega$ matches the Doppler-shifted ion cyclotron frequency ${\omega }_c$ or its harmonic. Here, $k_{\Vert }$ is the wavenumber parallel to the background magnetic field, $v_{\Vert }$ is the ion parallel velocity, and $l=1,2,3\dots$ represents the harmonics of the wave. The $l=1$ resonance corresponds to the fundamental resonance, the $l=2$ resonance to the second harmonic resonance, and so on. Typically, only a small number of plasma ions resonate with the launched waves. In most cases, these are either minority ions for $l=1$ and majority ions with a finite Larmor radius with respect to the wavelength of the launched wave for $l>1$. In addition, there is direct electron damping of the launched waves by electron Landau damping and transit time magnetic pumping, which competes with ion cyclotron damping [3].

The different options for ICRF heating in ITER plasmas have been investigated in [4]. It was concluded that strong central absorption can be achieved in half-field placing the fundamental resonance of H in the plasma center using an ICRF frequency of 40 MHz in ⁴He plasmas. Furthermore, it was found that schemes with good absorption in H plasmas are lacking at half-field. To alleviate this situation, it was proposed to use a three-ion ICRF scheme at a higher magnetic field in the range of 3.3 T. In a three-ion scheme, a small concentration of a third ion species Z is added to the plasma that consists of two other ion species Y and X. The fundamental cyclotron resonance layer of the species Z is tuned so that it coincides with the mode conversion layer of the other two species [5]. It was proposed in [5] to add a small amount of ³He to an H plasma with a ⁴He minority at a magnetic field of 3.3 T, which was shown to give rise to good absorption at the fundamental ³He resonance at 40 MHz.

In this paper, we study the above two heating scenarios, i.e., fundamental H minority heating in H plasma at an ITER half-field of 2.65 T and the three-ion scheme ³He-H-⁴He in H plasma at a magnetic field of 3.3 T using the ICRF modeling code PION [6] integrated into the transport modeling workflow European Transport Solver (ETS) [7]. The aim is to predict the time evolution of the ICRF heating characteristics and plasma behavior when ICRF heating is applied in these conditions. While PION and ETS have been used separately for plasma heating modeling in the past, this paper reports the first results using the PION+ETS integration. We present results of predictive, self-consistent, time-dependent simulations and carry out H and ³He density scans to determine the effects of the concentration on the time evolution of the absorbed power density profiles, collisional power transfer, and the ion temperature. Particular attention is given to the resulting bulk ion heating and thermal ion temperature given their importance to overall fusion plasma performance and the fact that ICRF heating will be the only auxiliary heating scheme in ITER that can provide dominant bulk ion heating and access to the H mode [8]. The scans carried out in the concentration of resonant ion species are relevant because the concentration of resonant ion species affects ICRF power partitioning between the competing absorption mechanisms, the average energy of the resonant ions and, thereby, the fraction of ICRF power transferred from resonant ions to bulk ions and electrons in collisions with the background plasma. When the resonant ion energy is above the critical energy $E_{\mathrm{crit}}=14.8A{T}_{\mathrm{e}}{[{\sum }_{\mathrm{i}}{n}_{\mathrm{i}}{Z}_{\mathrm{i}}^2/\left(n_{\mathrm{e}}{A}_{\mathrm{i}}\right)]}^{2/3}$ (given in eV), where A is the atomic mass of the resonant species, $T_{\mathrm{e}}$ is the electronic temperature (given in eV), $n_{\mathrm{i}}$ is the ionic density (given in cm⁻³), $Z_{\mathrm{i}}$ is the atomic number (with the sum over i referring to all thermal ion species) and $n_{\mathrm{e}}$ is the electronic density (given in cm⁻³) [3], the ions are more likely to collide with electrons, resulting in dominant collisional bulk electron heating. If the energy is below the critical energy, bulk ion heating will dominate.

This paper is organized as follows. A brief introduction of the tools used in the modeling is given in Section 2. In Section 3, the results of the simulations are presented and compared to earlier studies using a number of ICRF modeling codes with fixed plasma parameters. Finally, Section 4 contains some final remarks and conclusions.

2. Methodology

The simulations in this paper have been conducted with the PION+ETS integration. In the following, these tools are briefly described.

2.1. PION

PION is a relatively fast ICRF modeling code based on simplified models [6]. It calculates the time evolution of the ICRF power absorption together with the velocity distribution functions of the resonant ions in a self-consistent way. The main features of PION can be divided into two procedures, i.e., the power deposition model and the Fokker–Planck calculations [9]. The power deposition model computes how the ions and electrons absorb the ICRF waves. The power deposition model of PION approximates full-wave codes like LION [10]. It decomposes the wave field into two parts: one part in the strong absorption limit and another part in the weak absorption limit. The time evolution of the velocity distribution function is calculated using a one-dimensional Fokker–Planck equation for the pitch angle-averaged distribution function. Both procedures are coupled by the computation of the dielectric tensor. The Fokker–Planck calculation provides the contributions to the dielectric tensor by the ICRF-accelerated resonant ions. These contributions are used for the calculation of the power deposition and modify the power partitioning and power absorption profiles.

A typical PION simulation involves several time steps. In each time step, the background plasma parameters are read, and the absorbed power deposition is calculated. Then, the result of this calculation is used as the input of the one-dimensional Fokker–Planck solver, which outputs a distribution function. This distribution function is then used to calculate the absorbed power in the next time step [9].

PION has been extensively validated against experimental data on JET [6,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32], AUG [28,33,34,35,36,37,38], DIII-D [39], and WEST (formerly Tore Supra) [40,41] for many minority and majority heating schemes. At JET, it is part of the second data processing chain. Recently, PION was integrated [42] into the ITER Modeling and Analysis Suite (IMAS) [43]. IMAS is the computational platform that supports plasma operations and research activities at ITER. It uses a data model that can describe both experimental and simulated data with the same representation. As part of the IMAS integration, the PION results in IMAS were compared with the results of the standalone PION code (outside IMAS), and overall, good agreement was found. Furthermore, verification of PION’s data handling within the ETS framework was carried out in the initial stages of the integration, including checks on retrieved ion species and flux surface mapping, which influence many other variables in PION such as temperature and density. Regarding the handling of input and output of variables calculated by PION, there are a number of flags, such as in the output files that were used to verify the input and output data.

In this work, we integrate PION into the transport modeling workflow of the European Transport Solver (ETS) within IMAS. This integration is relevant because it provides the capabilities to simulate the evolution of a plasma discharge. Both interpretative and predictive simulations are possible. Furthermore, the integration of PION into IMAS has allowed collective development of integrated modeling tools and workflows.

2.2. ETS

The ETS is one of the transport modeling workflows within the IMAS framework. It is a modular package of physics modules combined into a workflow, where PION has been included as one of the Heating and Current Drive (H&CD) codes. Other heating codes integrated into ETS as H&CD modules include CYRANO [44] or StixRedist [45]. The ETS has been developed with the objective of building the capabilities to compute the full discharge evolution of a power plant at the tokamak scale. To meet this objective, the ETS counts with a high degree of modularity, a separation of physics and numeric parts, a flexible workflow, and the ability to both treat several ion components (including impurities) and use stiff transport models [7]. The ETS functions as a suite of validated codes containing several transport actors integrated into its workflow which use different models, such as neoclassical or gyrokinetic transport models.

The ETS is formed out of coupled codes where the information exchange takes place through well-defined generalized Interface Data Structures (IDSs) acting as standardized interfaces [46]. This is the standard layered structure used in IMAS, where the reactor data model is mapped to the solver data model through the IDSs. The IDSs contain physics definitions of the equilibrium, neoclassical transport and core sources, transport, impurities, and profile. The IDS equilibrium represents the equilibrium at the previous time step, and the IDS core source represents the sources of current, electron and ion energy, momentum, and particles, whereas the IDS core transport represents the transport coefficients of these quantities. In each iteration, the ETS core code reads the input from the equilibrium, core source and transport IDSs, as well as the core profile representation of the plasma state at the previous time step. The ETS then passes the input to the physics modules, which solve the transport equations for the density of current, the ion and electron density, the ion and electron temperature, and the toroidal velocity. The core code will then output a core profile containing a new plasma state consisting of the new plasma composition, ionic and electronic temperatures and densities, and various global, time-dependent quantities calculated from the 1D profiles.

3. Modeling and Results

In this section, we use PION+ETS integration to study H minority heating in ⁴He plasma and three-ion-scheme H:⁴He (85%:15%) with a ³He minority at 2.65 T and 3.3 T, respectively, in ITER. As discussed in the introduction, these schemes have been identified [4,5] as promising ICRF schemes for heating ITER non-active plasmas.

3.1. Fundamental H Minority Heating in ⁴He Plasma at 2.65 T/7.5 MA

For the study of fundamental H ($\omega ={\omega }_H$) minority heating in ITER ⁴He plasma, synthetic ITER shot 110005 with a pulse duration of 647 s was used. The plasma was pre-heated using 20 MW ECRF heating. The PION+ETS simulation was started during the flat-top phase, at $t_i=300$ s, with the plasma and ICRF parameters as shown in

Table 1. Plasma composition (with the minority ion species in brackets), heating scheme, magnetic field ($B_0$), ICRF frequency (f), ICRF power ($P_{ICRF}$), central electron density ($n_e^0$) and temperature ($T_e^0$).

Plasma	Heating	${\mathit{B}}_0$	f	${\mathit{P}}_{\mathbf{ICRF}}$	${\mathit{n}}_{\mathit{e}}^0\times {10}^{19}$	${\mathit{T}}_{\mathit{e}}^0$
	Scheme	(T)	(MHz)	(MW)	(m−3)	(keV)
4He-(H)	$\omega ={\omega }_H$	2.65	40	20	3.3	10

and Figure 1. An ICRF frequency of 40 MHz was chosen to place the fundamental H resonance in the plasma center. The ICRF power of 20 MW was chosen based on the ITER Research Plan [1]. In the simulation set-up, the temperature evolution of the ions and electrons was set to be predictive, whilst the density evolution was set to be interpretative. The chosen transport model uses a combination of a neoclassical model and a multi-ion model; a simplified analytical expression that uses transport coefficients. The H concentration was constant both in radius and in time and was varied between 1.0% and 10% from simulation to simulation as in [42]. These percentages are calculated in terms of the electron density shown in Table 1. The simulation was performed with a full antenna spectrum discretized by 100 toroidal mode numbers N. Finally, the duration of the simulation was chosen to be 8 s to allow ample time for the evolution of the plasma toward a new steady state.

Figure 2 shows the power density absorption profile as given by PION+ETS at t = 308 s. There are three competing absorption mechanisms, i.e., fundamental H damping, 2nd harmonic ⁴He damping and direct electron damping. Among them, the fundamental H absorption is the dominating mechanism. As shown in Figure 2, most of the ICRF power is absorbed by resonant H ions independently of the H concentration. The H resonance is located at s = 0.03 on the low-field side (LFS) of the plasma. Here, s stands for the square root of the normalized poloidal flux surface. Figure 2 also shows the single-pass H absorption (SPA) coefficients, which measure how much of the ICRF wave is absorbed the first time it travels through the plasma [3]. The SPA coefficients given here are considered at the ICRF resonance with respect to the dominant toroidal mode number N = 54. As we can see from Figure 2, the SPA on H increases with the H concentration in the range of H concentration considered (1.0–10%). For the lowest H concentration of 1.0%, the SPA on H is low enough (80%) for significant ⁴He absorption (20% of the ICRF power, cf.

Table 2. H concentrations, power absorbed by resonant H and ⁴He ions ($P_{abs,H}$, $P_{abs{,}^{4}He}$), fractions of collisional power transferred from resonant ions to bulk ions ($P_{ci}/P_c$) and background electrons ($P_{ce}/P_c$), critical energy ($E_{crit}$) and average energy of the fast H ions ($\langle E_{fast,H}\rangle$) as given by PION+ETS.

H	${\mathit{P}}_{\mathbf{abs},\mathit{H}}$	${\mathit{P}}_{\mathbf{abs}{,}^4\mathbf{He}}$	${\mathit{P}}_{\mathbf{ci}}/\mathit{P}$	${\mathit{P}}_{\mathbf{ce}}/\mathit{P}$	${\mathit{E}}_{\mathbf{crit}}$	$\langle {\mathit{E}}_{\mathbf{fast},\mathit{H}}\rangle$
(%)	(MW)	(MW)	(%)	(%)	(keV)	(keV)
1.0	11.5	3.92	34.2	65.8	158	1719
2.5	15.2	0.73	26.8	73.2	153	568
5.0	15.6	0.40	39.9	60.1	154	366
10	15.7	0.25	48.8	52.2	173	459

), to take place. The ⁴He absorption arises because the chosen ICRF frequency also coincides with the 2nd harmonic ⁴He resonance. Consequently, when H damping decreases as the H concentration is decreased, ⁴He absorption by majority ⁴He damping starts to compete with the dominant H damping. As shown by Figure 2, direct electron damping is rather small and also takes place mainly off-axis for all H concentrations considered.

Figure 3 shows the collisional power density transfer profiles at $t=308$ s. In minority heating, the ICRH wave accelerates the minority species, in this case H, to non-thermal velocities, larger than the velocities of the thermal H population, thereby building up a fast ion tail in the H distribution function. The heat transfer from this fast ion population to the thermal ions and electrons has a strong dependence on this fast ion tail, as discussed above in the introduction. The average energy of the H ions in the tail of the fast ion distribution function is higher (in the range of 459–1719 keV, cf. Table 2) than their critical energy (158–173 keV) for all H concentrations considered. Therefore, the H ions will collide mainly with the electron population and transfer their energy to them. As the H concentration is increased to 10%, the average energy of the fast H decreases until $\langle E_{\mathrm{fast},H}\rangle \sim 2.5E_{\mathrm{crit}}$, resulting in a balanced power equipartition and $P_{\mathrm{ci}}/P_{\mathrm{c}}\sim 0.5$, which agrees with the equation for total energy given up by the resonant particles transferred into the thermal ions of the plasma in [3].

Figure 4 shows the time evolution of the thermal ion temperature at the location of the ICRF resonance at the normalized flux surface $s=0.03$. The results suggest that at lower H concentrations, the time evolution of the plasma is more nonlinear due to the evolution of the ICRF power deposition in time when the fast resonant ion populations build up. We note, however, that the transient evolution in the first seconds of the simulations shown in Figure 4 depends on the parameters used in the transport model and may not be observed experimentally. Also, it takes a surprisingly long time for the plasma to reach a new steady state. The temperatures at the end of the simulation at $t=308$ s are in the range of 11.9–15.0 keV, with the lowest $T_i=11.9$ keV with an H concentration of 2.5% and the highest $T_i=15.0$ keV with an H concentration of 10%. As shown in Figure 4, the ion temperature increases as the H concentration increases in the range of 2.5 to 10%. The exception to this trend is the case with an H concentration of 1.0% for which the ion temperature is close to that for an H concentration of 5.0% and higher than that for an H concentration of 2.5%. At the low H concentration of 1.0%, 2nd harmonic ⁴He damping is significant, as discussed above, and contributes mainly to collisional bulk ion heating. Moreover, it has a more peaked profile around the resonance located at $s=0.03$. This explains its relatively good performance in terms of bulk ion heating and ion temperature.

Prior to this work, the H minority scenario in an ITER ⁴He plasma was modeled in [4,42,47,48] using fixed background plasma parameters. In [4], good absorption was found with combined SPA coefficients summed over electrons and ion species close to 1 for H concentrations in the range of 2–8%, which is consistent with the SPA values shown in Figure 1. In [42], PION was used as a stand-alone code within IMAS (PION+IMAS) to study H minority heating in ⁴He plasmas with H minority concentrations ranging from 1% to 9.2%. An increase in H power absorption with an increasing H concentration from 1% to 5% was found, with a slight decrease in H absorption when the H concentration was increased to 10%. In [47], a wider range of H concentrations up to 19% at a lower magnetic field of 2.5 T and a higher electron density of $5.1\times {10}^{19}$ m⁻³ was explored to benchmark full-wave ICRF codes. Significant differences in the ICRF power partitioning between different full-wave codes were reported, with some of the codes suggesting a maximum H absorption around an H concentration of 5%. The simulations carried out by [48] using the 1D TOMCAT code [49] provided power absorption percentages for fundamental H, 2nd harmonic ⁴He, and direct electron damping at 72%, 6%, and 22%, respectively, for an H concentration of 5%. These were, again, very consistent with the results from PION+ETS, with percentages for those same absorption mechanisms at 78%, 2%, and 20%, respectively, although TOMCAT calculated a slightly higher absorption for the 2nd harmonic ⁴He at the expense of fundamental H absorption. The ion absorption was notably central, whereas electron absorption tended to be flatter and more off-axis. In this aspect, PION+ETS, PION+IMAS, and TOMCAT coincided. However, these earlier results for fixed plasma parameters in [42,47] are in contrast to the findings of our PION+ETS simulations regarding an optimum H concentration to maximize H absorption. Previous studies reported maximum H absorption below 10%, whereas in PION+ETS simulations, H absorption increased across the range of 1.0–10%, albeit minimally from 5.0% to 10%, reflecting the plasma temperature’s self-consistent evolution with ICRF heating.

3.2. Three-Ion Scheme ³He-H-⁴He in H Plasma at 3.3 T/8.8 MA

The three-ion scheme ³He-H-⁴He was studied with the PION+ETS integration using the synthetic ITER discharge 104010 at 3.3 T with the main ion composition H:⁴He of 85%:15% and a small ³He concentration in the range of 0.01–0.20%. These concentrations were chosen to allow a direct comparison with the modeling performed in [4]. This synthetic discharge has only one time slice in the discharge flat-top phase at $t_i=500$ s when the plasma is pre-heated using 30 MW of ECRF heating. The plasma density and the ion and electron temperatures are as shown in

Table 3. Plasma composition (with the minority ion species in brackets), heating scheme, magnetic field ($B_0$), ICRF frequency (f), ICRF power ($P_{ICRF}$), central electron density ($n_e^0$) and temperature ($T_e^0$).

Plasma	Heating	${\mathit{B}}_0$	f	${\mathit{P}}_{\mathbf{ICRF}}$	${\mathit{n}}_{\mathit{e}}^0\times {10}^{19}$.	${\mathit{T}}_{\mathit{e}}^0$
	Scheme	(T)	(MHz)	(MW)	(m−3)	(keV)
H-4He-(3He)	$\omega ={{\omega }_3}_{He}$	3.3	40	20	4.9	12

and Figure 5. The PION+ETS simulation was started at $t=500$ s, and the duration of the simulation was 5 s to let the plasma evolve towards its new steady state. The fundamental resonance of the ³He minority ($\omega ={{\omega }_3}_{He}$) was targeted using an ICRF frequency of 40 MHz and 20 MW of ICRF power. The simulation setup of the ETS transport model is the same as that employed in the case of the H minority scheme at 2.65 T studied above in Section 3.1.

The competing absorption mechanisms as given by PION+ETS are fundamental ³He damping and direct electron damping. Figure 6 shows that the ³He absorption takes place much more off-axis than the power deposition in the H minority scenario at 2.65 T (see Figure 1). The ³He resonance is located in the high-field side (HFS) of the plasma at s = 0.62. The electron damping takes place over the whole radial profile, but it is more prominent on-axis, where the electron temperature and density are highest [50]. In

Table 4. ³He concentrations, power absorbed by resonant ³He ions and electrons ($P_{abs{,}^{3}He}$, $P_{abs,e}$), fractions of collisional power transferred from resonant ions to bulk ions ($P_{ci}/P_c$) and background electrons ($P_{ce}/P_c$), critical energy ($E_{crit}$) and average energy of the fast ³He ions ($\langle E_{fast{,}^{3}He}\rangle$) as given by PION+ETS.

3He	${\mathit{P}}_{\mathbf{abs}{,}^3\mathbf{He}}$	${\mathit{P}}_{\mathbf{abs},\mathit{e}}$	${\mathit{P}}_{\mathbf{ci}}/{\mathit{P}}_{\mathit{c}}$	${\mathit{P}}_{\mathbf{ce}}/{\mathit{P}}_{\mathit{c}}$	${\mathit{E}}_{\mathit{c}\mathit{r}\mathit{i}\mathit{t}}$	$\langle {\mathit{E}}_{\mathbf{fast}{,}^3\mathbf{He}}\rangle$
(%)	(MW)	(MW)	(%)	(%)	(keV)	(keV)
0.01	4.26	14.0	17.1	82.9	601	775
0.05	8.56	9.39	51.9	48.1	510	169
0.10	10.5	7.18	55.7	44.3	486	71.9
0.20	11.3	6.08	43.8	56.2	496	102

, it can be seen that most of the power is absorbed by the ³He resonance for the ³He concentrations above 0.05%. Below this concentration, the dominating mechanism is direct electron damping. This can also be understood in terms of the SPA, which is very low (7%) for the ³He concentration of 0.01%, resulting in most of the power in the ICRF wave not being absorbed at the resonance by the resonant ³He ions but at the center of the plasma by the electrons. From the results in Table 4, we can see the trend of increasing power absorbed with increasing ³He concentration, with a maximum of 65% at a ³He concentration of 0.20%. The SPA is also highest (89%) at this concentration.

In terms of the collisional power transfer shown in Figure 7, there is dominant electron heating for the lowest and highest ³He concentrations of 0.01% and 0.20%, and dominant bulk ion heating for 0.05% and 0.10%. The average energy of the fast ³He ions in the tail of the fast ion distribution function is higher in the case of the lowest concentration, but lower in every other case (in the range of 775–71.9 keV c.f. Table 4) than their critical energy (601–486 keV). Therefore, the ³He ions will collide mainly with the bulk ions and transfer their energy to them. It should be noted that the collisional transfer-related values in Table 4 do not seem to follow the trend seen in the H minority scheme at 2.65 T studied above in Section 3.1, where a high $\langle E_{\mathrm{fast}}\rangle$ value and a low $E_{crit}$ value result in dominant electron heating, and as these values converge, bulk ion heating becomes more relevant, according to [3]. The reason for this might be that the collisional power deposition profiles are broader in this case with a HFS resonance and a lower SPA. Therefore, the volume-integrated collisional powers $P_{\mathrm{ci}}$ and $P_{\mathrm{ce}}$ do not follow the scaling expected from the local $\langle E_{\mathrm{fast}}\rangle$ and $E_{crit}$ at the resonance, as given in Table 4. If we consider the local values of $p_{\mathrm{ci}}$ and $p_{\mathrm{ce}}$ at the resonance $s=0.62$ in Figure 7, it can be seen that, apart from the lowest minority concentration case, the $p_{\mathrm{ce}}$ and $p_{\mathrm{ci}}$ profiles seem to meet close to the resonance, resulting in a relatively equivalent local power partitioning between bulk ion and electrons, which is consistent with $\langle E_{\mathrm{fast}}\rangle$ and $E_{crit}$ values in Table 4.

Figure 8 shows the time evolution of the thermal ion temperature at different ³He concentrations. In this scenario, the temperatures range from 5.78 keV to 5.92 keV at $t_f=505$ s, with the lowest $T_i$ = 5.78 keV at a ³He concentration of 0.01% and the highest $T_i$ = 5.92 keV at a ³He concentration of 0.20%. As shown in Figure 8, the ion temperature increases as the ³He concentration increases in the range of 0.01 to 0.20%. It should be noted that the transient evolution in the first seconds of the simulation is quite similar to the evolution in the H minority scheme at 2.65 T and also depends on the parameters used in the transport model. The highest ³He concentration yields the largest ICRF absorption, SPA and, consequently, the highest final ion temperature. It is also worth noting that the profiles for all concentrations have a lower temperature at the end of the simulation than at the beginning. This can be expected since the plasma was initially heated by a higher ECRH power than the ICRF power that was then applied during the simulation. Even though a percentage of the ICRF power has been absorbed by the resonant ions, it has not been enough to increase the ionic temperature.

Previously, the three-ion ICRF scheme ³He-H-⁴He at 3.3 T in H plasma was modeled [4] using TORIC [51], with a lower electron density of $3.4\times {10}^{19}{\mathrm{m}}^{-3}$ and fixed plasma parameters. Effective damping was noted for ⁴He (10–15%) and ³He (0.05%). Competing absorption mechanisms included ³He (absorbing 70% ICRF power), direct electron damping (30%), and minor absorption by H ions at the plasma edge (not simulated in PION+ETS here). A combined SPA of 0.8–0.9 for direct electron heating and off-axis ³He ion heating was quoted [4]. Our time-evolving ETS+PION results at $n_e=4.9\times {10}^{19}{\mathrm{m}}^{-3}$ show comparable, albeit somewhat smaller, ³He absorption of ∼45% of ICRF power at a ³He concentration of 0.05% (c.f. Table 4), and stronger ³He absorption of 65% of ICRF power (SPA = 89%) at a higher ³He concentration of 0.20% (c.f. Figure 4).

4. Conclusions

In this paper, we presented the results of predictive simulations of two ICRF heating schemes in the ITER non-activated phase using for the first time integrated modeling with the ICRF modeling code PION integrated into the European Transport Solver (ETS) workflow within the ITER Analysis and Modeling Suite (IMAS). For the H minority scenario in the ⁴He plasma at 2.65 T, H damping was found to be a strong ICRF power absorption mechanism compared to the competing absorption mechanisms. The H power absorption and SPA increased with the H concentration and reached a maximum of ∼80% and a single pass absorption coefficient of SPA $=99$% at an H concentration of 10%, which was the highest value of the H concentration considered in this study. Electron heating dominated over bulk ion heating for every concentration except for an H concentration of 10%, where the collisional power equipartition was balanced. For the three-ion scheme ³He-H-⁴He at 3.3 T, the ³He resonance was the main absorption mechanism for concentrations above 0.05%, absorbing up to 65% at a ³He concentration of 0.20%. However, SPA values were generally lower compared to H minority heating, with a maximum SPA $=89$% at the ³He concentration of 0.20%, and the increase in ionic temperature for the concentration scan was almost negligible (∼0.2 keV). Overall, our results suggest that the plasma response to changes in ICRF heating, e.g., via changes in minority ion concentration as studied here, can be highly non-linear. Self-consistent simulations of ICRF and plasma transport physics are required in order to optimize the resulting plasma performance. There are plans for more comparisons between codes to keep validating the results, such as between PION as an H&CD actor within ETS and the ICRF heating code StixReDist [45] within ETS. Further work is in progress and will be reported elsewhere to further exploit the capabilities of the workflow integration and study the effect of ICRF heating on the plasma performance in ITER.