# ICRF heating schemes for the HL-2M tokamak

L.F. Lu, B. Lu, X.J. Zhang, L. Colas, Guillaume Urbanczyk, Z. Wang, Z.J. Li, B.L. Hao, L. Xue, M. Xue, et al.

► To cite this version:

L.F. Lu, B. Lu, X.J. Zhang, L. Colas, Guillaume Urbanczyk, et al. ICRF heating schemes for the HL-2M tokamak. Nuclear Fusion, 2023, 63 (6), pp.066023. 10.1088/1741-4326/acc4dc hal-05018605

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# ICRF heating schemes for the HL-2M tokamak

L.F. Lu<fnref n="1" />*, B. Lu<fnref n="1" />, X.J. Zhang<fnref n="2" />, L. Colas<fnref n="3" />, G. Urbanczyk<fnref n="2" />,<fnref n="5" /> and A.P. Sun<fnref n="1" />

E-mail: lulingfeng@swip.ac.cn

Received 23 November 2022, revised 19 February 2023

Accepted for publication 16 March 2023

Published 21 April 2023

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CrossMark

## Abstract

The HL-2M tokamak is a new medium-sized tokamak at SouthWestern Institute of Physics. Two of its key missions are to achieve 10 keV ion temperature and investigate the behavior of energetic particles relevant to burning plasmas. A 6 MW ion cyclotron range of frequencies (ICRF) heating power is embedded in the next upgrade program of HL-2M. In order to facilitate the engineering design of the ICRF system, this paper analyses the main ICRF heating schemes for HL-2M, in terms of ion heating and energetic ion generation in particular. D(H) minority heating and the 2nd harmonic D will act as the main ion heating schemes, for which the optimal RF frequency range 27–33 MHz, antenna parallel wavenumber $k_{‖} \sim 8 \text{ m}^{-1}$ are proposed and strong single pass absorption is expected under typical HL-2M plasma parameters. Full wave simulations carried out via TORIC/steady-state Fokker–Planck quasilinear solver and TRANSP codes suggest that by adopting three ion scheme or synergetic heating on neutral beam injection D ions by the 2nd harmonic D, energetic ions with energy at MeV level can be produced. This study shows that ICRF heating could play significant roles in ion heating, energetic ion generation in HL-2M.

Keywords: ICRF, HL-2M, energetic particles

(Some figures may appear in colour only in the online journal)

## 1. Introduction

Ion cyclotron resonance heating (ICRH) is the only auxiliary heating method which can directly heat the fuel ions in future fusion reactors. In the present-day tokamaks, its typical

frequency is in the range of 20–70 MHz. At Southwestern Institute of Physics (SWIP), we tried ICRH for the first time in the MM-2U magnetic mirror (1989) [1] and later installed 800 kW ICRH in the HL-1M tokamak (1994) [2]. However, the plasma parameters at that time were too low for the fast wave (FW) antenna to achieve good performance. Only about half of the power was coupled to the plasma in HL-1M. After HL-1M, ICRH was unfortunately discarded by the succeeding machines in SWIP. Particularly, it was missing over 20 years’ operation of the HL-2A tokamak. Now our new machine, the HL-2M tokamak, has been built and commissioned successfully to have the first plasma at the end of 2020 [3]. Two upcoming major goals of the HL-2M tokamak are to achieve more than 10 keV ion temperature and to conduct energetic

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹ Southwestern Institute of Physics, PO Box 432, Chengdu 610041, China</footnote>

<footnote n="2">² Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China</footnote>

<footnote n="3">³ CEA, IRFM, F-13108 Saint-Paul-Lez-Durance, France</footnote>

<footnote n="4">⁴ Shenzhen University, Shenzhen 518060, China</footnote>

<footnote n="5">⁵ Current address: Max-Planck-Institut für Plasmaphysik, Boltzmannstrasse</footnote>

<footnote n="2">², Garching 85748, Germany</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
particle studies relevant to burning plasmas [3, 4]. A 6 MW ICRH is included in the next stage of the HL-2M upgrade program.

Before going to the engineering design of the ICRH system for HL-2M, it is important to conduct heating scheme analyses to have a general view of the ICRH performance in HL-2M and set limits on the operation parameters. Among all the auxiliary heating methods, ICRH has the most abundant heating schemes [5]. On one hand, it can directly deposit power on electrons through non-collisional mechanisms such as Landau damping and transit-time magnetic pumping, or indirectly via mode conversion (MC) to the electrostatic waves. On the other hand, ion heating can be achieved by the minority heating and higher harmonic heating. With the typical parameters of a fusion reactor, i.e. ITER, the minority heating and the 2nd harmonic heating are considered as the main ion heating schemes [6], whereas the recently demonstrated three ion scheme [7–9] and synergetic heating on neutral beam injection (NBI) ions are among the most efficient ways to produce energetic ions [10, 11], whose behavior is essential to study burning plasma physics. After being properly demonstrated in JET [11] and C-Mod [12], the three ion scheme has been further examined in the latest JET DT campaign and becomes a potential candidate to be used in future reactors.

This paper will investigate the main heating schemes under typical HL-2M plasma parameters, in particular, the minority heating, the 2nd harmonic heating, the three ion scheme and the synergy with NBI. The structure of this paper is as follows. Section 2 gives a brief introduction to the HL-2M tokamak; section 3 shows a general view of the expected ion cyclotron range of frequencies (ICRF) heating schemes in HL-2M; section 4 conducts the single pass absorption (SPA) analyses for the minority and the 2nd harmonic heating schemes. Section 5 discusses the full wave simulations of the three ion scheme and the synergetic heating on NBI ions, ending up with an estimation of the distribution functions of the ICRH generated energetic ions. Section 6 is the conclusion.

## 2. General description of the HL-2M tokamak

HL-2M is a new medium-sized copper conductor, carbon wall tokamak in SWIP, whose main plasma parameters are illustrated in table 1. The numbers inside brackets are the designed values. It is dedicated to study the high performance plasmas, energetic particles relevant to burning plasmas and critical technical issues related to the future fusion reactors, such as testing the advanced divertor concepts and high heat flux plasma facing components [3]. It has achieved the first plasma at the end of 2020 and 1 MA plasma current recently in October 2022. For the moment, a heating system consists of 5 MW NBI, 5 MW ECRH and 2 MW LHCD has been equipped. Soon after the first 1 MA milestone, HL-2M will turn into the high performance operation phase. 10 keV ion temperature is another key mission it wants to reach in that phase. Accordingly, an enhanced heating power including 6 MW ICRH is envisaged.

<table><caption>**Table 1.** Main parameters of the HL-2M tokamak [4].</caption><thead><tr><td>Parameters</td><td>Value</td></tr></thead><tbody><tr><td>Plasma current I<sub>p</sub> (MA)</td><td>2.5(3.0)</td></tr><tr><td>Toroidal field B<sub>t</sub> (T)</td><td>2.2(3.0)</td></tr><tr><td>Major radius R<sub>0</sub> (m)</td><td>1.78</td></tr><tr><td>Minor radius a (m)</td><td>0.65</td></tr><tr><td>Elongation k</td><td>1.8–2.0</td></tr><tr><td>Triangularity δ</td><td>>0.5</td></tr><tr><td>Pulse length (s)</td><td>>5 s</td></tr></tbody></table>

<table><caption>**Table 2.** Typical plasma parameters in HL-2M discharge under three operation scenarios obtained from METIS simulation.</caption><thead><tr><th rowspan="2">parameter</th><th colspan="3">Scenario</th></tr><tr><th>Baseline</th><th>Hybrid</th><th>Steady-state</th></tr></thead><tbody><tr><td>I<sub>p</sub> (MA)/B<sub>0</sub> (T)</td><td>2.5/2.2</td><td>1.4/2.0</td><td>1.0/1.8</td></tr><tr><td>T<sub>e0</sub>/T<sub>i0</sub> (keV)</td><td>10/12</td><td>7/9.5</td><td>6.2/6</td></tr><tr><td>n<sub>e0</sub> (10<sup>19</sup>)/f<sub>G</sub></td><td>11/0.58</td><td>6.5/0.62</td><td>5.6/0.74</td></tr><tr><td>P<sub>NBI</sub>/P<sub>IC</sub>/P<sub>LH</sub>/P<sub>EC</sub></td><td>6/4/2/6</td><td>4/3/1/2</td><td>4/2/2/6</td></tr><tr><td>P<sub>NBI</sub>/P<sub>LH</sub>/P<sub>EC</sub> [4]</td><td>15/0/8</td><td>12/1/4</td><td>10/1/6.5</td></tr></tbody></table>

Based on the experiment program of the next operation phase, the general magnetic field of HL-2M is around 2 T and the plasma current is around 1–2.5 MA. HL-2M has 20 toroidal field coils, with a maximum magnetic ripple of 0.7% at the edge of the middle plane. This paper considers three typical plasma scenarios designed for the HL-2M high performance operation, i.e. the baseline, the hybrid and the steady-state [4, 13, 14]. The ICRH relevant plasma parameters in these three scenarios are shown in table 2, i.e. $B_0$ the central magnetic field, $I_p$ the plasma current, $T_{e0}(T_{i0})$ the central electron (ion) temperature, $n_{e0}$ the central electron density and $f_G$ the Greenwald fraction. The baseline scenario is the conventional ELMY H mode discharge, where the inductive current accounts for a significant fraction and the safety factor increases monotonously with the normalized minor radius and it is around 3 at 95% flux surface (q95). While in the steady-state scenario, the current is nearly fully non-inductive with a significant bootstrap current fraction. The safety factor usually has a reverse shear with the central safety factor $q_0$ larger than 1.5. The hybrid scenario can be regarded as a transitional scenario between the baseline and the steady-state scenarios whose q profile has weak or low magnetic shear at center. The parameters in table 2 are optimized by the METIS code [15]. The corresponding auxiliary heating power combinations to realize these plasma scenarios are provided (units in MW) as well. As a reference, previous results [4] on the power combinations without adopting ICRH are also shown. From table 2, a significant reduction of the NBI power can be expected while achieving similar ion temperatures when ICRH is included.

## 3. ICRH ion heating schemes in HL-2M

ICRH uses poloidally oriented phased array strap to excite the FW, whose typical wavelength inside the plasma is a few
centimeters. At the ion cyclotron resonance, the FW has a right-handed polarization, which is the same as the electrons rotating around the magnetic field. Thus in a single ion species plasma, the FW cannot directly heat ions in the cold plasma limit [16]. Hot plasma correction allows some heating. This is generally not efficient, except for D-NBI ions [17–20], whose Doppler shift is large enough. Although the antenna is made intentionally to excite the FW, another branch of radio frequency (RF) wave is also parasitically excited. The slow wave can only appear in the low density region and thus cannot be used as the heating wave [21], even though it has proper polarizations to heat ions. It has been demonstrated both theoretically and experimentally that when an additional ion species, so called the minority ion, is introduced, an ion-ion hybrid resonance could appear and the left-handed polarized component of the FW could be enhanced near this resonance. In addition, if the cyclotron resonance of the minority ion is close to the ion-ion hybrid resonance, so that the Doppler broadening of the cyclotron resonance could cover the ion-ion hybrid layer, the FW can then be used to heat the minority ions. This is the standard minority heating scheme. Higher harmonic heating occurs due to the fact that the wave electric field has a space gradient, so that the ions would feel a net acceleration within one ion gyration. Unlike the fundamental ion cyclotron heating, the left-handed polarization is present at the harmonic resonance. The heating efficiency is better when the ion Larmor radius is larger. Therefore, the harmonic heating performs better with a high ion temperature. Among all the harmonic heating schemes, the 2nd harmonic heating is being the most frequently utilized.

Deuterium (D) will be the primary ion species in HL-2M due to its relatively low H mode threshold. The hydrogen (H) minority is the most frequently used minority heating scheme. Figure 1(a) shows the RF frequency ranges and $B_0$ for the D(H) minority heating as well as the 2nd harmonic H/D heating schemes to be implemented in HL-2M. Figure 1(b) shows the radial locations of typical cyclotron resonances with varies of $B_0$. An ICRH heating scheme generally performs well if it has a high SPA and the absorption region is located on axis [22]. At the same $B_0$, D($^3$He) plasma usually requires a lower RF frequency in order to have the same location of the power deposition as D(H). D(H) minority heating at $f = 27$ MHz, D($^3$He) minority heating at lower frequency $f = 18$ MHz, can be expected with $B_0 = 1.8$ T. The first priority is to have the ICRH system being optimized for the H minority heating in a D plasma, due to the fact that D($^3$He) minority heating usually has a much lower SPA efficiency.

The 2nd harmonic heating of D, $^3$He and H can be accessed around $B_0 = 2.0$ T at frequencies of 30 MHz, 40 MHz and 61 MHz respectively. The 2nd harmonic $^3$He heating will require very large amounts of $^3$He in the machine, which is impractical from the economic point of view and it was tried without much success in JET, i.e. ion heating efficiency <0.3 [23]. Hydrogen plasma is envisaged in the non-active phase of ITER operation [24]. In HL-2M, we could also use H plasma to minimize the activation of the machine during the initial phase and in the high performance operation phase when the heating capability is sufficient to achieve H mode. Thus if

<figure><img src="image_4.png" /><figcaption>**Figure 1.** (a) RF frequency and magnetic field ranges for ICRH minority and the 2nd harmonic heating in HL-2M; (b) locations of the cyclotron resonances for different ion species under varies $B_0$. D in red, $^3$He in blue, H in black, the 2nd harmonic $^3$He in yellow and the 2nd harmonic H in green. The numbers inside brackets represent $B_0$. Fundamental $^3$He with $B_0 = 3.0$ T overlaps with fundamental H at $B_0 = 2.0$ T. The green rectangles indicate the two operation frequency ranges. The 1st rectangle is optimized for D(H) minority heating and the 2nd rectangle is optimized for the 2nd harmonic H, obtained by the SPA analyses in section 4.</figcaption></figure>

additional budget is available, the 2nd harmonic H can also be a candidate. The two optimal frequency ranges, going to be discussed in section 4, are shown by green rectangles in figure 1. Last but not the least, $^4$He has the same charge-mass ratio as D, thus $^4$He(H) minority heating can also be accessed in $^4$He plasma in the similar experimental conditions as D(H).

In between two cyclotron resonances of each two ion pairs, an ion-ion hybrid layer or the so-called MC layer could appear. A FW could be mode converted to an ion Bernstein wave (IBW) and another ion cyclotron wave (ICW) at this layer. Those two waves are strongly damped on electrons through the Landau damping mechanism. This is the fundamentals of the MC heating. If in addition, the MC layer is well separated with the cyclotron resonance, the MC heating can be effective. Finally, when a third ion species is introduced, either through manually injection or using intrinsic impurities, one may have double MC layers both taking place inside the plasma [25]. In this case, the three ion scheme is efficient when the two MC layers are close to the cyclotron resonance of the third ion species.
# 4. SPA analyses

## 4.1. SPA for the D(H) and D($^3$He) minority heating

SPA analysis [26] is the most convenient way to have a quick view of heating effectiveness. This section focuses on SPA analysis of the most frequently used ion heating schemes, i.e. the minority heating and the 2nd harmonic heating. The SPA efficiency is calculated by $1 - \exp(-2\eta)$, where $\eta$ is the tunnelling factor, indicating the transferred wave power. The explicit formula of the tunnelling factor for the minority heating can be expressed as the following [26],

$$2\eta_M = \frac{\pi}{2} \frac{\omega_{pM}}{c} \frac{n_m}{n_M} \frac{Z_m}{Z_M} R \times \begin{cases} 1/(1+\sigma_M^2) & \text{D(H)} \\ 1/9(1+\sigma_M^2) & \text{D($^3$He)} \end{cases} \quad (1)$$

$$\sigma_M^2 = \frac{\pi}{4} \left( \frac{n_m}{n_M} \frac{M}{m} \frac{Z_m^2}{Z_M^2} \right)^2 \left( 1 - \frac{\omega_{cM}^2}{\omega_0^2} \right)^2 \left( \frac{\omega_0}{k_{//}v_{lm}} \right)^2 \quad (2)$$

where $\omega_p$, $\omega_c$, $\omega_0$, $n$, $Z$, $c$, $k_{//}$, $v_t$ and $R$ represent the plasma frequency, cyclotron frequency, wave frequency, plasma density, atomic charge, light speed, antenna parallel wave number, particle thermal speed and the major radius, respectively. Subscripts $m$ and $M$ indicate the minority and majority ions. Expression in the brackets of equation (1) essentially stands for the wave polarization [26], i.e. Eplus/Ey = (Ex + iEy)/Ey, where $x$ and $y$ adopting the same notation as Stix [16] and Eplus is the left-handed polarized electric field component. For the D(H) minority heating, the 2nd harmonic D heating occurs simultaneously, whose tunnelling factor takes the following form [26]

$$2\eta_H = \frac{\pi}{2} \frac{\omega_{pM}}{c} \beta_M R \frac{1}{1 + \sigma_H^2} \quad (3)$$

$$\sigma_H^2 = \frac{3\sqrt{\pi}}{4} \beta_M \frac{\omega_0}{k_{//}v_{lm}} \quad (4)$$

where $\beta_M \propto n_M T_M / B_0^2$ is the ion beta.

SPA calculation for D(H) minority heating under typical steady-state operation scenario of HL-2M (i.e. wave frequency $f = 27$ MHz, antenna parallel wave number $k_{//} = 8.4 \text{ m}^{-1}$, central plasma density $5.6 \times 10^{19} \text{ m}^{-3}$) suggests that the SPA efficiency could exceed 85% with central ion temperature above 4 keV and around 5% minority concentration, see figure 2(a). Note that figure 2 accounts for both the H minority heating and the 2nd harmonic D heating. The distance between the minority cyclotron resonance and the ion-ion hybrid resonance is proportional to the minority concentration, i.e. $R_0 n_m / n_M$. Thus the smaller of the minority concentration, the closer the minority cyclotron resonance to the ion-ion hybrid resonance, hence the larger the left-handed polarized component will be, which finally leads to a higher SPA efficiency. On the other hand, with too low minority concentration, the SPA decreases as lack of resonant particles. Besides, with higher $k_{//}$, the Doppler broadening of the fundamental resonance $\delta = (k_{//}v_{lm} / \omega_{cm})R$ increases, which will also give rise

<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) SPA (H minority heating + 2nd harmonic D heating) VS minority concentration and minority ion temperature in a D(H) plasma with a fixed $k_{//} = 8.4 \text{ m}^{-1}$; two red cross signs refer to the lower and upper limits of the proposed minority concentrations in table 3; (b) SPA (H minority heating + 2nd harmonic D heating) VS $k_{//}$ and minority ion temperature with a fixed H concentration of 5%. Red cross sign indicates the suggested minimum $k_{//}$ in table 3. $f = 27$ MHz, $B_0 = 1.8$ T, other parameters are the same as the steady-state scenario shown in table 2.</figcaption></figure>

to a higher SPA efficiency, as shown in figure 2(b). For energetic ion tails generated by this minority heating [27], the SPA efficiency is generally well above 90%.

As a comparison, the SPA efficiency of D($^3$He) minority heating is also computed. Figure 3 is the SPA result for the D($^3$He) minority heating under the same $B_0$ as figure 2. Besides the Doppler broadening of $^3$He cyclotron resonance is smaller than that of H under the same $B_0$ and $T_i$. D($^3$He) has a much smaller depolarization factor as shown in equation (1), which leads to a significant reduction of the SPA. As we can see in figure 3, the SPA is apparently worse than figure 2. Nevertheless, heavier $^3$He minority ions are sometimes preferable than lighter H in terms of bulk ion heating even at the expense of reduced SPA.

A complete study of the SPA efficiencies for D(H) and D($^3$He) minority heating under three operation scenarios is shown in table 3. The RF frequency is chosen so that it equals to the cyclotron frequency of the minority ion at the adopted $B_0$. Moreover, more constraints on plasma parameters and $k_{//}$ can be derived to fulfil certain criterion of SPA values. For example, table 2 gives the maximum ion temperature in the
<table><caption>**Table 3.** SPA analyses for the minority heating in a deuterium plasma. Estimated SPA values and corresponding constraints for each operation scenario are given.</caption><thead><tr><th>Main ion</th><th>Heating scheme</th><th>Baseline</th><th>Hybrid</th><th>Steady-state</th></tr></thead><tbody><tr><td>D</td><td>n = 1 H</td><td>f = 33 MHz,<br>SPA > 0.96,<br>X(H) ~ 1%~12%,<br>k<sub>‖</sub> > 6.5 m<sup>-1</sup></td><td>f = 30 MHz,<br>SPA > 0.9,<br>X(H) ~ 1%~10%,<br>k<sub>‖</sub> > 6.8 m<sup>-1</sup></td><td>f = 27 MHz,<br>SPA > 0.85,<br>X(H) ~ 1.5%~8%,<br>k<sub>‖</sub> > 7 m<sup>-1</sup></td></tr><tr><td>D</td><td>n = 1 <sup>3</sup>He</td><td>f = 22 MHz,<br>SPA > 0.3,<br>X(<sup>3</sup>He) ~ 2.4%~8%,<br>k<sub>‖</sub> > 7 m<sup>-1</sup></td><td>f = 20 MHz,<br>SPA > 0.25,<br>X(<sup>3</sup>He) ~ 2.5%~7%,<br>k<sub>‖</sub> > 7 m<sup>-1</sup></td><td>f = 18 MHz,<br>SPA > 0.2,<br>X(<sup>3</sup>He) ~ 2%~7.5%,<br>k<sub>‖</sub> > 7 m<sup>-1</sup></td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Figure 3.** SPA (<sup>3</sup>He minority heating only) efficiency of the D(<sup>3</sup>He) minority heating for the steady-state scenario, *f* = 18 MHz, other parameters are the same as figure 2. (a) SPA VS minority concentration with a fixed *k*<sub>‖</sub> = 8.4 m<sup>-1</sup>; (b) SPA VS *k*<sub>‖</sub> with a fixed <sup>3</sup>He concentration = 5%.</figcaption></figure>

steady-state scenario is 6 keV. With this minority ion temperature, the lower and upper limits of the minority concentration to achieve SPA > 0.85 can be determined, as it is shown by the red cross signs in figure 2(a). Similarly, a minimum *k*<sub>‖</sub> can be found as indicated by the red cross sign in figure 2(b). The constraints on the minority concentration is chosen by assuming *k*<sub>‖</sub> = 8.4 m<sup>-1</sup>. This parallel wavenumber is close to the two strap antenna used in ASDEX-U [28]. Note since both the first wall and divertor in HL-2M are coated by the carbon-fiber-reinforced composite at present, it is probably not necessary to adopt the latest three strap [29] or four strap [22] antenna to mitigate the metallic impurities. From table 3, D(H) minority

heating generally performs well with a minority concentration of 2%~8%. Higher than 12% will move the ion-ion hybrid resonance too far away from the H cyclotron resonance so that the polarization deteriorates. In that case, full wave simulation shows the MC heating may become significant. The lower limits of *k*<sub>‖</sub> in table 3 come from the cases where the minority concentration is set to be 5%. From table 3, to ensure a good SPA in D(H) minority heating schemes, *k*<sub>‖</sub> should be larger than 7 m<sup>-1</sup>. Compared to D(H) plasma, the main differences in D(<sup>3</sup>He) are the lower RF frequency and relatively lower SPA, i.e. 3~4 times lower than D(H). In practice, the other limitation of this heating scheme is that the <sup>3</sup>He is very expensive and should be used in a small amount.

## 4.2. SPA for the 2nd harmonic D and H heating

The 2nd harmonic heating, along with the minority heating, have been tested in the D-T campaign of JET [30, 31] and TFTR [32] tokamaks, and thus are natural candidates for the ITER D-T phase. The 2nd harmonic heating generally favors a relatively low magnetic field so as to shift the harmonic resonance inside the plasma. In addition, the 2nd harmonic heating is also more efficient with a lower magnetic field since the tuningelling factor is proportional to the ion beta. From figure 1(b), the 2nd harmonic resonance heating of D and H can be attempted. Among these heating schemes, the 2nd harmonic H heating requires a distinct frequency range from the current H minority heating oriented design, as it is shown in figure 1. Nevertheless, as mentioned in section 3, it can still be a backup heating scheme when additional budget is available. In the following analyses, we shall focus on the 2nd harmonic D and H heating.

In D(<sup>3</sup>He) or D(H) plasma, the 2nd harmonic D heating could be accessed with $B_0 = 2.2$ T at a moderate frequency, i.e. 33 MHz from figure 1. The radial location of the 2nd harmonic resonance of D is then right on axis, i.e. 1.8 m. Similarly, in D(H) or H(D) plasmas, the 2nd harmonic H heating can be accessed at a higher frequency, i.e. *f* = 67 MHz under $B_0 = 2.2$ T. At this frequency, the radial location of the 2nd harmonic H resonance is located at *R* = 1.78 m and it is the only resonance layer inside the plasma.

Figure 4(a) shows the SPA efficiency for the 2nd harmonic D heating in a D(<sup>3</sup>He) plasma with *f* = 33 MHz and $B_0 = 2.2$ T.
<figure><img src="image_7.png" /><figcaption>**Figure 4.** (a) SPA (2nd harmonic D heating only) VS the majority concentration and the majority ion temperature for D($^3$He) plasma, *f* = 33 MHz. (b) SPA (2nd harmonic H heating only) VS the minority concentration and the majority ion temperature for H(D) plasma, *f* = 67 MHz. Other parameters are the same as the baseline scenario in table 2.</figcaption></figure>

The maximum SPA is above 80% when the majority ion (D) temperature exceeds a certain threshold, i.e. 6.8 keV. This temperature threshold increases with the decrease of the majority concentration as the number of resonant (majority) particles decreasing. Figure 4(b) shows similar results in H(D) plasma, where the ion temperature threshold above which the maximum SPA could reach 80% is slightly lower than figure 4(a). Given the maximum ion temperature, i.e. 12 keV in the baseline scenario listed in table 2, the minimum concentration of the majority ion to guarantee SPA > 0.8 can be deduced from figure 4. Those constraints are summarized in table 4. Compared to the minority heating, the SPA value of 2nd harmonic heating shows looser constraints on the minority concentration.

This section mainly studies the ICRH ion heating schemes, SPA values in tables 3 and 4 could even become larger if we further include the electron heating schemes, which may occur simultaneously with the considered ion heating schemes. For example, adding a third minority species, e.g. $^3$He, in H(D) plasma will prompt the three ion scheme. Alternatively, the MC heating could occur if the minority concentration in a two-component plasma is large enough.

Summarizing tables 3 and 4, a RF frequency range in between 27–33 MHz is suggested to cover the D(H) minority heating and the 2nd harmonic D heating. *k*<sub>||</sub> should generally larger than 7 m<sup>-1</sup> in order to guarantee a strong SPA.

<table><caption>**Table 4.** SPA analyses for the 2nd harmonic heating. SPA values and corresponding constraints for each operation scenario are given.</caption><thead><tr><th>Main ion</th><th>Heating scheme</th><th>Baseline</th><th>Hybrid</th><th>Steady-state</th></tr></thead><tbody><tr><td>D</td><td>n = 2 D</td><td>f = 33 MHz,<br>SPA > 0.8,<br>T(D) > 6.8 keV<br>X(D) > 63%<br>k<sub>||</sub> > 5.3 m<sup>-1</sup></td><td>f = 30 MHz,<br>SPA > 0.7,<br>T(D) > 7 keV<br>X(D) > 90%<br>k<sub>||</sub> > 7 m<sup>-1</sup></td><td>f = 27 MHz,<br>SPA > 0.6,<br>T(D) > 4.6 keV<br>X(D) > 91%<br>k<sub>||</sub> > 7 m<sup>-1</sup></td></tr><tr><td>H</td><td>n = 2 H</td><td>f = 67 MHz,<br>SPA > 0.8,<br>T(H) > 6 keV<br>X(H) > 60%<br>k<sub>||</sub> > 5.3 m<sup>-1</sup></td><td>f = 61 MHz,<br>SPA > 0.7,<br>T(H) > 6 keV<br>X(H) > 70%<br>k<sub>||</sub> > 6 m<sup>-1</sup></td><td>f = 55 MHz,<br>SPA > 0.6,<br>T(H) > 3.8 keV<br>X(H) > 70%<br>k<sub>||</sub> > 6 m<sup>-1</sup></td></tr></tbody></table>

The minority concentration should be no more than 12% for H minority. The 2nd harmonic D heating performs well once the bulk ion temperature exceeds 7 keV. To take advantage of the 2nd harmonic H heating, an additional heating system operating at a frequency range of 55–67 MHz is needed.

### 4.3. Power allocation on each plasma species

The aforementioned methodology used gives a first impression of the global performance for a given ICRH scenario, however, strictly speaking, the simple polarization approximation used in the analytical expression is valid if one (minority) ion species is at low concentration and thus the polarization is imposed by the other (majority) ion species. It may fail when the two ion species have similar concentrations. The SPA analysis cannot calculate the power allocations on each plasma species either. Therefore, we further did a similar exercise using a proper 1D FW solver, i.e. TOMCAT [33], which accounts for the actual RF fields created in a multi-species plasma and the kinetic profiles. TOMCAT can give the SPA for all species, i.e. both electrons and ions. Table 5 estimates the overall SPA values for each heating scheme under three plasma scenarios. In addition, the power allocations on each plasma species are also shown at some specific ion concentrations.

## 5. Generation of energetic ions by ICRH

Besides the 10 keV ion temperature, another key mission of HL-2M is to investigate the behavior of energetic particles relevant to the burning plasmas. ICRH generated anisotropic (perpendicular) distribution tails have been observed in varies machines. Among all the ICRH-solely heating schemes, the three ion scheme is the most efficient in terms of energetic ion generation. A three ion scheme could be achieved when the charge-mass ratio of the third ion is in between the other two ions, i.e. $(Z/A)_2 < (Z/A)_3 < (Z/A)_1$. In principle, any of the ion combinations fulfill this relation could be used. An example of three ion scheme could be realized by adding minority $^3$He in H(D) plasmas. It is worth mentioning that since $^4$He has the same charge-mass ratio as D, the ion combination of this three ion scheme can also be replaced by H-$^3$He-$^4$He. The
<table><caption>**Table 5.** Overall SPA value and power partition on each plasma species obtained by TOMCAT.</caption><thead><tr><th>Main ion</th><th>Heating scheme</th><th>Baseline</th><th>Hybrid</th><th>Steady-state</th></tr></thead><tbody><tr><td rowspan="3">D</td><td rowspan="3">n = 1 H</td><td>SPA ~ 1,<br>e(40%),<br>H(30%),<br>D(30%)@<br>X(H) = 5%</td><td>SPA ~ 1,<br>e(20%)<br>H(50%)<br>D(30%)@<br>X(H) = 5%</td><td>SPA ~ 0.95,<br>e(20%)<br>H(50%)<br>D(25%)@<br>X(H) = 5%</td></tr><tr><td>SPA ~ 0.8,<br>e(36%)<br><sup>3</sup>He(40%)<br>D(4%)@<br>X(<sup>3</sup>He) = 5%</td><td>SPA ~ 0.52,<br>e(20%)<br><sup>3</sup>He(30%)<br>D(2%)@<br>X(<sup>3</sup>He) = 5%</td><td>SPA ~ 0.4<br>e(15%)<br><sup>3</sup>He(25%)<br>@<br>X(<sup>3</sup>He) = 5%</td></tr><tr><td>SPA ~ 0.97,<br>e(44%)<br>D(53%)@<br>X(D) = 90%</td><td>SPA ~ 0.86<br>e(30%)<br>D(56%)@<br>X(D) = 90%</td><td>SPA > 0.77<br>e(29%)<br>D(48%)@<br>X(D) = 90%</td></tr><tr><td rowspan="3"><sup>4</sup>He</td><td rowspan="3">n = 1 H</td><td>SPA ~ 1<br>e(37%)<br>H(51%)<br><sup>4</sup>He(12%)@<br>X(H) = 10%</td><td>SPA ~ 0.98<br>e(20%)<br>H(69%)<br><sup>4</sup>He(9%)@<br>X(H) = 10%</td><td>SPA ~ 0.99<br>e(19%)<br>H(74%)<br><sup>4</sup>He(7%)@<br>X(H) = 10%</td></tr><tr><td>SPA ~ 1<br>e(60%)<br>H(40%)@<br>X(H) = 70%</td><td>SPA ~ 0.99<br>e(37%)<br>H(62%)@<br>X(H) = 70%</td><td>SPA ~ 0.98<br>e(39%)<br>H(59%)@<br>X(H) = 70%</td></tr><tr><td></td><td></td><td></td></tr></tbody></table>

fundamental resonance of the third ion is then sandwiched between two MC layers even though the concentration of the third ion can be extremely low, i.e. ten times less than the typical minority concentration used in the minority heating. Since the concentration of the third ion is very low, the distance between its cyclotron resonance and two adjacent MC layers are very small. Therefore, most of the power will be efficiently damped on a small quantity of ions and then generate considerable energetic ions. The energetic ions can in turn transfer its energy to electrons or ions during its slowing down, provided that they are well confined.

Stix firstly proposed simple analytic formulae to model the energetic ion tail [27] produced by the minortiy heating scheme. More sophisticated modeling of the energetic ions is incorporated by iterating between TORIC [34] and the steady-state Fokker-Planck quasilinear solver (SSFPQL) [35]. The TORIC code solves the full wave equations with the kinetic dielectric tensor of the hot plasmas in a 2D radial-poloidal cross section of a real 3D tokamak. A Maxwellian velocity distribution and 100% of power absorption are assumed in the code. Simulation adopts a realistic magnetic equilibrium of a typical discharge in HL-2M as inputs. Since no measured plasma profile is available at this stage, we used the simulated plasma profiles (figure 5) from the baseline scenario listed in table 2. The SSFPQL uses the output from a standard run of TORIC to provide the realistic distribution functions, radial profiles of energetic ion tails generated by ICRH, and calculate the collisional power exchange between energetic ions and the background thermal particles.

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Typical plasma profiles of the HL-2M baseline scenario. The abscissa $\rho$ represents the normalized minor radius, covering the region from the magnetic axis to the last closed flux surface.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Locations of the double MC layers as well as the cyclotron resonances in the H$^{-}$He-D three ion scheme. The magnetic axis locates at $R = 1.8$ m. The following parameters are used, $X(D) = 23.6\%$, $X(H) = 70\%$, $X(<sup>3</sup>He) = 0.2\%$, $X(C) = 1\%$, $f = 28$ MHz, $B_{0} = 2.8$ T, $n_{0} = 11 \times 10^{19}$ m$^{-3}$. The horizontal black dashed line indicates the $k_{\parallel}$ used in figure 7.</figcaption></figure>

### 5.1. ICRF three ion scheme

Figure 6 depicts the locations of the double MC layers in this H$^{-}$He-D heating scheme. The concentration of the minority species, i.e. $X(<sup>3</sup>He)$, is adjusted to be 0.2% in order to reduce the distance between the minority cyclotron resonance and the neighboring MC layers. The frequency and ion concentration are tuned so that the fundamental resonance of $^{3}$He ($\Omega_{\text{imp}}$) is on axis. The fundamental resonances of the minority ion (D) and the majority ion (H) locate at $R = 1.37$ m and $R = 2.7$ m, respectively. The details of the power allocations of each plasma species are shown in figure 7, where 95% of the power is absorbed by $^{3}$He ions at its cyclotron resonance and only 0.07%(0.01%) is absorbed by D(C) ions at their cyclotron resonances $\Omega_{\text{min}}$. The electron power absorption is dominated by the FW direct damping, which accounts for only 4.7% of the total RF power. A weak MC heating occurs in the high field side MC layer at $\rho = 0.25$, i.e. at the D-H hybrid resonance.

Figure 8 shows the 2D contour of the left-handed polarized component Eplus. The abscissa is the distance to the magnetic axis. The MC mainly takes place off-axis around the D-H hybrid resonance, whereas the largest Eplus occurs on-axis around the $^{3}$He resonance layer, i.e. the black vertical line. The right figure is a zoom in of the MC region of the left figure. Here one could further observe the wave patterns of the mode
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Radial power deposition profiles of ions and electrons, $k_{\parallel} = 8.4 \text{ m}^{-1}$, other plasma parameters are the same as in figure 6.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 8.** 2D contour of Ez field, plasma parameters are the same as in figure 7, X is the radial position centered at the magnetic axis, Z is the vertical direction. The black vertical line indicates the cyclotron resonance of $^3$He. The right figure is a zoom in of the region enclosed by the dashed rectangle in the left figure. The red vertical line represents the MC layer.</figcaption></figure>

converted IBW and ICW near the high field side MC layer, i.e. the red vertical curve, as we have seen in figure 6. The IBW mainly deposits its power on the high field side of the MC layer while the ICW propagates to the low field side of the MC layer.

The three ion scheme is prone to generate energetic ions. We will now use TORIC + SSFPQL to investigate the questions of how much energy is carried by the energetic ions and how the energy is transferred to the thermal particles. Figure 9(a) shows the average energy carried out by the energetic $^3$He ions in this three ion scheme with only 1 MW ICRH power. The perpendicular energy $W_{\perp}$ could reach more than 600 keV(1000 keV) with 1 MW(6 MW) ICRH. The central bulk ion temperature used in these simulations is about 12 keV, which already requires a sufficient NBI power for pre-heating, i.e. 6 MW for the baseline scenario. Here we neglected the interplay between the NBI generated energetic ions and the RF waves. The criterion energy above which the energetic ions mainly transfer the power to electrons [36] is about 366 keV for this H-$^3$He-D plasma, according to $E_{crit} = 14.8 A_f T_e (\sum_j \frac{n_j Z_f^2}{n_e A_j})^{2/3}$ with $T_e = 10$ keV, $j$ sum over all the bulk ion species, Z and A the atomic charge and mass, subscript f

<figure><img src="image_12.png" /><figcaption>**Figure 9.** TORIC + SSFPQL simulation with the same parameters as in figure 6, i.e. baseline scenario with $I_p = 2.5$ MA. (a) Average energy of $^3$He energetic ions in H-$^3$He-D heating scheme with input ICRH power 6 MW (circle) & 1 MW(cross). (b) Power transferred through collisions from the energetic $^3$He ions to each thermal species. The input ICRH power is 1 MW.</figcaption></figure>

represents the energetic ion. One can immediately know that most part of the power carried by the energetic $^3$He ions will be transferred to the electrons. Figure 9(b) shows the profile of the power density transferred from energetic ions to the bulk particles through collisions. The electron (cyan dots) indeed acquires the majority fraction of power. The power density in figure 9(b) is proportional to the input ICRH power. With 6 MW ICRH, the peak power density transferred to electrons is around $6 \times 10^6 \text{ W m}^{-3}$.

## 5.2. Synergetic heating with NBI

Given the typical NBI energy in HL-2M, i.e. 80 keV–120 keV, the synergy between the ICRH and NBI [37–39] could also play an important role in the generation of energetic ions. An example of the ICRF heating of NBI D ions is modeled with the TRANSP code [40]. In TRANSP, the NUBEAM code is coupled to the TORIC code via a RF kick operator. Figure 10 shows the variation of the distribution function (integrated over poloidal angle $\theta$ and $\rho$) of the NBI D ions with RF kick operator off (a) and on (b), respectively. In figures 10(a), a pulsed 5 MW NBI is injected during 2–5 s, where the distribution function is picked at 3.2 s. As a comparison, the typical timescale of the slow down process is about 34 ms. Thus figure 10(a) calculates the distribution function after the beam ions are slowed down. Although the maximum distribution
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Integrated energetic ion distribution function VS pitch angle and energy, (a) RF kick operator off; (b) RF kick operator on. $P_{\text{NBI}} = 5$ MW, beam energy 80 keV, $P_{\text{ICRF}} = 6$ MW, $f_0 = 30$ MHz, $B_0 = 2.0$ T, $I_p = 2.0$ MA, other parameters are the same as the hybrid scenario in table 2.</figcaption></figure>

function occurs at $v_{\parallel}/v = 0.6$, it fills all the values of $v_{\parallel}$. Figure 10(a) is similar as figures in [19, 20].

In figure 10(b), D(H) plasma with a minority concentration of 2% is assumed. The wave frequency and $B_0$ are chosen to be $f_0 = 30$ MHz and 2.0 T so that the 2nd harmonic D resonance (without Doppler shifted, for thermal D ions) locates on axis. A total of 6 MW ICRH is applied in combination with 5 MW NBI. Among this 6 MW RF power, about 1 MW power directly interacts with the NBI D ions. As expected, the NBI ions are being accelerated to a much higher energy, i.e. more than 800 keV. Figure 10(b) shows the distribution function integrated over all radial positions. For typical D-NBI injection in HL-2M, $v_{\parallel} = 1.7 \times 10^6$ m s$^{-1}$ ($v_{\parallel}/v = 0.6$, $E_{\text{NBI}} = 80$ keV), corresponding a Doppler shift of the 2nd D resonance is about $\delta R_{\text{fast}} = n_{\text{tor}}v_{\parallel}/\omega_0 = 18$ cm with $n_{\text{tor}} = 20$. So one could expect the maximum power absorption occurs at 18 cm away from the magnetic axis.

Similarly, in H(D) plasma, $D_{\text{beam}}$ can also serve as a third ion minority where the Dopper shifted ion cyclotron resonance of $D_{\text{beam}}$ can be placed at the ion-ion hybrid layer of the thermal species [11, 41].

Dedicated study is required to give detailed analyses on the losses of the energetic ions. In our crude calculation using TRANSP/ORBIT [42] combination, the first orbit loss of the energetic particle is only 1% with $I_p = 2.5$ MA and 5% with $I_p = 1.5$ MA. The ripple loss is also in the order of a few percent at $I_p = 2.5$ MA. Moreover, we also known from previous experience of TFTR, the global loss of MeV alpha particles (first orbit + TF ripple loss) is only about a few percent with $I_p = 2.5$ MA, while it increases to 25% if $I_p = 1$ MA [43]. One can thus expect that the energetic ions can be well confined at the adopted plasma current in the baseline scenario, whereas for the other two scenarios, the confinement may become problematic.

## 6. Discussion and conclusion

Our new HL-2M tokamak is now operating at mega-ampere plasma current. After additional heating power is equipped, 10 keV ion temperature is envisaged and it will become an important facility to conduct energetic particle studies relevant to the burning plasmas. ICRH will play a key role in ion heating and energetic ion generation. A large variety of ICRF ion heating schemes are analysed for the HL-2M tokamak and estimations of their SPA efficiency are provided. Among all the heating schemes, D(H) minority heating can be the main ion heating scheme in the start-up phase for a D plasma. The 2nd harmonic D heating can then take over when the bulk ion temperature is already high, i.e. above 7 keV. To achieve a strong SPA efficiency, RF wave frequency 27–33 MHz and $k_{\parallel} > 7$ m$^{-1}$ are proposed. Provided the typical port size of HL-2M, 450 mm × 500 mm, $k_{\parallel}$ should be larger than $13$ m$^{-1}$ in order to make a dipole phasing two strap antenna insertable into the port. Such a large $k_{\parallel}$ is unfavorable from the edge power coupling point of view. An in-vessel installation of the antenna will be needed in order to guarantee $k_{\parallel} \approx 8$ m$^{-1}$. To design the matching system, a frequency of 30 MHz can be assigned, corresponding to the operational magnetic field $B_0 = 2.0$ T. The 2nd harmonic H at a frequency range of 55–67 MHz can be a backup heating system. $^4$He(H) minority heating can also be attempted for a $^4$He plasma.

The H-$^3$He–D, H-$^3$He-$^4$He and H–D$_{\text{beam}}$–D are among the potential three ion schemes to generate energetic particles. Preliminary assessments of the energetic ions produced by the three ion scheme are provided. The three ion scheme, like the minority heating scheme, is sensitive to the ion concentrations. Compared to the minority heating, the three ion scheme even relies more on the measurement precision of the gas puffing or impurity control. On the contrary, the 2nd harmonic heating is more resilient to the ion concentration and the wave polarization and thus it can operate in a broad range of parameters. Heating NBI ions using 2nd harmonic D heating can be another useful strategy in relation to the generation of energetic ions. Both TORIC/SSFPQL and
TRANSP simulations show energetic ions with energy at MeV level can be produced by ICRH in the baseline scenario and a significant power exchange to electrons can be expected. Note the SSFPQL solver integrated with the TORIC code is based on a rather drastically simplified model. A more sophisticated Fokker-Planck solver will be considered in the future. Finally, heating schemes which can produce very energetic ions are not the best way to favor bulk ion heating, since they preferably heat electrons.

A crude estimation for the baseline scenario using TRANSP/ORBIT suite suggests the ripple loss and the first orbit loss of the energetic particles are in a few percent with $I_p = 2.5$ MA. More dedicated studies are needed on the losses of the energetic particles caused by other mechanisms, e.g. electromagnetic perturbations, MHD instabilities, etc.

The results of this study can give important guidance for the engineering design of the HL-2M ICRH system.

## Acknowledgments

The TRANSP code is provided by PPPL at https://transp.pppl.gov. The TORIC code is provided by IPP Garching. This work is supported by National Magnetic Confinement Fusion Science Program of China under the Contract Number 2022YFE03090002 and China National Nuclear Corporation Fundamental Research Program under Contract Number CNNC-JCYJ-202236.

## ORCID iDs

L. Colas https://orcid.org/0000-0002-4573-3326

G. Urbanczyk https://orcid.org/0000-0002-4026-6802

B.L. Hao https://orcid.org/0000-0003-3009-0660

S. Wang https://orcid.org/0000-0001-6480-7004

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