Plasma heating by electron cyclotron wave and the temperature effects on lower hybrid current drive on EAST

This paper presents the progress in the long—pulse operation of the electron cyclotron (EC) system and the achievements in high—electron temperature plasmas by the combined EC and lower hybrid (LH) waves heating since the EC system was built in 2015. An electron temperature of up to 12 keV with a duration over 100 s was realized by the simultaneous heating of EC and LH waves at the line-averaged density nˉe ∼ 1.8 × 1019 m−3. The plasma heating effect strongly depends on the location of EC power deposition. H-mode plasmas with solely EC wave auxiliary heating have been obtained on EAST for the first time. These H-mode discharges show an enhanced confinement factor H 98(y,2) around 1.0, which is higher than the previous H-mode using LH power alone (Xu et al 2011 Nucl. Fusion 51 072001). The total heating power is very close to the threshold value for L–H transition according to the international tokamak scaling. In addition to the temperature effects inside the separatrix, higher electron temperature produced by EC wave is found to reduce the LH power loss in the scrape-off layer due to collisional absorption, which is beneficial to further increase the LH current drive efficiency. Ray-tracing/Fokker–Planck modeling results indicate that higher electron temperature can shorten the LH wave propagation on EAST in a multiple-pass regime, thus decreasing the collisional dissipation.

current drive efficiency, collisional absorption (Some figures may appear in colour only in the online journal) * Authors to whom any correspondence should be addressed.
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Introduction
Electron cyclotron resonance heating (ECRH), as an effective core heating tool, has been a well-established approach in tokamak magnetic confinement devices [1][2][3]. Usually, the EC power is launched as narrow Gaussian beams, which gives rise to highly localized power deposition at the cyclotron resonance layer. Consequently, ECRH and electron cyclotron current drive (ECCD) are recognized to be an effective method for controlling the electron temperature and current profiles in plasmas. An electron temperature (T e ) of up to 26 keV was achieved in JT-60U by injecting EC power of 2.9 MW into the center of a reversed shear plasma produced by the lower hybrid (LH) waves [4]. Unlike other radio frequency waves, such as LH and ion cyclotron (IC) waves, EC waves can propagate in the vacuum and the coupling is insensitive to the plasma parameters at the edge. As a result, the EC antenna can be placed far away from the plasma boundary, which greatly reduces the risk of damage by plasma-material interactions, especially in a thermonuclear environment. Because of these advantages, a EC system consisting of 20 MW (delivered power) at 170 GHz has been considered on ITER [5] and it was also proposed to be installed on China Fusion Engineering Test Reactor (CFETR) [6]. On EAST tokamak, which is characterized by steady-state longpulse operation, the EC system consists of four gyrotron at 140 GHz (corresponding to the magnetic field B t = 2.5 T for resonance) with total nominal power of 4 MW [7][8][9][10]. EC waves are injected from the lower field side of the torus as an extraordinary mode (X-mode). Each of the EC antennas consists of two mirrors with active water cooling, one fixed focusing mirror and one steerable plane mirror. The locations of the steerable plane mirrors are (R, Z) = (3.0 m, −0.3 m) and (3.0 m, 0.3 m) for #1, #2 and #3, #4 gyrotrons, respectively. The launch angles of the steerable mirror can be continuously varied within the range of ⩽30 • in the poloidal direction, so that the EC power deposition location can be controlled from the plasma center to the edge. Namely, the poloidal injection angles (α) to the vertical positive direction can be changed from 65 • to 95 • for #1 and #2 gyrotrons, as illustrated in figure 1. The toroidal injection angles (β) can be varied between 155 • and 205 • for different ECCD requirements. The maximally allowed angle of 205 • corresponds to the refractive index parallel to the magnetic field N || ∼ 0.42 (co-ECCD). The cut-off density for the second X-mode EC wave at 140 GHz is as high as 1.9 × 10 20 m −3 (corresponding to a line-averaged densityn e ∼ 1.3 × 10 20 m −3 ) according to the CMA diagram, which gives a great margin of operation on EAST (n e < 6.0 × 10 19 m −3 in normal operation).
Lower hybrid current drive (LHCD), characterized by the highest CD efficiency with respect to other auxiliary heating and CD methods, has proven to be the main non-inductive method for sustaining long-pulse operation in present tokamaks [11,12]. Experiments on JT-60 [13], Alcator C-Mod [14], JET [15], Tore-Supra [16] and ASDEX [17] show that the LHCD efficiency was as high as 1-3.5 (10 19 AW −1 m −2 ). Here, the LHCD efficiency (η) is defined as wheren e is the line-averaged density, R the major radius of the device, I LH the driven current by LH wave and P LH the LH power. LHCD system is also proposed on ITER [18] and CFETR [19] for off-axis current profile control.  [23], and a super I-mode plasma characterized by both edge transport barriers and internal transport barriers with a pulse length of 1056 s was achieved recently (other parameters are: I p = 330 kA,n e = 1.8 × 10 19 m −3 , divertor configuration) [24].
The recent progress in high-electron temperature and longpulse operation is presented in section 2. Following this, the Hmode characterization with ECRH as the sole auxiliary heating source is given in section 3. The temperature effects by ECRH on LHCD efficiency are studied in section 4. Finally, we conclude with a summary in section 5.

Progress in long-pulse and high-electron temperature operation
The first EC system was developed on EAST in 2015 with one gyrotron, and the EC power injected into plasma was at the level of ∼0.5 MW then. Thanks to the continuous increase in the number of gyrotrons and the improvement of the system, significant progress in high-power and long-pulse operation has been achieved. As shown in figure 2, the pulse duration has been extended to ∼1056 s with P EC ∼ 0.55 MW (output by 1 gyrotrons) in 2021, corresponding to the EC energy injected into the plasma ∼0.58 GJ [24,25]. High power of 1.6 MW (output by 3 gyrotrons) injected into H-mode plasmas with pulse duration ∼310 s has been achieved in 2022 [26]. The maximum power coupled into plasmas was ∼2.0 MW but with short pulse length (∼10 s). The main factor limiting the power level coupled to plasmas in long-pulse operation (>100 s) is the overcurrent fault of the gyrotron. The risk of this fault  will increase with both the power level and the pulse length. It is worth pointing out that although the EC system consists of four gyrotrons, only three gyrotrons operate in the plasma experiments at the same time. At present, the No. 1 gyrotron is undergoing repair due to the air leakage issue. The main parameters of the high-electron temperature plasmas produced by the combined LH and EC waves are summarized in table 1. At the beginning of the system development, the available EC power is only 0.5 MW. As a result, the central electron temperature (T e0 ) is in the range of 4-5 keV [27]. With the EC power increasing, the T e0 increases significantly. When 1.4 MW EC Table 1. Main parameters of the high-electron temperature plasmas by the combined LH and EC waves. power injecting into the plasma center sustained by 2.4 MW LH wave, the T e0 is as high as 12 keV. Figure 3 plots the T e profiles of these high T e0 discharges measured by the Thomson scattering system [28]. The T e profiles show a steep gradient inside ρ ∼ 0.2, resulting from the EC power deposition very close to the plasma center, as indicated by the green dotted line. The EC waves are launched perpendicularly (toroidal angle β = 180 • ) and the plasmas are in L-mode with slightly low density for these three discharges. A typical waveform (#98958) of long-pulse and high-electron temperature plasma by the combined LH and on-axis EC heating is illustrated in figure 4. The pulse length is over 100 s with line-averaged densityn e ∼ 1.8 × 10 19 m −3 and loop voltage V loop ∼ 0. The calculated LH current is peaked at ρ ∼ 0.35 due to slightly high N || = 2.26, consistent with the experimental hard x-ray (HXR) profile, which helps to optimize the magnetic shear [29]. A direct on-axis heating of EC wave is critical for highelectron temperature production and effective plasma heating, as evidenced by figure 5. The increments of the plasma stored energy (W MHD ) and of the T e0 when the constant EC power is injected into an ohmic plasma are plotted as a function of EC power deposition locations. We changed the EC  power location by sweeping the steerable mirror shot by shot. It is seen that when the EC power is deposited close to the plasma periphery (ρ ∼ 0.78), both the increments of the W MHD and of the T e0 are very small (∆W MHD ∼ 3.0 kJ and ∆T e0 ∼ 0.04 keV), while with very central heating (ρ ∼ 0.05), the incremental central electron temperature ∆T e0 reached up to 1.0 keV with the EC power of 0.42 MW. The existence of a helical m/n = 1/1 mode plays a key role in sustaining the high T e0 plasmas, as pointed out in [30], where m is the poloidal mode number and n the toroidal mode number. The m/n = 1/1 mode is periodically destabilized by the small-scale turbulence driven by high electron temperature gradient, serving as a sink to release the turbulence free energy, which causes a modulation of the turbulence. This self-regulation system serves as an automatic controller, which dynamically forces the electron temperature gradient in a proper region to sustain the kinetic equilibrium.

H-mode characterization
The first H-mode plasmas on EAST were obtained in 2010 with the LH power alone [31]. The confinement enhancement factor H 98(y,2) with respect to the so-called IPB98(y,2) scaling [32] was in the range of 0.6-1.1. At present, it is easy to get Hmode plasmas during normal operation by the combined LH, EC, IC and (or) neutral beam injection heating [23]. However, the H-mode plasmas with ECRH as the sole auxiliary heating source were realized in 2022 for the first time on EAST. The H-mode plasmas using ECRH power alone was firstly observed on DIIID in the 1980s [33], and then reproduced on COMPASS-D [34] and ASDEX Upgrade [35]. Figure 6 displays the time evolution of several key plasma parameters in a typical H-mode discharge (#115676). The plasma current (I p ) is 0.45 MA with an upper single null (USN) divertor configuration and magnetic field on axis B t = 2.5 T to assure effective plasma heating by EC wave. The EC power was injected during the I p ramp-up phase with toroidal injection angle of 200 • (co-ECCD), in order to save the magnetic flux consumption. A favorable B t direction (namely, B t × ∇B t towards the primary X-point) and lithium coating were utilized to minimize the threshold power for L-H transition. The L-H transition was triggered at 3.3 s, evidenced by a sharp drop of D α emission in the divertor chamber, an apparent increase in the plasma stored energy (∆W MHD ∼ 42 kJ) and in the line-averaged electron density, although the gas fueling by supersonic molecular beam injection (SMBI) stopped. After the L-H transition, the discharge entered a quiescent H phase with ELMs free or small ELMs. The H 89 and H 98(y,2) confinement improvement factors with respect to the ITER89-P [36] and IPB98(y,2) [32] scaling laws are about 1.5 and 1.0, respectively, which are 25% and 36% higher than those in L-mode. The total heating power at the L-H transition, P tot = P EC (1.35 MW) + P OH (0.18 MW) is ∼1.53 MW, which is slightly above the threshold power (∼1.45 MW) required for an L-H transition according to the scaling law [37]. The T e0 measured by EC emission diagnostic [38] decreases from 2.4 to 2.3 keV after the L-H transition due to the increase in electron density, and the T i0 by a toroidal x-ray crystal spectrometer system [39] increases from 0.9 to 1.1 keV as a result of both the electron-ion heat exchange and confinement improvements. In addition, the loop voltage (V loop ) drops by ∼0.11 V, mainly attributed to the significant increase in bootstrap current (I BS ) indicated by the poloidal beta β p (I BS ∝ β p ).
Reliable access to the H-mode has been demonstrated in the range of operational parameters as below: I p = 0.3-0.5 MA, n e = 3.3-5.2 (10 19 m −3 ), B t = 2.5 T, and P EC = 1.1-1.8 MW.
The H 98(y,2) factor for these H-mode discharges is within the range of 0.8-1.2, while for the L-mode it is within 0.65-0.95, as shown in figure 7. It is seen that the energy confinement time is much higher for most data points in L-mode than that in H-mode. This is because the EC power in most L-mode discharges is much lower, namely, P EC = 0.35-0.8 MW. Compared with the previous H-mode with LH alone reported in [31], these H-mode discharges show higher confinement. This is because the LH heating effects will become poor at high density, as observed in [40]. With the increase in available ECRH power, the dependence of global confinement on the plasma current, heating power, and plasma density will be investigated in depth in the future.

Temperature effects on LHCD efficiency
Strong Landau damping will take place when the LH waves reach the region where the thermal velocity  υ th ≡ (kT e /m e ) 1/2 ⩾ 1/3.5υ ph , where υ ph ≡ c/N || , is the parallel (to the background magnetic field) phase velocity of LH waves in the plasmas. This corresponds to the required condition [41] for full Landau damping. Consequently, the electron temperature profile has effects on the location of LH power deposition, and also on the velocity of the resonant electrons which is related to the CD efficiency. The effects of ECRH on plasma performance and current profile sustained with LH heating and current drive only were studied in [42,43] and in [44] previously. In this paper, we focus on the effects of the different T e profiles produced by ECRH on LHCD efficiency.

Experimental observations
As given in section 2, the plasma heating by ECRH strongly depends on the EC power location. Figure 8 figure 9. The plasma stored energy (W MHD ) of #81481 (∼197 kJ) is higher by a factor of ∼1.7 than that of #81490 (116 kJ). The HXR emission, a proxy for the density of the fast electrons generated by LHCD, is also higher by a factor of ∼1.72 for #81481, indicating a higher LHCD efficiency. Note that the four sharp increase in HXR signal is due to the neutral beam blips for charge exchange recombination spectroscopy (CXRS) measurements. As plotted in  figure 10, the HXR profiles, measured by a 20-chord poloidally viewing diagnostic, show a higher intensity and a more peaked shape for #81481. The loop voltage (V loop ) is decreased by ∼0.18 V, suggesting a higher non-inductive current fraction, which consists of LH, EC and bootstrap current. The EC current calculated by TORAY code and the bootstrap current by Sauter model for discharge #81481 are ∼35 kA and ∼175 kA, respectively. Since the V loop is as low as ∼20 mV, the ohmic current could be ignored. As a result, we get the LH current ∼190 kA, which is higher by a factor of ∼5.4 than the EC current. Besides, the internal inductance (l i ) is higher by ∼0.14, suggesting more plasma current at the core region. In addition to the above different observations inside the last closed flux surface (LCFS), we also detected two obvious differences in the scrape-off layer (SOL) region. The brightness level detected by a visible camera is much stronger for #81490 (off-axis EC absorption) as compared to #81481 (on-axis EC absorption) on the upper divertor region (USN configurations for these two discharges), the surface of the main limiter and near the LH antenna, as shown in figure 11. This result suggests more heat loads on the plasma facing components with lower T e0 , as a consequence of more parasitic absorption of LH power in SOL. Secondly, the particle flux measured by Langmuir probe array on upper outer divertor target plate [45] is increased by a factor of ∼1.4 near the strike point and by a factor of ∼3 in the private region as shown in figure 12. This implies that more LH power are dissipated in the SOL, leading to an enhanced ionization as found in [46].

Ray-tracing/Fokker-Planck modeling and analysis
It is well recognized that the LH current will increase with electron temperature and past modeling shows that the LHCD efficiency increases almost linearly with the volume-averaged electron temperature <T e > before it saturates at much high <T e > (∼20 keV) [15,47]. According to the CD theory [48], the ratio of driven current density J to the LH power density P D can be expressed as where ν is the electron-ion collision frequency, and υ || the parallel velocity of the resonant electrons which is ∼3.5υ th according to the Landau damping condition shown in equation (2). It was demonstrated in many devices that the LHCD efficiency grew with <T e >, such as in JT-60U [49], JET [15] and FTU [50] experiments. As shown in figure 9, the volume-averaged electron temperature is about 1.2 keV and 0.6 keV for #81481 and #81490, respectively. Therefore, it can be concluded that higher electron temperature produced by central EC heating is the first main mechanism responsible for the better LHCD efficiency observed in discharge #81481. In addition, the power loss in SOL due to the collisional dissipation is less, which should be the second reason, as analyzed below.
A combined ray-tracing Fokker-Planck model of GEN-RAY/CQL3D [51,52] is utilized to estimate the electron temperature effects on the collisional absorption of LH power in SOL. The wave propagations including in the SOL and the variation in N || along the propagations are calculated by the ray-tracing code, GENRAY. The electron temperature and density profiles assumed for the simulations are shown in figure 9. The launched power spectrum with 2.16 ⩽ N || ⩽ 2.36 is divided into 13 rays and four poloidal launching locations are considered. The same electron density and temperature profiles in SOL are supposed for both discharges as follows: n e (T e ) = n ea (T ea ) × e −r/λ , where n ea (T ea ) = 0.85 × 10 19 m −3 (55 eV) is the density (temperature) value at the LCFS, λ = 2 cm (1 cm) the density (temperature) decay length, and r is the distance from the LCFS. Only non-resonant damping due to electron-ion collisions is considered as a loss term.
The calculated ray trajectories in the poloidal plane are shown in figures 13(a) and (b) for #81481 and #81490, respectively. It is clear that for #81490 with lower T e0 , the LH rays undergo much longer propagations in the main plasmas and also in SOL before the LH power is fully absorbed. As a result, the fraction of power loss (P cl /P tot ) due to collision in SOL is as high as ∼39% for #81490, while it is only ∼6% for #81481 with higher T e0 . Figures 14(a) and (b) illustrate the N || pattern (black lines) along the ray trajectories calculated by GENRAY code versus the normalized radius ρ. The red lines represent the strong Landau damping condition as given in expression (2). The blue lines denote the local value of accessibility condition N || acc . It is seen that the spectral gap between the N || required for Landau damping (red lines) and the launched N ||0 = 2.26 is as high as 2.8 for the lower T e0 case at the plasma center, while the spectral gap is only 0.54 for #81481 with higher T e0 . Landau damping absorption of LH waves does not occur even when the rays penetrate the core region for lower T e0 case, and the rays continue to propagate until the upshift of N || becomes large enough induced by the toroidicity effect. The LH current density profiles by CQL3D Fokker-Planck solver are indicated by the yellow lines in figure 14. Compared with #81490, there is significant additional LH current in the plasma core for the case of #81481, which is consistent with the experimental measurements of internal inductance (l i ) as shown in figure 8. In addition, the calculated line-integrated HXR emission shows a good agreement with the experimental measurements (see figure 10). It is worth pointing out that in our modeling the synergy effect in the phase space between LH and EC waves is neglected, which will also increase with the rise of the electron temperature.
In order to investigate the temperature dependence of collisional absorption, a series of simulations is performed with different T e profiles (shown in figure 15), but with the same density profile inside the LCFS and the same density/temperature profiles in SOL. The calculated results are shown in figure 16. It is seen that the power ratio of collisional dissipation to the total power (P cl /P tot ) decreases greatly with T e0 increasing when T e0 is less than 4.0 keV, and the P cl /P tot is less than 10% with T e0 increasing to 4.5 keV. On the contrary, the power fraction by electron Landau damping (P ELD /P tot ) taking place in the main plasmas increases with T e0 . It is worth mentioning that by adding the collisional absorption of LH power in the model, the calculations show dramatically improved agreement with the experiments on Alcator C-Mod [53]. Meanwhile, the numerical calculations with FTU parameters indicate that the parasitic power loss by a collision can be reduced with a hotter plasma edge, thereby increasing the LHCD efficiency [54]. Ray trajectories in the poloidal plane calculated with the GENRAY code, including propagation in the SOL region for #81481 with higher T e0 (a) and for #81490 with lower T e0 (b). The color bar denotes the normalized ray power to the initial power. The thick red curve indicates the last closed flux surface, and the four black asterisks at the low field side represent the poloidal launching locations. The power ratio of the collisional damping to the total power is indicated for both discharges.

Summary
Effective plasma heating effects by EC wave have been demonstrated in EAST long-pulse plasmas. The electron temperature of up to 12 keV with duration over 100 s was achieved by the combined heating of EC and LH waves at the lineaveraged densityn e ∼ 1.8 × 10 19 m −3 . The pulse length has been extended to 1056 s with moderate EC power ∼0.55 MW. It is found that the heating effects depend significantly on the EC power deposition location and very central heating is critical for high-electron temperature production. H-mode plasmas with EC wave as the sole auxiliary heating source has been obtained on EAST for the first time. They show better global confinement than the past H-mode using LH power alone. The threshold power for H-mode access is slightly above the value according to the scaling law. Due to the limited available EC heating power, the H-mode scaling of confinement with plasma current, plasma density and heating power has not been investigated in detail.
It is well recognized that higher electron temperature will improve the LHCD efficiency. In our experiments, the measurements by a visible camera and Langmuir probe array on divertor indicate that higher electron temperature produced by central EC heating is also beneficial to reduce the power loss of LH wave in SOL. Modeling results show that higher electron temperature can shorten the spectral gap between the N || required for Landau damping and the initial N || at the launching point, in the weak damping regime on EAST. Therefore, fewer passes between the plasma edge and center are needed to bridge the spectral gap, leading to less LH power absorption in the SOL by collisional damping. As for ITER [55] and CFETR [56] with much high electron temperatures, most of the LH power will be absorbed in the first single pass. It is foreseen that the effects of collisional damping in the SOL absorption could be ignored.
Additional two gyrotron units are under development, and the total nominal power will be expanded to 6.0 MW. The next plan will focus on the study of H-mode plasmas in wider plasma parameters with more available EC heating power. Besides, the ECCD current will become substantial with the system upgraded. As shown in figure 17, the predicted EC current by GENRAY code with L-mode n e and T e profiles can be as high as 180 kA with P EC = 2.0 MW, n e0 = 2 × 10 19 m −3 and T e0 = 6.0 keV. In these simulations with parametric scan, the launch angles are fixed and the EC currents are located in a narrow region of ρ < 0.11. Hence, the predicted EC currents are expected to mainly depend on the local values (ρ < 0.11) of n e and T e . The ECCD efficiency and possible synergy effects with LHCD as found on Tore-Supra [57] will be considered in future work.