Particle pump-out induced by trapped electron mode turbulence in electron cyclotron heated plasmas on XuanLong-50 spherical torus

Particle pump-out effects induced by low-frequency (<200 kHz) density fluctuations were observed in solely electron cyclotron wave (ECW)-heated plasmas on the spherical torus XuanLong-50 (EXL-50) without a central solenoid. The intensity of the relative density fluctuations increases with increasing ECW power and decays when the ECW is turned off while sustaining the plasma current. The electron densities are maintained relatively high and steady when the density fluctuations are completely absent, indicating that the outward transport of electrons is dominated by the particle pump-out effect of the ECW. The density fluctuations are modulated by a supersonic molecular beam injection pulse and the modulation amplitude decreases with increasing electron density at the same ECW injection power and decreasing ECW power at the same electron density, respectively. Analysis revealed that a critical value of electron temperature gradient (ETG) triggers the density fluctuations, and the intensity of the relative density fluctuations is positively correlated with the ETG and approximately inversely proportional to the effective collision frequency. With plasma parameters similar to those of EXL-50 experiments, the HD7 code simulations demonstrate that trapped electron mode (TEM) turbulence can be excited by ETG higher than the critical value observed in the experiment. In addition, the dependence of the mode growth rate (supposed to be proportional to the saturation level of fluctuations in quasi-linear theory) and the measured intensity of the density fluctuations is comparable. The simulated outward particle flux integrated over the poloidal wave number spectrum is significant and proportional to ETG. These observations demonstrate that the density fluctuation is TEM turbulence, which is driven by ETG and induces particle pump-out when the electron density/effective electron collision frequency is low. The potential relevance of this work with the controls of plasma profiles, impurities, helium ash, and heat transport in future reactors of similar low effective collision frequency is also discussed.

Particle pump-out effects induced by low-frequency (<200 kHz) density fluctuations were observed in solely electron cyclotron wave (ECW)-heated plasmas on the spherical torus XuanLong-50 (EXL-50) without a central solenoid. The intensity of the relative density fluctuations increases with increasing ECW power and decays when the ECW is turned off while sustaining the plasma current. The electron densities are maintained relatively high and steady when the density fluctuations are completely absent, indicating that the outward transport of electrons is dominated by the particle pump-out effect of the ECW. The density fluctuations are modulated by a supersonic molecular beam injection pulse and the modulation amplitude decreases with increasing electron density at the same ECW injection power and decreasing ECW power at the same electron density, respectively. Analysis revealed that a critical value of electron temperature gradient (ETG) triggers the density fluctuations, and the intensity of the relative density fluctuations is positively correlated with the ETG and approximately inversely proportional to the effective collision frequency. With plasma parameters similar to those of EXL-50 experiments, the HD7 code simulations demonstrate that trapped electron mode (TEM) turbulence can be excited by ETG higher than the critical value observed in the experiment. In addition, the dependence of the mode growth rate (supposed to be proportional to the saturation level of fluctuations in quasi-linear theory) and the measured intensity of the density fluctuations is comparable. The simulated outward particle flux integrated over the poloidal wave number spectrum is significant and proportional to ETG. These observations demonstrate * Authors to whom any correspondence should be addressed.
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Introduction
One of the most important subjects in tokamak plasma physics studies is the mechanism for density profile evolution. It has been noted that the peaking of the density profile results from an inward particle pinch, but the physical nature of this pinch remains unclear. It is generally observed in experiments that electron cyclotron heating (ECH) exerts an effect of density pump-out and pinch-in on tokamaks [1][2][3][4][5] and stellarators [6][7][8]. It is also generally accepted theoretically that trapped electron mode (TEM) and ion temperature gradient (ITG) mode turbulence-induced transport are the main physical mechanisms leading to particle pump-out and pinch-in, respectively, as is usually observed in magnetically confined plasmas with auxiliary heating, especially electron cyclotron resonance heating (ECRH) [9][10][11][12][13][14][15][16]. Fable et al showed that the density profile peaking is maximum at the transition between TEM and ITG instabilities. Adding ECRH to TEM plasmas (increasing Te/Ti increases TEM) thus flattens the density, and adding ECRH to ITG plasmas leads to peaking because the microinstabilities move from ITG toward TEM [14]. Experiments with the on-axis ECRH were conducted in the ASDEX Upgrade. Electron cyclotron wave (ECW) pump-out effect appeared significantly at low plasma density, but the effect decayed with increasing density (pinch-in) [1,2]. In DIII-D, it is shown that the density pump-out and pinch-in are not the result of a change in turbulence type (i.e., not caused by a change from ITG to TEM) but are the result of a change in the turbulence drive (an increase in linear growth rates) [4]. The results of Korea Superconducting Tokamak Advanced Research (KSTAR) show that TEM and ITG coexist in space with mixed heating by neutral beam injection and ECRH [17,18]. When adding ECH, the turbulence shifts from ITG-dominated to TEM-dominated, but the density does not flatten out, and the profile remains basically the same even with a tendency to peak. In the Tore Supra tokamak, a reversal of the particle convective velocity and an increase in the particle flux have been observed using modulated ion cyclotron resonance heating, which corresponds to the ITG-TEM transition [19]. The effect of the ITG and TEM turbulence interconversion on the plasma density and temperature was also observed in the EAST I-mode experiment [20]. The study shows that TEM and ITG mode conversion plays an important role in the stable operation of the I-mode temperature and density profiles. Nevertheless, direct experimental observations of TEM turbulence and the influence of its intensity on particle pump-out in solely ECRH-induced plasmas in magnetic confinement devices are lacking.
This paper presents experiments on TEM turbulence driven by electron temperature gradients (ETGs) in plasmas solely induced by ECW (off-axis) injection in EXL-50, where the effect of ITG turbulence can be neglected because there is no direct ion heating and the ITG is lower than ETG in low effective collisions. Therefore, the particle pump-out effect induced by TEM turbulence could be more significant. The equilibrium of an ECW plasma without a central solenoid has been widely demonstrated [21][22][23][24][25][26], and the existence of plasma equilibrium provides a fundamental platform for the study of turbulence transport. Low-frequency density fluctuations and the corresponding particle pump-out effect were clearly observed with Thomson scattering diagnostics [27] and microwave interferometer [28] in EXL-50 ECW plasma. The experimental results show that the intensity of density fluctuations increases with the increase in the heating power under similar fueling. The density fluctuations are modulated by the supersonic molecular beam injection (SMBI) pulse and the modulation amplitude decreases with increasing electron density at the same ECW injection power and decreasing ECW power at the same electron density, respectively. Meanwhile, a critical value of ETG triggers the density fluctuations, and the relative density fluctuation intensity is positively correlated with the ETG and reversely correlated with the effective collision frequency. The HD7 code [29][30][31] simulations show that collisionless TEM turbulence can be excited and induce an appreciable outward particle flux. The growth rate and the induced quasilinear outward particle flux of the TEM increase with the ETG and decrease with the increase in the effective collision frequency. The experimental observations and analysis demonstrate that TEM turbulence can be excited and the particle pump-out effect of ECW is dominated by TEM turbulence.
Future devices, such as ITER, will partly depend on electron cyclotron and alpha particles-heated electrons to deliver power to the plasma. Particle transport is not as commonly studied as heat transport, which results in a less validated capability to predict density profiles. Current predictions for the ITER scenarios all assume a flat density profile [32,33,34]. However, a large multi-machine database demonstrates an inverse correlation between the peaking of the density and collisionality [35,36]. Based on this correlation and the fact that ITER is planned to operate at low collisionality, one might assume that the density profile is peaked in the core. The characteristics of the outward particle transport induced by TEM turbulence under low collisionality are crucial for density profile regulation, impurity transport regulation [37][38][39][40][41][42], and helium ash exhaust [43,45] in fusion plasma, whereas the investigation of TEM turbulence is also important to avoid confinement degradation.
This paper is organized as follows. The EXL-50 torus and HD7 code are introduced in the second section. The pumpout experiments in EXL-50 are set in the third section, and the summary and discussion are set in the fourth section.

Spherical torus EXL-50 and HD7 code
EXL-50 is a medium-sized spherical torus without a central solenoid. The major radius of EXL-50 is approximately 0.58 m, the minor radius is approximately 0.41 m, the toroidal magnetic field Bt (r ∼ 0.48 m) is approximately 0.5 T, and the aspect ratio of A > 1. 45. At present, EXL-50 has three ECW systems (28 GHz, O-mode injection), a 50 kW system (gyrotron source power ∼50 kW) is used to start the plasma [46], and two 400 kW systems (gyrotron source power ∼400 kW) are used to heat plasma and drive higher currents [47]. The fundamental resonance layer is at r = 0.23 m. There exists 2-4 harmonic resonance layers at 28 GHz in the vacuum chamber. The plasma electron density and temperature profiles are measured by TS. The TS is designed with a time resolution of 20 ms and an electron density measurement lower limit of approximately 10 18 m −3 . Due to the limitations of the current plasma discharge parameters, the TS system needs to average multiple laser pulses to improve the signal-to-noise ratio. Figure 1 shows the typical density and temperature profiles measured by TS (averaged over 10 laser pulses), where the black and blue lines correspond to ECW input powers of 310 kW and 170 kW, respectively. The plasma density fluctuations and line-integrated density are measured using a microwave interferometer [28]. According to the forward scattering theory, the interferometer measures the maximum fluctuation wave number k ∼ 5 cm −1 [48], and TEM-induced density fluctuations can be observed.
The gyrokinetic code HD7 [29] was developed to solve the integral eigenmode equations and calculate quasi-linear transport, which has been applied in the studies of microinstabilities and induced turbulent transport in toroidal plasmas. HD7 code has been widely used to analyze the characteristics of multiple instabilities, such as electrostatic ITG mode, TEM, impurity mode and ETG mode, among others; the electromagnetic version of Alfven ITG mode, kinetic ballooning mode, micro-tearing mode, and so on; and also consider various effects, such as impurity kinetic effects, velocity shear, temperature anisotropy, electromagnetic perturbation and elongated cross-section effects, among others. In contrast, the HD7 code has been satisfactorily benchmarked with other numerical simulation codes, such as GTC, GENE, and GYRO [49,50]. In addition, the code HD7 has been proven to provide valuable support for experimental data analysis [19,51].

Experimental results and simulation
EXL-50 has multiple ECW heating systems so that the heating power effect on plasma parameters can be investigated by controlling the heating system turn-on sequence. Figure 2 shows that the plasma parameters change for the addition of a second ECW system and turn-off ECR heating in typical EXL-50 ECH plasma. In the background of 170-kW ECW heating, 140 kW ECW power (second ECW system) was injected at 2.4 s ( figure 2(a)). The plasma current did not change much; the plasma density slowly increased and remained stable for a period (maybe due to the increase in recycling as indicated by the Ha signal in figure 2(a) after the injection of 140 kW ECW. In contrast, the plasma density increases from 25 × 10 17 m −2 to 35 × 10 17 m −2 , after turning off the second ECW. Comparing the Ha signals (figure 2(a3)) and the power spectrum of the density fluctuations (figure 2(a4)) before and after the injection of 140-kW ECW, it is found that the boundary recirculation and turbulence intensity increase significantly after ECW injection, indicating that the outward particle transport is correlated with the density fluctuations and increases. A reverse behavior is more clearly observed when the ECW is turned off, as shown in figure 2(b). The plasma current remains approximately steady, when the plasma density increases from 20 × 10 17 m −2 to 35, after the ECW power is turned off completely at 0.9 s. At the same time, the Ha signal and density turbulence intensities decrease, indicating that the ECW turn-off results in a reduction in the driving source of turbulence and corresponding particle loss. These experimental phenomena are consistent with the particle pump-out effect of ECW [1,2]; that is, there may be an ECW pump-out effect in EXL-50 experiment. It should be mentioned that the plasma density can maintain a plateau of nearly 80 ms without  turbulent fluctuations after the ECW is turned off, which shows that the plasma particle transport of EXL-50 ECRW is significantly improved when the turbulent transport is suppressed. Figure 3 show the time evolutions of the line-integrated plasma density (a) and the spectrum of the density fluctuations, modulated by the SMBI pulse of the same intensity during 2.46-2.57 s. The ECW powers are about 170 kW and 150 kW before and after 2.5 s, respectively. The density achieved in the plasma with 170 kW ECW power is lower than that with 150-kW powers, whereas the amplitudes of density modulation are approximately the same. For example, the plasma density increases rapidly to 35 × 10 17 m −2 and remains steady for a period when the SMBI is injected at t = 2.52-2.54 s for 2 ms, whereas it does to 32 × 10 17 m −2 and then decays rapidly. In contrast, the intensity of the density fluctuation spectrum for with 170 kW ECW power is higher than that with 150-kW power. The density fluctuations are even suppressed completely when the density is the highest in the latter case. In summary, the above observations indicate that the achieved plasma density is high when the injected ECW power and intensity of the density fluctuation spectrum are both low. The relationship between the ECW power and intensity of density fluctuations is the same as that presented in figure 2. Due to experimental constraints, a direct causal relationship between the increase in fluctuations and outward particle transport could not be established. Nevertheless, given the pivotal role of turbulence in transport, it is plausible that the observed outward transport may have been induced by the fluctuations. The correlation between density and the intensity of its fluctuations may be explained as follows. The electron collision frequency increases and suppresses the density fluctuations when the electron density increases and the temperature is constant. However, the electron temperature may decrease when the ECW power decreases from 170 kW to 150 kW, which may induce further increase in collision frequency and suppression of turbulence.
To further confirm the effects of the collision frequency on the turbulent fluctuations, we statistically analyzed about 50 plasma discharges in EXL-50, and the results are given in figure 4 (the red dashed lines are the fitting curves). Relative density fluctuations (δn el /n el ≡ 1 where the symbol < > stands for an average of three spatial positions (red double-arrowed region in figure 1) and five laser pulses, q is the safety factor, ε = 1/A. The trend of the intensity of turbulent fluctuations decreases with the increase in electron density is illustrated in figure 4(a) despite that the data scattering is non-negligible. The latter is due to the fact that the dependence of the TEM turbulence intensity on electron density is embodied in the collisionality, which also depends on plasma temperature, among others. It should be mentioned that the statistics contain different ECW powers and fueling, which may affect the intensity of density fluctuations at the same density.
The identification of the driving mechanism for the turbulent fluctuations of the density is one aim of this study. From the theoretical point of view, TEM is one of the most plausible candidates. It is well accepted that TEM can be excited by the gradient of plasma temperature or density [44]. The relationship between the intensity of density fluctuations and the the gradient of electron temperature is investigated. Figure 5 shows that the intensity of density fluctuations is positively correlated with the ETG at r ∼ 0.34 m (averaged over 10 laser pulses) and that there is a critical value (∼3) of ETG triggering density fluctuations. With plasma parameters similar to those of the EXL-50 experiments, the HD7 code simulations  (a detailed introduction will be provided below) depict that TEM turbulence can be excited by ETG higher than the critical value observed in the experiment. The growth rate of the mode (the blue line is supposed to be proportional to the saturation level of fluctuations in the quasi-linear theory) increases with increasing ETG parameter R/L Te and its behavior is comparable to that of the measured intensity of the density fluctuations. Here, is the scale length of the electron temperature. This outcome suggests that the observed density fluctuations and associated outward particle transport are induced by TEM turbulence driven by ETG in EXL-50 plasmas [15]. It is important to note that density fluctuations are not quantitatively comparable to the linear growth rate. To compare density fluctuations to simulations, nonlinear runs are necessary, which are left for future works.
To further verify the experimental conjecture, the theoretical simulation results in accordance with the experimental parameters are presented with a gyrokinetic code HD7, which solves an integral eigenmode equation and has been extensively applied in the studies of micro-instabilities [38] and turbulent transport [46]. The ballooning representation for the axisymmetric toroidal magnetic configuration is employed to reduce the system to a one-dimensional problem in an extended poloidal (ballooning) angle space. The s − α equilibrium model with circular flux surfaces is adopted [34]. The parameters used in this simulation are R/L Ti = 0.0, T e /T i = 5.0, ε = r/R = 0.7, and m i /m e = 1836. Figure 6 shows the normalized (a) real frequencies ω * r (a.u.), (b) growth rates γ * (a.u.), and (c) electron particle fluxes Γ * e (a.u.) versus ETG R/L Te for different effective collision frequencies. It is important to note that the real frequencies and growth rates are for a fixed k θ ρ s , which corresponds to the maximum growth rates of the modes. The simulation revealed that the unstable poloidal wave vector k θ ρ s for TEM in this work was in the range of k θ ρ s ∼ (0 ∼ 2.5), which is not displayed here. The summed particle fluxes are obtained by integrating over the complete unstable k θ ρ s spectrum, that is Γ e−sum =´Γ e (k θ ρ s ) d (k θ ρ s ), rather than restricted to an individual characteristic poloidal wave-vector k θ ρ s . Here, ω r > 0 means propagation in the electron diamagnetic drift direction. As is well known, TEM is considered to be driven by density and temperature gradients, that is, ∇n e -TEM and ∇T e -TEM, respectively. In the simulation corresponding to the experimental parameters, it is noticeable in figure 6 that the unstable mode is temperature gradient-driven TEM (∇T e -TEM). In addition, the outward particle fluxes are enhanced with the increase of ETG R/L Te . Furthermore, normalized (a) real frequencies ω * r (a.u.), (b) growth rates γ * (a.u.), and (c) electron particle fluxes Γ * e (a.u.) versus effective collision frequency v eff for different electron density/temperature gradients are given in figure 7. It is shown that the growth rate of the TEM turbulence and the electron particle flux decrease with the increase in the effective collision frequency v eff . The above results are qualitatively consistent with the experimental observations.

Summary and discussion
Low-frequency (<200 kHz) density fluctuations, driven by ETG and producing strong outward particle transport, were observed in solely ECW-driven plasmas on the spherical torus EXL-50 and identified as TEM turbulence. The TEM turbulence increases with enhancement of ECW power and decays after ECW is turned off while sustaining the plasma currentined. The electron density is maintained relatively high and steady when the turbulence decays completely, indicating that the outward transport of electrons is dominated by the particle pump-out effect of ECW. The turbulence is modulated by SMBI pulses at the same ECW injection power. Analysis indicates that the intensity of TEM turbulence is positively correlated with the ETG and inversely correlated with the effective collision frequency. Moreover, there is a critical value of ETG for triggering TEM. Both turning off the ECW power injection and enhancing the SMBI injection, respectively, can achieve TEM turbulence suppression and plasma density increase. This indicates that the particle pump-out effect of ECW is mainly caused by TEM turbulence. Under parameters similar to the experimental ones of EXL-50, the HD7 code simulation shows that the ETG can drive TEM and cause outward particle transport. The outward particle flux induced by the TEM turbulence is positively correlated with the ETG and inversely correlated with the effective collision frequency. The experimental observations and numerical analysis demonstrate that the density fluctuation is TEM turbulence, which is driven by ETG and induces particle pump-out when the electron density/effective electron collision frequency is low. This suggests that the density profile can be adjusted by controlling the TEM turbulence intensity. Although this physics picture is reasonable and acceptable, the lack of possibility to probe causality between increased fluctuations and increased particle transport experimentally due to limitations of diagnostics has to be resolved in future experiments. For future reactors with low effective collision frequency, the control of plasma profiles, impurities, helium ash, and heat transport may be achieved by ECW-excited TEM, whereas the analysis of the mechanisms is also important for avoiding confinement degradation.