# Design and analysis of a PAM launcher at 4.6 GHz for a new LHCD system on EAST

M.H. Li, L. Liu, Y. Yang, L.M. Zhao, W.D. Ma, T.A. Zhou, M. Wang, W.D. Ma, C.B. Wu, B.J. Ding, et al.

► To cite this version:

M.H. Li, L. Liu, Y. Yang, L.M. Zhao, W.D. Ma, et al., Design and analysis of a PAM launcher at 4.6 GHz for a new LHCD system on EAST. Nuclear Fusion, 2024, 64 (3), pp.036017. 10.1088/1741-4326/ad22f4. cea-04783111

HAL Id: cea-04783111

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Submitted on 14 Nov 2024

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# Design and analysis of a PAM launcher at 4.6 GHz for a new LHCD system on EAST

M.H. Li<fnref n="1" /> ID, L. Liu<fnref n="1" />,*, Y. Yang<fnref n="1" />,*, L.M. Zhao<fnref n="1" />, W.D. Ma<fnref n="1" />, T.A. Zhou<fnref n="1" />, M. Wang<fnref n="1" />, W.Q. Ma<fnref n="1" />,<fnref n="2" />, C.B. Wu<fnref n="1" />, B.J. Ding<fnref n="1" /> ID, H. Jia<fnref n="1" />, Z.G. Wu<fnref n="1" />, W.Y. Zhou<fnref n="1" />, X.L. Li<fnref n="1" />, L. Yin<fnref n="1" />, J. Hillairet<fnref n="3" /> ID, Y. Savoye-Peysson<fnref n="3" />, M. Goniche<fnref n="3" />, A. Ekedahl<fnref n="3" /> ID and X.Z. Gong<fnref n="1" />

E-mail: liuliang@ipp.ac.cn and yangyon@ipp.ac.cn

Received 3 October 2023, revised 27 December 2023

Accepted for publication 26 January 2024

Published 9 February 2024

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CrossMark

## Abstract

To improve the Current Drive (CD) capability in long-pulse (up to ~1000 s) H-mode operation, it has been decided to develop a new Lower Hybrid Current Drive system at 4.6 GHz with an active cooling Passive Active Multijunction (PAM) launcher on EAST. In this paper, both the radio frequency (RF) and the physical properties of this PAM are studied numerically. The same nominal parallel refractive index ($N_‖ = k_‖c/ω$, where $k_‖$ is the parallel wavenumber, c the velocity of light, and $ω$ the wave angular frequency) of 2.04 as the existing 4.6 GHz Full Active Multijunction (FAM) is chosen. Ray-tracing calculations indicate that good accessibility could be achieved when the LH waves radiate with this nominal $N_‖$ in typical long-pulse H-mode plasmas. The coupling performance in terms of power reflection coefficient ($R_C$), power spectrum, maximum electric field, power directivity ($D_P$) and global CD capability is evaluated with the ALOHA code based on the linear coupling theory. Good coupling performance with averaged $R_C \le 1\%$ and $D_P \sim 70\%$ could be expected with the density ($n_e$) in front of the PAM close to the cut-off value ($n_{e\_co}$). The simulated $R_C$ remains below 6.5% over a wide density range $0.5 \le n_e/n_{e\_co} \le 10$, which is similar to the plasma edge conditions produced by Edge Localized Mode activity. A detailed comparison with the existing 4.6 GHz FAM launcher is also performed.

Keywords: LHCD, PAM launcher, coupling performance, current drive efficiency

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

## 1. Introduction

Lower Hybrid (LH) waves can be absorbed efficiently by electrons through Landau damping, accelerating these resonant

electrons in the direction parallel to the confined magnetic field [1]. As these fast electrons are little collisional, they can create a toroidal current efficiently in tokamak plasma [2]. The high efficiency of Lower Hybrid Current Drive (LHCD) has been demonstrated experimentally in JET [3], JT-60 U [4], and Alcator C-Mod [5]. Recently, encouraging results of efficient LHCD effects at a line-averaged density up to $\bar{n}_e \sim 1.5 \times 10^{20} \text{ m}^{-3}$ have been obtained on FTU [6] and Alcator C-Mod [7]. Calculations indicate that LH waves could drive off-axis current efficiently (at normalized radius $\rho \ge 0.6$) on ITER [8] with CD efficiency ($\eta_{CD} \equiv I_{LH}R\bar{n}_e/P_{LH}$,

<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. 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 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China</footnote>

<footnote n="2">² Institutes of Physical Science and Information Technology, Anhui University, Hefei 230601, China</footnote>

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

<footnote>* Authors to whom any correspondence should be addressed.</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Evolution of the LH system on EAST. The total source power and the type of the launcher for each system is indicated.</figcaption></figure>

where $I_{\text{LH}}$ is the current driven by LH waves, $R$ the major radius, and $P_{\text{LH}}$ the total power of the power spectrum) as high as $\sim 1.6 \times 10^{19} \text{AW}^{-1} \text{m}^{-2}$, and on CFETR [9] with $\eta_{\text{CD}} \sim 2.8 \times 10^{19} \text{AW}^{-1} \text{m}^{-2}$, which is crucial for sustaining the steady-state operation and optimizing the current density profile.

LHCD is the main tool for long-pulse operation and the main electron heating source on EAST. Figure 1 shows the evolution of the LH system on EAST tokamak. Before 2014, there was only one LHCD system with a Full Active Multijunction (FAM) launcher, frequency at 2.45 GHz (referred to as LH1) and total source power of 4.0 MW. The main achievement in long-pulse operation with this system (only) was an L-mode discharge (#43336) with a pulse length of $\sim 411$ s realized in 2012 [10], as portrayed in figure 2. Other parameters are: $P_{\text{LH1}} = 1.1$ MW, $I_p = 270$ kA, $\bar{n}_e = 1.1 \times 10^{19} \text{m}^{-3}$. In 2014, a 4.6 GHz/6.0 MW high power system (referred to as LH2) with a FAM launcher was developed. Significant progress has been achieved recently with the combination of LH2 and Electron Cyclotron (EC) waves, including 1056 s I-mode (injected LH energy $\sim 1.1$ GJ) [11] and 403 s H-mode [12] plasmas. Other parameters for I- (H) mode are: $P_{\text{LH2}} = 1.1$ (1.6) MW, $P_{\text{EC}} = 0.55$ (1.75) MW, $I_p = 330$ (300) kA, $\bar{n}_e = 1.8$ (3.6) $\times 10^{19} \text{m}^{-3}$. In 2021, the FAM launcher of LH1 system was upgraded to a Passive Active Multijunction (PAM) and the experimental results clearly verified the advantages of the PAM launcher in long-distance coupling [13]. Because the 2.45 GHz LHCD exhibited much poorer CD and plasma heating effects with respect to the 4.6 GHz waves [14–17], especially in the high-density H-mode experiments, it is rarely used now in the long-pulse operation. Figure 3 compares the CD and plasma heating effects of 2.45 GHz and 4.6 GHz waves in one discharge with similar LH power ($\sim 2.0$ MW) and plasma density ($\bar{n}_e \sim 3.0 \times 10^{19} \text{m}^{-3}$). It is noticeable that the CD and plasma heating with 4.6 GHz waves are much better from the comparison of loop voltage and plasma stored energy, namely, $V_{\text{loop}}$: 0.44 V (2.45 GHz) vs 0.2 V (4.6 GHz), and $W_{\text{MHD}}$: 50 kJ

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Maximum pulse length at different LH power level for the 2.45 GHz FAM (circles) and 4.6 GHz FAM launchers (triangles), respectively. The data points without marking correspond to L-mode discharges.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Comparison of CD and plasma heating (power absorption) effects between LH1 (2.45 GHz) and LH2 (4.6 GHz) systems in the same discharge with equivalent LH power. $\bar{n}_e$ line averaged electron density; $V_{\text{loop}}$ loop voltage; $P_{\text{LH}}$ LH power; $W_{\text{MHD}}$ plasma stored energy.</figcaption></figure>

(2.45 GHz) vs 81 kJ (4.6 GHz). Previous studies [15, 18] suggest that the dominant mechanism responsible for the weaker LHCD effects of 2.45 GHz waves is the parasitic power loss resulting from Parametric Decay Instability (PDIs), the growth rate of which is inversely proportional to the square of wave frequency [19]. Note that the power directivity ($D_p$) of the $N_{\text{ll}}$ spectrum is almost the same for both antennas (i.e. $D_p \sim 75\%–78\%$) [20], where $D_p$ is defined as the power ratio in positive $N_{\text{ll}}$ to the total radiated power. To enhance the CD capability in long-pulse ($\sim 1000$ s) H-mode operation, the 2.45 GHz system will be replaced by a new 4.6 GHz/4.0 MW system with a PAM launcher at the end of 2024.
The PAM concept was proposed by Bibet et al in the mid-1990s [21], with the purpose of LHCD application in reactor tokamaks. For a PAM launcher, between any two consecutive active waveguides on the same row, a passive one is inserted. By optimizing the depth of the passive waveguide (to be a quarter of wavelength $λ_g$ in waveguide. For 4.6 GHz, $λ_g/4 \sim 21.5$ mm), a strong cross-coupling exists between the active and passive waveguides, which guarantees the consistent E-field (amplitude and phase) at the front surface. This power, fed by the cross-coupling via the plasma edge, will be reflected again to the plasma by the perfectly conductive bottom (short circuit) of the passive waveguide. In fact, the waveguide cross-coupling is highest when the density at the launcher mouth ($n_e$) reduces to near the cut-off value ($n_{e\_co}$) [22]. As a result, the PAM launcher keeps a good coupling property even when the edge density is close to the cut-off value. In other words, the PAM launcher can be located farther away from the main plasmas than the FAM, which is favorable for long-pulse operation. In addition, efficient active cooling of the front face, thanks to the cooling circuit behind but close to each passive waveguide, allows the PAM to withstand higher thermal loads than the common FAM. During the EAST experiments, it was found that the power handling capability of the 4.6 GHz FAM launcher was, at least partly, limited by the strong plasma-antenna interactions, such as ‘hot spot’ issue and impurity production by arcing event [23, 24].

A detailed conceptual study of PAM launchers at 3.7 GHz and 5.0 GHz was carried out for JET [25] and ITER [26, 27], although the LHCD system has been removed on both machines. The PAM characteristic of good coupling with the edge density very close or even lower than the cut-off value has been demonstrated on several devices, for instance, FTU with wave frequency at 8.0 GHz [28], Tore Supra [29] and HL-2A [30] with 3.7 GHz, and EAST with 2.45 GHz [13]. It is well known that the wave frequency ($f$) on a reactor could not be too high, because high frequency means high electron density required for coupling ($n_{e\_co} \propto f^2$); and $f$ could not be too low to avoid PDIs (as discussed above) and to reduce the parasitic power absorption by alpha particles (low frequency corresponds to small perpendicular refractive index) [31]. Hence, this PAM launcher at 4.6 GHz being developed on EAST would provide more valuable references than the existing PAM launchers to the application on future reactors (for example, CFETR [32]). What is more, it enables a direct comparison with the present FAM launcher in the same H-mode plasmas.

This paper is organized as follows. In section 2, we focus on the physics rationale for determining the optimal $N_‖$. The layout and geometry of the new PAM launcher are given in section 3. Section 4 shows the radio frequency (RF) properties of the optimized PAM module. In section 5, the coupling performance in terms of power reflection coefficient, power directivity and electric field is simulated and compared with the existing FAM launcher at 4.6 GHz. Section 6 is devoted to the summary and discussion.

<figure><img src="image_7.png" /><figcaption>Figure 4. Schematic diagram of a PAM launcher viewing at the top. $\Delta = b_A + b_P + s$ is the geometrical toroidal periodicity of the waveguides, $b_A$ and $b_P$ the active and passive waveguide width, $s$ the width of the septum, $L_P$ the depth of a passive waveguide. The locations of cooling pipes behind the passive waveguides are also indicated.</figcaption></figure>

## 2. Determination of the optimal $N_‖$

The parallel refractive index ($N_‖$) is a critical parameter in determining the LH waves propagation and power deposition. From the physics aspect, the optimal $N_‖$ should be slightly greater than a critical value of $N_‖^{acc}$ given by [33]

$$N_‖^{acc} = \frac{\omega_{pe}}{\omega_{ce}} + \sqrt{1 + \left(\frac{\omega_{pe}}{\omega_{ce}}\right)^2 - \left(\frac{\omega_{pi}}{\omega}\right)^2} \quad (1)$$

where $\omega_{pe}$ ($\omega_{pi}$) is the local electron (ion) plasma frequency, $\omega_{ce}$ the local EC frequency, and $\omega$ the angular frequency of LH wave. In this case, high CD efficiency can be obtained in addition to satisfying the accessibility condition, since the CD efficiency is inversely proportional to the square of $N_‖$ [1]. On the other hand, from the technical aspect, the nominal $N_‖$ of each module is related to the front face geometry as following

$$N_{||0} = \frac{\delta\phi}{k\Delta} \quad (2)$$

where $\delta\phi$ is the internal geometrical phase shift between the two adjacent active waveguides, $k$ the vacuum wave number, and $\Delta$ the geometrical toroidal periodicity of the waveguides, i.e. the horizontal distance between successive active waveguides (see figure 4). For a PAM launcher, $\Delta$ is expressed by

$$\Delta = b_A + b_P + 2s \quad (3)$$

where $b_A$ and $b_P$ are the active and passive waveguide width, $s$ the width of the septum. Consequently, choosing $N_{||0}$ needs to consider the following factors together: the maximum power density in the active waveguides, the space for drilling cooling
<table><caption>**Table 1.** Representative H-mode plasmas achieved on EAST. $N_{||0}$ is the launched parallel refractive index ($N_{||}$) of the 4.6 GHz FAM launcher, and $N_{||acc}$ is the accessibility criterion calculated with the line-averaged density ($\bar{n}_e$) and the magnetic field ($B_t$) at plasma center.</caption><thead><tr><th>Shot No.</th><th>B<sub>t</sub> (T)</th><th>¯n<sub>e</sub> (10<sup>19</sup>/m<sup>3</sup>)</th><th>Pulse length (s)</th><th>N<sub>||0</sub></th><th>N<sub>||</sub><sup>acc</sup></th></tr></thead><tbody><tr><td>#67341</td><td>2.5</td><td>3.1</td><td>60</td><td>2.04</td><td>1.92</td></tr><tr><td>#73999</td><td>2.5</td><td>2.8</td><td>102</td><td>2.04</td><td>1.88</td></tr><tr><td>#80307</td><td>2.5</td><td>4.7</td><td>9</td><td>2.26</td><td>2.2</td></tr><tr><td>#90949</td><td>2.5</td><td>4.2</td><td>64</td><td>2.26</td><td>2.1</td></tr><tr><td>#122254</td><td>2.5</td><td>3.6</td><td>403</td><td>2.04</td><td>2.02</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>**Figure 5.** Experimental density ($n_e$) and local accessibility criterion ($N_{||acc}$) as a function of normalized radius ($\rho$) at low field side, for typical H-mode discharge #122254 with moderate line-averaged density and discharge #80307 with relatively high density. For the typical discharge #80307 with higher density, a higher $B_t = 2.8$ T is required to fulfil the wave accessibility condition through the pedestal region.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Ray trajectories in the poloidal cross section calculated with the ray-tracing code C3PO. (a) and (b) correspond to the density profiles of #122254 and #80307, respectively. $N_{||0} = 2.04$ and typical H-mode temperature profile with $T_{e0} = 7$ keV are assumed for both cases. The magnetic fields at plasma center are 2.5 T and 2.8 T for (a) and (b), respectively. The red thick curves denote the strong linear Landau damping. The red circles at the low field side represent the six rows of the designed PAM antenna.</figcaption></figure>

pipes behind the passive waveguides, the mechanical robustness, and the available space of the port for installation.

The main function of this new PAM launcher is to enhance the CD capability in long-pulse H-mode operation (i.e. to extend the plasma current or plasma density). We consider the long-pulse H-mode plasmas as the target for choosing the optimal $N_{||}$. Table 1 displays the main plasma parameters of typical H-mode discharges and the initial $N_{||}$ of the 4.6 GHz FAM launcher in the experiments. All these shots were performed with $B_t = 2.5$ T. For the high $\beta_p$ H-mode discharges with relatively high density $\bar{n}_e \sim 4.2-4.7 (10^{19} m^{-3})$, but with short pulse length ($<100$ s), the launched $N_{||}$ was 2.26 to satisfy the accessibility, while the long-pulse H-mode (pulse length $>100$ s) discharges with moderate density $\bar{n}_e \sim 2.8-3.6 (10^{19} m^{-3})$ were realized with $N_{||} \sim 2.04$ (the nominal $N_{||}$ of the 4.6 GHz FAM). Thus, the same $N_{||}$ of 2.04 as the 4.6 GHz FAM is eventually chosen for the new 4.6 GHz PAM launcher.

Figure 5 plots the experimental density profiles for a typical long-pulse ($\sim 403$ s) H-mode discharge #122254 with moderate line-averaged density ($\bar{n}_e \sim 3.6 \times 10^{19} m^{-3}$) and

another high $\beta_p$ discharge #80307 with relatively high density ($\bar{n}_e \sim 4.7 \times 10^{19} m^{-3}$). The local accessibility condition ($N_{||acc}$) calculated by expression (1) as a function of normalized radius ($\rho$) at low field side is also shown. It is seen that the nominal $N_{||}$ of 2.04 can satisfy the wave accessibility through the pedestal region for the case of moderate line-averaged density ($\bar{n}_e \sim 3.6 \times 10^{19} m^{-3}$) with normal $B_t = 2.5$ T, while for the case of high density ($\bar{n}_e \sim 4.7 \times 10^{19} m^{-3}$), a higher $B_t$ of 2.8 T is required. It is worth pointing out that with this value $B_t = 2.8$ T, the ECRH (with frequency of 140 GHz) power, another important electron heating source on EAST [34], cannot be deposited on axis. In tokamak magnetic configurations, the $N_{||}$ will evolve along the ray paths due to the toroidal effects [35]. Figures 6(a) and (b) show the ray trajectories in the poloidal cross section computed by the ray-tracing code C3PO [36], which considers the toroidal effects, for #122254 with $\bar{n}_e \sim 3.6 \times 10^{19} m^{-3}$, $B_t = 2.5$ T, and #80307 with $\bar{n}_e \sim 4.7 \times 10^{19} m^{-3}$, $B_t = 2.8$ T, respectively. It is supposed that the LH waves start to propagate from the Last Closed Flux Surface (LCFS) and the propagation is limited inside the LCFS. The initial $N_{||} = 2.04$ and six poloidal
locations which correspond to the six rows of the new PAM
antenna are considered. It is found that no cold mode con-
version (at the mode conversion point, the rays will reflect
back to the plasma edge) occurs before the waves are fully
absorbed, and all the rays can penetrate into the plasma core
region for both cases. After several passes (from the LCFS
into the plasma and back to the LCFS), a strong linear Landau
damping takes place when the $N_\parallel$ is upshifted to meet the
damping condition $N_\parallel \sim 6.5/\sqrt{T_e}$ (keV)[37]. In the simula-
tions, the damping is calculated using Maxwellian distribu-
tion function and a typical value in H-mode of $T_{c0} = 7$ keV
is assumed. The modelling results indicate that most of the
LH power is located at $\rho \le 0.4$, as desirable. In this region
the electron temperature is usually high, hence to get high CD
efficiency.

3. Layout and geometry of the launcher

The 4.6 GHz PAM will use the same port of the 2.45 GHz
loader, but occupies ~ the lower 2/3 space of port B, as illus-
trated in figure 7. The upper space is allocated to a new ECRH
system. The lower space is more convenient for the installation
and maintenance of LHCD antenna since it is much heavier
than that of ECRH, and it is expected to move in the radial
direction during the experiments. The PAM launcher is fed
by eight Continuous Wave (CW) 4.6 GHz/500 kW klystrons
(made by Aerospace Information Research Institute, Chinese
Academy of Sciences). Each klystron has two output windows,
which are connected to the upper and lower parts of the PAM,
respectively. The whole launcher consists of the multijunc-
tion at the front and the TE10–TE30 mode converters at the
rear, which splits the input power into three poloidal rows.
Thanks to a moveable guideway and a corrugated tube, the
PAM can move radially in various scenarios with different
densities. Behind each passive waveguide which is made of
stainless steel, a cooling pipe with dimensions of 5 mm (in
toroidal direction) × 12 mm is drilled. To maximize the heat
exchange, the cooling circuit is designed to have a snakelike
configuration. The cooling ducts closest to the front face are
optimized to match the shape of the PAM, and a moderate dis-
tance of ~40 mm (to the bottom of the passive waveguide)
is chosen as a balance of effective colling of the front surface
and the risk of leakage. The cooling pipes are close together
on the front end, while on the back end they are far apart, as
shown in figure 6(a). To protect the antenna from plasma heat
load, two guarder limiters with tungsten coated and with active
cooling at both sides of the PAM are installed (see figure 7(b)).
The cooling loops are separate for the PAM launcher and
the limiters, for the purpose of convenient identification if a
leak occurs during the experiment. One Langmuir probe is
equipped on the top of the launcher to measure the electron
density and temperature for physical study in the experiments.
To get a homogeneous coupling performance along differ-
ent waveguides rows (in poloidal direction) and columns (in
toroidal direction), both toroidal and poloidal shapes of the

PAM will be machined into a curved surface to match the
field lines.

The detailed dimensions of the front face are determ-
ined as illustrated in figure 8 by considering the following
aspects together: (1) choose the optimal $N_\parallel = 2.04$ on phys-
ics; (2) maximize the injected power; (3) minimize the power
density in active waveguides; (4) use the space of the port
as much as possible. To guarantee the propagation of the
fundamental mode TE₁₀ only, i.e. those unexpected higher
modes TEm₀ (*m* = 2, 3......) are cut-off, the height (*a*) of
the waveguide must be in the range of $\lambda_0/2 < a < \lambda_0$,
where $\lambda_0$ (~ 65.2 mm for 4.6 GHz) is the wavelength in
vacuum. For the sake of convenient connection to the trans-
mission lines, which are the WR229 standard waveguides
(with dimensions of height 58.17 mm × width 29.08 mm),
the height of the waveguide *a* = 58.2 mm is ultimately picked
up. This value of height also makes full use of the space
in poloidal direction. For the width (*b*) of the waveguide,
it must warrant the undesirable TE₀₁ mode (and all higher
TE₀ₙ modes, *n* = 2, 3......) to be cut-off, which leads to
$b < \lambda_0/2 \sim 32.6$ mm. For bi-junction based FAM, it is nat-
urally to adopt a geometrical phase shifter $\delta\phi = 90^\circ$, so that
the RF waves reflected at the plasmas-antenna interface will
be totally reflected back to the plasmas at the *E*-plane junc-
tion (i.e. self-matching effect), due to the fact that the local
phase difference between the two active waveguides is equal
to 180° (two passes through the phase shifter). While for
a PAM, detailed calculations in [21] indicate that the phase
shifter $\delta\phi$ should be in the range of $90^\circ < \delta\phi/2 < 270^\circ$.
Consequently, for bi-junction based PAM, we should choose a
geometrical phase shifter $\delta\phi = 270^\circ$ (which makes the phase
difference after two passes through the phase shifter to be
180°) to realize the self-matching performance. Finally, to
have the expected $N_\parallel0 = 2.04$ (which means that the geomet-
rical toroidal periodicity $\Delta = b_A + b_P + 2s$ ought to be
24 mm), the active (passive) waveguide width and the septum
width are chosen to be $b_A$ ($b_P$) = 10 (8) mm, $s = 3$ mm,
respectively.

The PAM launcher is composed of eight modules in tor-
oidal direction, and of two modules in poloidal direction (fed
by one klystron). Each PAM module is divided into three
waveguides in the poloidal direction (by one TE₁₀–TE₃₀ mode
converter) and then each row into two active waveguides in
the toroidal direction (by one *E*-plane bi-junction), as shown
in figure 9. The height and width of the whole antenna are
489.2 mm and 398 mm. The total 96 active waveguides (each
with dimensions $b_A \times a = 10 \text{ mm} \times 58.2 \text{ mm}$) result in
a radiative surface of 0.0559 m². Thus, the averaged power
density in active waveguides is estimated to be $4 \times 80\%$
MW/0.0559 m² ~ 57.2 MW m⁻² with the maximum input
power of $4 \times 80\%$ MW (here, we consider 20% transmission
power loss). This value is about 85% of the empirical weak
conditioning limit [38] expressed by $3.2 \times f^2 b_A$ (MW m⁻²),
where *f* is the LH frequency in GHz and $b_A$ the width of active
waveguide in cm.
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Side view of the 4.6 GHz PAM (a), and schematic of the entire launcher with active cooling (b). The PAM will be installed on the lower part of port B (occupying ~2/3 space of port B). The upper part is assigned to a new ECRH system.</figcaption></figure>

## 4. RF properties of one module

As illustrated in figure 9, the RF components in one module include (from the input to output), curvilinear taper, TE₁₀−TE₃₀ mode converter, H-plane splitter, E-plane taper, E-plane bi-junction and 270° stepping phase shifter. Power division is realized by one TE₁₀−TE₃₀ mode converter and three 270° E-plane bi-junctions, leading to a structure having one input waveguide and six (secondary) output waveguides per module. The built-in phase shifter is optimized by adding two steps in the straight waveguide, thus reducing the height of the waveguide. If the steps are too high, it will increase the

strength of the electric field and the *S*₁₁ parameter of the input port, and if the steps are too low, it will increase the length of the multijunction. RF studies mainly focus on the optimization of the following components, which have a direct influence on the coupling performance: (1) the ensemble to achieve the lowest intrinsic power reflection towards the input (minimal *S*₁₁); (2) the poloidal power divider (composed of the input taper, mode converter and poloidal splitter) to have the highest conversion efficiency from TE₁₀ to TE₃₀ mode and divide the RF power into three poloidal rows equally; (3) the E-plane bi-junction to halve the power between the two outputs waveguides; (4) the built-in phase shifter to make the
<figure><img src="image_11.png" /><figcaption>Figure 8. Front view of the 4.6 GHz PAM launcher with its dimensions. The white and gray rectangles represent the active and passive waveguides, respectively. The PAM launcher is composed of eight modules in toroidal direction and of two modules in poloidal direction (indicated by the red rectangle).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 9. Structure of a PAM module and E-field pattern with a matched load and an input RF power of 200 kW. One module consists of six active (output) waveguides marked with numbers 2–7. Port 1 represents the input of the module.</figcaption></figure>

phase difference between the two outputs waveguides at 270°. The amplitude of scattering matrix (S) elements calculated by RF software ANSYS-Ansoft HFSS versus frequency of the optimized module is plotted in figure 10. Although the minimal $S_{11} \sim -40$ dB is located at 4.59 GHz, the PAM achieves the required RF performance of low intrinsic reflection ($S_{11} \sim -37$ dB at 4.6 GHz). Note that the frequency point with minimal $S_{11}$ is shifted by ~10 MHz from 4.6 GHz artificially because the $S_{11}$ increases dramatically for frequencies lower than 4.59 GHz. The transmission parameters ($S_{21}-S_{71}$) do not meet the ideal splitting of -7.78 dB, but they are very close to this value (i.e. $S_{21}-S_{71} \sim -7.78 \pm 0.4$ dB). It is worth mentioning that this slightly biased power splitting (33 ± 3 kW if one module is fed by 200 kW) has a negligible effect on the toroidal power spectrum. Finally, the phase shifts between the two successive outputs in each row are very close to the required 270° (i.e. $S_{31}-S_{21}$, $S_{51}-S_{41}$, $S_{71}-S_{61} \sim 270° \pm 0.3°$, as shown in figure 11) in the range of klystron operating frequency, 4.6 GHz ± 2 MHz.

## 5. Coupling characteristics and analysis

The coupling characteristics in terms of the directivity of the power spectrum, the power reflection coefficient ($R_C$), and the electron field at the antenna mouth are computed by the ALOHA code [39], which is based on the linear coupling theory mainly due to M. Brambilla [40]. The density conditions in front of the antenna consider more realistic plasma profiles with two density gradients denoted by the first ($\lambda_{n1}$, near the antenna mouth) and second ($\lambda_{n2}$, in the far scrape-off layer (SOL)) density decay length, as shown in figure 12. In order to compute analytically the surface admittance of plasma medium, two linear profiles with different decay lengths are assumed in the modelling, which are defined as

$$ 
\left. 
\begin{aligned}
n_e(d) &= n_{e0} + \frac{n_{e0}}{\lambda_{n1}} d, & 0 \le d \le w_1 \\
n_e(d) &= n_{ew1} + \frac{n_{ew1}}{\lambda_{n2}} (d - w_1), & w_1 < d
\end{aligned}
\right\} (4)
$$
<figure><img src="image_13.png" /><figcaption>**Figure 10.** Amplitude of the scattering matrix (S) parameters versus frequency of the optimized antenna module. The order of port number is shown in figure 8. The curves of S<sub>21</sub> and S<sub>61</sub>, S<sub>31</sub> and S<sub>71</sub> are overlapped. Note that the red line represents the value of S<sub>11</sub>/4.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 11.** Phase difference between S<sub>31</sub> and S<sub>21</sub>, S<sub>51</sub> and S<sub>41</sub>, S<sub>71</sub> and S<sub>61</sub> in degrees versus frequency.</figcaption></figure>

where $n_{e0}$ is the electron density at the antenna mouth, $d$ the distance to the launcher ($d=0$ represents the location of PAM), $w_1$ the thickness of the first layer, and $n_{ew1} = n_{e0} + n_{e0}w_1/\lambda_{n1}$. The first $\lambda_{n1}$ is assumed to be 2 mm with the plasma layer width $w_1 = 2$ mm, corresponding to the distance between the guard limiters and the front face of the antenna. A typical density decay length of $\lambda_{n2} = 1.5$ cm is adopted according to [41], with the assumption of infinite extent. In addition to the fundamental mode $TE_{10}$, the first two (evanescent) $TM_{1n}$ modes are considered. Vacuum gap between the antenna and the first layer of the plasma is not taken into account and only one-half of the PAM, namely, only one module in the poloidal direction but all the eight modules in the toroidal direction is modelled. Since the plasma conductivity is much larger in the toroidal direction than in the poloidal direction, there is low coupling between rows of waveguide, unless the direct connection by magnetic field due to the tilt

<figure><img src="image_15.png" /><figcaption>**Figure 12.** Electronic density profiles in the SOL assumed in ALOHA modelling. Two linear profiles with different decay lengths (the first one $\lambda_{n1} = 2$ mm with the plasma layer width $w_1 = 2$ mm, and the second $\lambda_{n2} = 1.5$ cm) are considered. $n_{e0}$ is the electron density at the antenna mouth, and $d$ is the distance to the launcher. $d=0$ represents the location of PAM and $d > 0$ means getting close to the LCFS.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 13.** Averaged power reflection coefficient ($R_C$), power directivity ($D_p$), and $N_{\parallel}$-weighted directivity ($\delta_{CD}$) versus electron density calculated with the ALOHA code for the designed PAM (red) and the existing FAM (blue) launchers. The first ($\lambda_{n1}$) and second ($\lambda_{n2}$) density decay length assumed in the calculations are 2 mm and 1.5 cm, respectively.</figcaption></figure>

angle. Thus, each of the rows are indeed independent to the others, and has its own power spectrum.

Figure 13 shows the averaged $R_C$ (over the eight modules), power directivity ($D_p$), and $N_{\parallel}$-weighted directivity ($\delta_{CD}$) versus the electron density at the launcher mouth for the
new PAM with nominal phasing between adjacent modules $\Delta\phi = 180^{\circ}$ and the existing FAM with nominal $\Delta\phi = 90^{\circ}$. The peak value of $N_{\parallel}$ is $\sim 2.04$ for both launchers. The detailed structure of the FAM launcher was provided in [42]. Here, the $N_{\parallel}$ weighted directivity $\delta_{CD}$ is defined as [43]

$$ \delta_{CD} = (1 - R_c) \frac{N_{\parallel peak}^2}{P} \times \left( \int_{1}^{+\infty} \frac{1}{N_{\parallel}^2} P(N_{\parallel}) dN_{\parallel} - \int_{-\infty}^{-1} \frac{1}{N_{\parallel}^2} P(N_{\parallel}) dN_{\parallel} \right) \quad (5) $$

where $N_{\parallel peak}$ is the $N_{\parallel}$ peak having the highest amplitude in the power spectrum and $P$ the power density as a function of $N_{\parallel}$. As a matter of fact, the $\delta_{CD}$ is usually taken as an indicator of the CD efficiency since $\eta_{CD} \propto 1/N_{\parallel}^2$ according to the N.J. Fisch's theory [1]. The calculations suggest that the $R_C$ can be less than 1% around the cut-off density of 4.6 GHz wave $n_{e\_co} \sim 2.6 \times 10^{17} \text{ m}^{-3}$, and the coupling performance with $R_C \le 6.5\%$ can be kept when the density varies in the range of $0.5n_{e\_co} - 10n_{e\_co}$, which is like the plasma edge conditions induced by large Edge Localized Modes pacing [44]. While for the FAM, higher density is required for optimal coupling, namely, $n_e \ge 4n_{e\_co} \sim 1 \times 10^{18} \text{ m}^{-3}$, but it has a good coupling (i.e. $R_C \le 5.0\%$) even with density up to $4 \times 10^{18} \text{ m}^{-3}$ ($\sim 15n_{e\_co}$), as revealed in [20]. The $D_P$ ($\delta_{CD}$) can be as high as $\sim 70\%$ (55%) with density $n_e \sim 0.5n_{e\_co}$, but it is reduced by a factor of $\sim 1.2$ (2.2) when the density increases to $10n_{e\_co}$. Regarding the FAM, the highest $D_P$ ($\delta_{CD}$) is $\sim 78.6\%$ (68%) with $n_e \sim 2n_{e\_co}$, and it exhibits better directivity than the PAM when the density $n_e > n_{e\_co}$, as expected (which is due to the fact that the FAM has a greater number of waveguides than the PAM in the toroidal direction).

As depicted in figure 14, the PAM has a reasonably large $N_{\parallel}$ flexibility ($N_{\parallel} = 2.04 \pm 0.65$) for different density scenarios by changing the phasing between adjacent modules ($\Delta\phi$). In contrast to the FAM, the power directivity ($D_P$) shows a strong sensitivity to the phasing between modules. The maximum $D_P$ ($\sim 70\%$) for the cases of edge density $n_e = 2n_{e\_co}$ and $5n_{e\_co}$ is near $\Delta\phi = 120^{\circ}$, and for the case of $n_e = 0.5n_{e\_co}$, it corresponds to a wider range of $\Delta\phi = [120^{\circ}-180^{\circ}]$. Moreover, the power directivity drops to $\sim 51\%$ when $\Delta\phi = 0^{\circ}$, suggesting only heating effect. The $R_C$ ($\le 3.5\%$) is acceptable when $n_e = 0.5-5$ ($n_{e\_co}$) for all different phasing.

The maximum electric field inside the PAM module is as low as $\sim 3.49 \text{ kV cm}^{-1}$ with perfect load ($R = 0$) and 200 kW input power (see figure 9). However, this field could increase with unmatched load, which is the case during the real experiment. The maximum electric field inside the PAM and at the mouth of the active and passive waveguides as a function of edge density is plotted in figure 15 (each module fed by 200 kW). It is found that the electric field inside the launcher is minimal around the cut-off density, which is naturally correlated with the power reflection, while at the plasma-antenna interface, the E field is higher when $n_e$ decreases towards $n_{e\_co}$.

<figure><img src="image_17.png" /><figcaption>Figure 14. Averaged power reflection coefficient ($R_C$) and power directivity ($D_P$) versus the phasing ($\Delta\phi$) between adjacent modules for different edge densities. Value of $N_{\parallel}$ at maximum power density versus the phasing is also shown.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 15. Maximal electric field inside the PAM and at the mouth of the active and passive waveguides, power handling capability, and cross-coupling parameter ($S_{P,A}$) between the active and passive waveguides versus edge density. The E field is calculated with the assumption of 3.2 MW (200 kW per module) incident power. The power handling capability is estimated with the limitation of $E_{max} < E_{thrs} \sim 6.4 \text{ kV cm}^{-1}$.</figcaption></figure>

The maximum electric field of the PAM is located in the passive waveguides with the density range of $n_e \le 5.4n_{e\_co}$ (in particular around $n_{e\_co}$). Hence, in this density range the power handling capability is limited by the maximal tolerable E-field in the passive waveguides. If we adopt the linear scaling of the E-field threshold with the frequency found in [45], which gives
<figure><img src="image_19.png" /><figcaption>Figure 16. Normalized power spectrum for the PAM and FAM launchers. The plasma edge density and the phasing are 1.8 × 10¹⁷ m⁻³ (10 × 10¹⁷/m⁻³) and 180° (90°) for PAM (FAM). Only the first and second peaks of Nᵢₗ lobe are shown. The full width of the Nᵢₗ lobe ΔNᵢₗ is ~0.32 (from 1.88 to 2.2).</figcaption></figure>

a value of ~6.4 kV cm⁻¹ to avoid a RF breakdown at 4.6 GHz, the PAM has a power handling of only ~2.4 MW around nₑ co. Much better power handling of >3.2 MW could be achieved at nₑ = 2–3nₑ co, together with very low power reflected to the generator (Rₑ ~ 1%). The fact of large E-field in passive waveguide is a result of strong cross-coupling between the active and passive waveguides via the plasma edge. When nₑ decreases from 10nₑ co to nₑ co, the cross-coupling parameter (Sₚ-A) between the active and passive waveguides increases from −12.0 dB to the highest value ~−8.6 dB (see the bottom panel in figure 15).

Figure 16 compares the power spectra of the PAM and FAM launchers, which are calculated with the nominal phasing (180° and 90°) and the optimal density (1.8 × 10¹⁷ m⁻³ and 10 × 10¹⁷ m⁻³). Note that the feeding power for both launchers are the same, namely, ∫⁺∞ ∫⁻∞ P(Nᵢᵢ) dNᵢᵢ = constant for both cases. Although the spectral width of the first main lobe is almost the same for both launchers (ΔNᵢᵢ ~ 0.32, Nᵢᵢ from 1.88 to 2.2), there are two obvious differences. The first difference is the power directivity. The Dₚ is lower by a factor ~1.1 for the PAM than the FAM (70% against 77%). The power fraction of the first main lobe driving co-current is similar for both the PAM and FAM (61.7% against 61.8%, estimated by ∫2.04+ΔNᵢᵢ/₂ ∫2.04−ΔNᵢᵢ/₂ P(Nᵢᵢ) dNᵢᵢ / ∫⁺∞ ∫⁻∞ P(Nᵢᵢ) dNᵢᵢ, where ΔNᵢᵢ ~ 0.32 is the full width of the first main lobe), while the second lobe driving current in the opposite direction takes up more power for the PAM (20.9% against 13.3%). The second difference is the Nᵢᵢ peak of the second lobe. The absolute Nᵢᵢ,₂ of the PAM is much lower than the FAM (Nᵢᵢ,₂ = −3.39 against −6.1), further leading to a lower δCD for the PAM (55% against 67%). The different values of the second Nᵢᵢ peak is attributable to the fact that the PAM adopts a 270° geometry phase shifter, while for the FAM, it is based on a 90° phase shifter. According to the theory, the radiated power spectrum is characterized by successive Nᵢᵢ peaks at

$$N_{||}(m) = \frac{\delta\phi + 2\pi m}{k\Delta} \quad (m = 0, \pm 1, \pm 2, \dots) \quad (6)$$

where δφ = 270° and 90° for the PAM and FAM, respectively. Consequently, the Nᵢᵢ peaks are closer to each other for the PAM compared to the FAM.

## 6. Summary and discussion

Due to the poor CD and heating effects of the 2.45 GHz LHCD system on EAST, it will be replaced by a new system at 4.6 GHz with a PAM launcher. The main goal of this new 4.6 GHz/4.0 MW (nominal source power) system is to enhance the CD capability in long-pulse (up to 1000 s) H-mode operation. An optimal Nᵢ₀ = 2.04 with a large flexibility ± 0.65 is determined under the constraints of the CD efficiency, the accessibility condition and the available space for installation. Calculations with the ray-tracing code C3PO indicate that the LH waves with the launched Nᵢᵢ of 2.04 can propagate into the plasma core and drive current inside ρ ~ 0.4 with typical long-pulse H-mode parameters (nᵣ ~ 3.6 × 10¹⁹ m⁻³, Tₑ₀ ~ 7 keV, Bᵣ = 2.5 T).

By optimizing the RF components, the PAM achieves the required performance of low intrinsic reflection (Sᵢ₁ ~ −37 dB at 4.6 GHz), balanced power splitting (S₂₁−S₇₁ ~ −7.78 ± 0.4 dB) and output phase shift (270° ± 0.3°). It is worth mentioning that the phase difference between the poloidal rows in one module, due to the poloidal power divider was not compensated. The ALOHA modeling of the top three rows (one module in poloidal direction) shows that the poloidal power spectrum is peaked at very small Nθ ~ 0.04, as depicted in figure 17.

A cooling circuit is designed behind each passive waveguide, which is the first advantage with respect to the FAM for
<figure><img src="image_20.png" /><figcaption>**Figure 17.** Poloidal power spectrum calculated with the top three rows (one module in poloidal direction). The spectrum is peaked at $N_{\theta} \sim 0.04$.</figcaption></figure>

long-pulse operation. In addition, the plasma-antenna coupling simulations reveal that the edge density for optimal coupling lies around the cut-off value ($n_{e\_co}$) as a result of the strong intercoupling between active and passive waveguides via the plasma edge; while for the existing FAM, higher density (≥4$n_{e\_co}$) is required, meaning that the new PAM can be located ~2 cm further away from the plasmas (considering the typical SOL density profile with $\lambda_{ne} \sim 1.5$ cm). The power directivity ($D_p$) of the $N_\parallel$ spectrum exhibits strong sensitivity to the phasing between modules. For the nominal phasing of 180° (corresponding to $N_\parallel = 2.04$) the maximum $D_p \sim 70\%$ is achievable, while for 0° ($N_\parallel = 1.4$) the power spectrum is almost symmetrical which is suitable for only heating scenario. Thus, an accurate phase control system is crucial for real plasma experiments. It is worth pointing out that, although around the cut-off density the power reflection is lowest, the electric field at the plasma-antenna interface is high, leading to a poor power handling. When the density increases to ~3$n_{e\_co}$, the PAM has a good power handling capability >3.2 MW.

Compared with the existing 4.6 GHz FAM launcher, the PAM exhibits lower power directivity (70% against 77%) as expected, and has a smaller (absolute) value of the second peak $N_\parallel$ (-3.39 against -6.1) driving counter-current, further resulting in a lower $N_\parallel$-weighted directivity ($\delta_{CD} \sim 55\%$ against 68%). If we take $\delta_{CD}$ as a scale of CD efficiency ($\eta_{CD}$), the estimated $\eta_{CD}$ is $\sim 0.61 \times 10^{19} \text{ AW}^{-1}\text{m}^{-2}$ for the PAM with typical H-mode plasma density ($\bar{n}_e \sim 3.6 \times 10^{19} \text{ m}^{-3}$) according to the experimental $\eta_{CD}$ ($\sim 0.75 \times 10^{19} \text{ AW}^{-1}\text{m}^{-2}$) of the FAM reported in [46], assuming the same electron temperature and effective charge number ($Z_{eff}$) as the typical H-mode discharges. Then, the LH current driven by the PAM in this typical H-mode plasma is $\sim 140$ kA, if 40% of the 4.0 MW

<figure><img src="image_21.png" /><figcaption>**Figure 18.** Electron temperature profiles used in the C3PO/LUKE simulations. The red solid and blue dashed lines correspond to the experimental data of #122254 and an increase of 15%, respectively.</figcaption></figure>

total source power can be coupled into the plasmas. To make the estimation more robust, ray-tracing/Fokker-Planck calculations with the C3PO/LUKE codes [47] are carried out. We consider the same plasma target of the 403 s H-mode plasma (#122254) for both the FAM and PAM antennas, which was achieved with the combination of 1.75 MW EC and 1.6 MW LH2 heating recently. The density and temperature profiles used for the simulation are shown in figure 5 (top panel) and figure 18. Only the first and second lobes of the power spectrum shown in figure 16 are modelled. Other parameters are: $P_{LH2} = P_{LH3} = 1.6$ MW, $Z_{eff} = 2.2$. The simulated results are summarized in table 2. It is found that the predicted CD efficiency of the FAM can match with the experiment when an empirical diffusion coefficient of the fast electrons $D_{st} = 1 \text{ m}^2\text{s}^{-1}$ is included in the calculation according to [48, 49]. The LH current driven by the PAM alone with 1.6 MW power is predicted to be $\sim 154$ kA, corresponding to a CD efficiency $\sim 0.66 \times 10^{19} \text{ AW}^{-1}\text{m}^{-2}$, which is very close to that estimated by the $N_\parallel$-weighted directivity ($\sim 0.61 \times 10^{19} \text{ AW}^{-1}\text{m}^{-2}$). When both launchers used simultaneously, the modelled LH current can be as high as $\sim 341$ kA (and $\sim 345$ kA with the assumption of $T_e$ increased by 15%).

The PAM launcher is scheduled to be installed on EAST at the end of 2024. At present, we have completed the technical research in processing a prototype of the water-cooling plate, which requires a high engineering technology especially in sealing and maintaining the shape unchanged. Good sealing performance and a small deformation of only $\sim 0.2$ mm have been achieved after a high temperature baking ($\ge 250$ °C for two hours) and with a high gas pressure $\sim 4$ Mpa. Future work will focus on the experimental investigation on the coupling and CD performance in long-pulse H-mode plasmas, and the comparison with the existing 4.6 GHz FAM, which could contribute to robust extrapolations to CFETR with the same LH wave frequency [32].
<table><caption>**Table 2.** The LH current ($I_{LH}$) and CD efficiency ($\eta_{CD}$) modelled by C3PO/LUKE codes with and without fast electrons diffusion ($D_{st} = 1 \text{ m}^2\text{s}^{-1}$). The density and temperature profiles assumed in the modelling are shown in figure 5 (top panel) and figure 18, respectively. The LH power is 1.6 MW for both the FAM and PAM launchers.</caption><thead><tr><th></th><th>η<sub>CD</sub> w/o diffusion<br>(10<sup>19</sup> AW<sup>-1</sup>m<sup>-2</sup>)</th><th>η<sub>CD</sub> with diffusion<br>(10<sup>19</sup> AW<sup>-1</sup>m<sup>-2</sup>)</th><th>I<sub>LH</sub> w/o<br>diffusion (kA)</th><th>I<sub>LH</sub> with<br>diffusion (kA)</th></tr></thead><tbody><tr><td>FAM (T<sub>e</sub>)</td><td>1.0</td><td>0.85</td><td>233</td><td>198</td></tr><tr><td>PAM (T<sub>e</sub>)</td><td>0.78</td><td>0.66</td><td>181</td><td>154</td></tr><tr><td>FAM + PAM (T<sub>e</sub>)</td><td>0.89</td><td>0.73</td><td>413</td><td>341</td></tr><tr><td>FAM + PAM (1.15 × T<sub>e</sub>)</td><td>0.92</td><td>0.74</td><td>430</td><td>345</td></tr></tbody></table>

## Acknowledgments

This work is supported by the Comprehensive Research Facility for Fusion Technology Program of China under Contract No. 2018-000052-73-01-001228, the National Natural Science Foundation of China (Grant Nos. 11775259, 11975266), and the National Key R&D Program of China (Grant No. 2017YFE0301100).

## ORCID iDs

M.H. Li https://orcid.org/0000-0002-3658-8243

B.J. Ding https://orcid.org/0000-0002-8445-4979

J. Hillairet https://orcid.org/0000-0002-1073-6383

A. Ekedahl https://orcid.org/0000-0002-0376-5119

## References

[1] Fisch N.J. 1987 *Rev. Mod. Phys.* **59** 175

[2] Fisch N.J. 1978 *Phys. Rev. Lett.* **41** 873

[3] Ekedahl A. *et al* 1998 *Nucl. Fusion* **38** 1397

[4] Ushigusa K. *et al* 2002 *Fusion Sci. Technol.* **42** 255

[5] Wilson J.R. *et al* 2009 *Nucl. Fusion* **49** 115015

[6] Cesario R. *et al* 2010 *Nat. Commun.* **1** 55

[7] Baek S.G. *et al* 2018 *Phys. Rev. Lett.* **121** 055001

[8] Decker J. *et al* 2011 *Nucl. Fusion* **51** 073025

[9] Wallace G.M. *et al* 2021 *Nucl. Fusion* **61** 106009

[10] Wan B.N., Li J., Guo H., Liang Y. and Xu G. 2013 *Nucl. Fusion* **53** 104006

[11] Song Y.T. *et al* 2023 *Sci. Adv.* **9** eabq5273

[12] Qian J.P. *et al* 2023 Development of long pulse high performance plasmas towards ITER and CFETR steady-state operation on EAST **49th Conf. on Plasma Physics of the European Physical Society (Bordeaux, France, 3–7 July)** (available at: https://eps2023.github.io/)

[13] Li M.H. *et al* 2023 *Nucl. Fusion* **63** 096014

[14] Li M.H. *et al* 2016 *Phys. Plasmas* **23** 102512

[15] Ding B.J. *et al* 2018 *Nucl. Fusion* **58** 126015

[16] Gu X., Shen B., Li M., Qian J., Moreau D., Ding S., Sun Y., Ding B. and Chen S. 2018 *Phys. Plasmas* **25** 092509

[17] Baek S.G. *et al* 2023 *AIP Conf. Proc.* **2984** 090004

[18] Li M.H. *et al* 2022 *Nucl. Fusion* **62** 126055

[19] Porkolab M. 1977 *Phys. Fluids* **20** 2058

[20] Li M.H. *et al* 2020 *AIP Conf. Proc.* **2254** 080005

[21] Bibet P., Litaudon X. and Moreau D. 1995 *Nucl. Fusion* **35** 1213

[22] Preynas M. *et al* 2011 *Nucl. Fusion* **51** 023001

[23] Wang M. *et al* 2022 *Nucl. Eng. Technol.* **54** 4102

[24] Wang B.G., Zhu D., Ding R., Gao B., Yan R., Li C., Xuan C., Yu B. and Chen J. 2023 *Nucl. Mater. Energy* **34** 101318

[25] Belo J.H. *et al* 2011 *Nucl. Fusion* **51** 083017

[26] Belo J.H., Goniche M., Hillairet J. and Bizarro J.P.S. 2015 *Fusion Eng. Des.* **96–97** 70

[27] Hoang G.T. *et al* 2009 *Nucl. Fusion* **49** 075001

[28] Pericoli Ridolfini V. *et al* 2005 *Nucl. Fusion* **45** 1085

[29] Ekedahl A. *et al* 2010 *Nucl. Fusion* **50** 112002

[30] Bai X.Y. *et al* 2017 *EPJ. Web Conf.* **157** 02001

[31] Barbato E. and Santini F. 1991 *Nucl. Fusion* **31** 673

[32] Liu L. *et al* 2023 *Fusion Eng. Des.* **189** 113444

[33] Stix T.H. 1962 *The Theory of Plasma Waves* (McGraw-Hill)

[34] Li M.H. *et al* 2023 *Nucl. Fusion* **63** 046019

[35] Bonoli P.T. and Englade R.C. 1986 *Phys. Fluids* **29** 2937

[36] Peysson Y., Decker J. and Morini L. 2012 *Plasma Phys. Control. Fusion* **54** 045003

[37] Brambilla M. 1978 *Nucl. Fusion* **18** 493

[38] Bora D. *et al* 2007 *Fusion Eng. Des.* **82** 141

[39] Hillairet J. *et al* 2010 *Nucl. Fusion* **50** 125010

[40] Brambilla M. 1979 *Nucl. Fusion* **19** 1343

[41] Huang J., Suzuki Y., Nojiri K. and Ashikawa N. 2021 *Plasma Sci. Technol.* **23** 084001

[42] Liu L. *et al* 2019 *Fusion Sci. Technol.* **75** 49

[43] Litaudon X. *et al* 1992 *Nucl. Fusion* **32** 1883

[44] Yang Q.Q. *et al* 2018 *Plasma Sci. Technol.* **20** 065101

[45] Goniche M., El Mhari C., Francisquez M., Anza S., Belo J.H., Hertout P. and Hillairet J. 2014 *Nucl. Fusion* **54** 013003

[46] Li M.H. *et al* 2023 *AIP Conf. Proc.* **2984** 090005

[47] Decker J. and Peysson Y. 2004 DKE: a fast numerical solver for the 3D drift kinetic equation Report EUR-CEA-FC-1736 (Euratom-CEA)

[48] Goniche M. *et al* 2017 *EPJ Web Conf.* **157** 03018

[49] Garofalo A.M. *et al* 2017 *Nucl. Fusion* **57** 076037