Radio-frequency measurements of energetic-electron-driven emissions using high-frequency magnetic probe on XuanLong-50 spherical torus

1.   Introduction

In tokamak and stellarator, energetic particles often cause instability because of wave–particle resonances, which deteriorate confinement and result in fast-ion and electron loss that can damage the plasma-facing components [1]. The instability caused by energetic particles (ions and electrons) has been studied in numerous nuclear fusion devices, including ASDEX-U [2–4], DIII-D [5–7], KSTAR [8], JET [9, 10], JT-60U [11], C-Mod [12], LHD [13, 14], EAST [15, 16], and HL-2A [17]. Neutral beam injection has been used to detect energetic ion-excited ion cyclotron emission [5, 10, 18–20]. The velocity anisotropy of runaway electrons during runaway discharge can stimulate electromagnetic radiation at various frequencies [21, 22]. High-frequency magnetic probes are frequently used to study energetic particle drive instabilities [3, 6, 8, 22, 23].

The XuanLong-50 (EXL-50) is a medium-sized spherical torus without a central solenoid. The EXL-50 uses three sets of electron cyclotron wave (ECW) systems with 28 GHz/50 kW and two sets of 28 GHz/400 kW to start up [24] and drive the plasma current. In a typical discharge, an ECW produces numerous energetic electrons with low electron density [25]. Therefore, the instability caused by spatial gradients and anisotropy in the electron distributions [26, 27] is a significant physical problem in the EXL-50. To address this problem, a high-frequency magnetic diagnostic is required to assess the instability of the energetic electron drive.

The general resonance condition for electron-wave coupling can be expressed as $\omega -k_{||}{v}_{||}-k_{\perp }{v}_{\mathrm{d}}-l{\omega }_{\mathrm{ce}}/\gamma ＝0,$ where $\omega$ is the instability frequency; $v_{||}$ is the parallel velocity of electrons; $v_{\mathrm{d}}$ is the orbital drift velocity; $k_{\perp }$ and $k_{||}$ are the perpendicular and parallel components of the wave-vector, respectively; ${\omega }_{\mathrm{ce}}$ is the electron cyclotron frequency; $\gamma$ is the relativity factor; and, l is an integer (l ＝ −1, 0, and +1 indicate anomalous Doppler resonance, Cherenkov resonance, and normal Doppler resonance, respectively). For energetic electron (> 100 keV) driven instability, $l＝-1$ or 0 will be measured by the high-frequency magnetic diagnostic.

In contrast to runaway discharges, where the parallel temperature of runaway electrons is higher than the vertical temperature [28–30], the latter of energetic electrons is of the same order as the former when the ECW heats the vertical temperature of electrons [31, 32]. However, the parallel temperature of energetic electrons (carrying plasma current) is significantly higher than those of the bulk electrons. The 'bump-on-tail' instability can theoretically still be induced by energetic electrons.

The EXL-50 exhibits high-frequency electromagnetic influence (1–120 MHz) and significant frequency chirping, as predicted by the Berk–Breizman model, as a result of the fully nonlinear interaction between energetic particles and waves [33–36]. The study of energetic particle instability is important for understanding the physical nature of wave–particle interactions and energetic particle confinement.

The remainder of this paper is organized as follows. Section 2 describes the diagnostic setup. Section 3 discusses measurements, preliminary analysis, and the scope for future work. Finally, section 4 presents the conclusion of the study.

2.   Diagnostic setup

2.1   EXL-50

The major radius of the EXL-50 is approximately 0.58 m (R₀ ＝ 0.58 m), the minor radius is approximately 0.41 m. The aspect ratio and the toroidal magnetic field (B_t) are approximately 1.5 and 1 T (at R ≈ 0.23 m), respectively. Currently, three sets of ECW systems (28 GHz, ECRH #1—source power of gyrotron ~50 kW—and ECRH #2 and #3—sources power of gyrotron ~400 kW) are used to heat the plasma and drive the plasma current (figure 1) [37, 38]. The hard x-ray (HXR) diagnostic of CdZnTe detectors measures HXR photons up to 300 keV [39]. Moreover, a LaBr3(Ce) scintillation detector placed approximately 20 m away from the torus center measures HXR photons up to 20 MeV (high energetic HXR in figure 1(a)).

Figure  1.  (a) Top view of EXL-50 spherical torus. The magnetic loop of the high-frequency magnetic probe, HXR, high energy HXR, and three sets of ECW heating systems are shown. (b) Photograph of the probe installed on the vacuum vessel of the EXL-50. (c) Structure of the loop for measuring toroidal magnetic fluctuation. The loop is located at the top of the low field side toroidal angle of 90° port.

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2.2   High-frequency magnetic diagnostic

According to Faraday's law, the electromotive force voltage ($V_{\mathrm{emf}}$) induced by a time-varying magnetic field (B) within the area enclosed (A) by a probe consisting of loops is $V_{\mathrm{emf}}＝-NA\frac{\mathrm{d}B}{\mathrm{d}t},$ where N is the turn of the loop. For a sinusoidally oscillating with frequency ($\omega$), when the circuit elements satisfy the conditions $R_{\mathrm{probe}}\ll R_{\mathrm{cable}},C_{\mathrm{probe}}\ll \frac{1}{\omega R_{\mathrm{probe}}},$ and $C_{\mathrm{probe}}\ll \frac{1}{{\omega }^2{L}_{\mathrm{probe}}},$ the probe voltage output ($V_{\mathrm{out}}$) can be approximated as [12]

where $R_{\mathrm{cable}}$ is the cable resistance, $\theta$ is the phase shift, and $R_{\mathrm{probe}},$ $L_{\mathrm{probe}},$ and $C_{\mathrm{probe}}$are the resistance, self-inductance, and capacitance of the probe, respectively. The signal-to-noise ratio of the probe can be optimized using equation (1). The optimal number of the turns (N_max) is $N_{\max }＝\sqrt{\frac{R_{\mathrm{cable}}}{\omega L_0}},$ where L₀ is the inductance of a single loop [12].

As shown in figure 1, the probe of the high-frequency magnetic diagnostic is located at R ≈ 1.56 m (behind the limiter ~4 cm) and Z ≈ 1 m of the EXL-50 90° port. The length and width of the loop are 7 cm and 5 cm, respectively. The L₀ (50–100 MHz) and $R_{\mathrm{cable}}$ values are approximately 0.2 μH and 50 $\mathrm{\Omega },$ respectively, whereas N_max is approximately 2 at $\omega ＝100\mathrm{MHz}.$ The probe is a double-turn copper loop parallel to the B_t direction (DC resistivity, ${\eta }_{\mathrm{cu}}＝1.72\times {10}^{-8}\mathrm{\Omega }\mathrm{m}$ at room temperature), with a Teflon isolation sleeve. The Teflon isolation sleeve is used to provide DC isolation, which is necessary to protect sensitive electronics. The diameter ($\varnothing$) and total length (d) of the copper loop are 1 mm and 48 cm, respectively. The probe resistance is approximated as $R_{\mathrm{probe}}＝{\displaystyle \frac{\eta d}{\mathrm{\pi }\varnothing \delta }}\approx 0.4\mathrm{\Omega }\ll 50\mathrm{\Omega },$ where $\delta ＝\sqrt{\frac{2\eta }{\omega \mu }}$ is the skin depth of the probe ($\mu \approx 4\mathrm{\pi }\times {10}^{-7}\mathrm{H}{\mathrm{m}}^{-1}$) [12]. A frame mode of stainless steel (316 L) is created to protect the loop. Although the frame attenuates the strength of the received signal, the EXL-50 plasma emission is strong, and therefore, the diagnosis has a high signal-to-noise ratio to satisfy the requirements of the experiments.

Figure 2 shows a block diagram of high-frequency magnetic diagnostics. Current changes are induced in the loop in the presence of radio-frequency (RF) emission in the vessel. A 0.5 m coaxial cable (RG142, 50 Ω from Lair Microwave) that can withstand a maximum baking temperature of 200 ℃ is used to transmit the signal to coaxial vacuum feedthrough (IFDCF012012, 50 Ω, floating shield, from Kurt J Lesker). The signal is transmitted to the airside via the feedthrough. A 15 m cable coaxial is used to isolate the electronics system (DC block, low-pass filter, RF limiter, and high-speed digitizer) from the device. The DC block (PE8212, 0.01–18 GHz, 50 Ω, breakdown voltage 200 V, from Pasternack) is utilized to isolate DC when the Teflon insulating sleeve ruptures. Low-pass filters (PE8722, DC-225 MHz, SMA 50 Ω, from Pasternack) are used to filter signals greater than 225 MHz. An RF limiter (HWLT0001300012, 0.001–3 GHz, SMA 50 Ω, HengWei Microwave) is installed to limit excessive voltage oscillations. Finally, the voltage oscillations are recorded using a high-speed digitizer (NI PXIe 5160) with an input impedance of 50 Ω. NI PXIe 5160 has a 10 bit depth, 500 MHz bandwidth, and 2.5 GS s⁻¹ sampling rate. Notably, a variety of low-pass filters (DC-30 MHz, DC-100 MHz, DC-130 MHz, DC-200 MHz, and DC-500 MHz) are used, depending on the sampling rate, to choose the filters.

Figure  2.  Schematic of the hardware for high-frequency magnetic diagnostic (50 Ω). The setup begins with the in-vessel loops and ends with the high-speed digitizer.

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Figure 3 shows, from top to bottom, plasma current, HXR intensity [38] (0–300 keV), and high-frequency oscillations for a typical small disruption discharge. In the EXL-50, the ECRH #1 (~20 kW injection power) is generally used to initiate the breakdown plasma and plasma current from 0.0 to 0.2 s [24]. Subsequently, System #2 (~140 kW injection power) is injected to achieve a high current and maintain the current flattop. As depicted in figure 3(a), the plasma current cannot increase because of disruption after the injection of high-power ECW.

Figure  3.  Time traces of (a) plasma current, (b) hard X-ray, and (c) raw trace of fluctuation.

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A steep drop in current is observed in System #2 in the presence of a strong HXR intensity and high-frequency signal. The acquisition system (1 MΩ, maximum input voltage 42 V) is damaged by the strong radiation after 0.5 s.

Following this discharge, an RF limiter is utilized to protect the acquisition system. The RF limiter operating in the frequency range of 1 MHz–3 GHz can handle up to 40 W of CW input power and 1000 W of transient input power. The main parameters of the RF limiter are as follows: a continuous wave input power of 40 W, peak power of 1000 W, and flat leakage of 12–18 dBm. Data with a raw signal voltage exceeding the limiter limit voltage (~2 V) are discarded.

3.   Experimental results

3.1   High-frequency (chirping) oscillation

Figure 4 depicts a typical steady-state plasma discharge of the EXL-50, with plasma density, current, high energy HXR intensity (1–20 MeV), and loop voltage from top to bottom. The high-frequency magnetic diagnostic data acquisition system operates between 3 and 3.5 s during discharge. The ECW power (System #3) is turned on at 2 s with an injection power of approximately 240 kW. The plasma current is approximately 120 kA, and the line integrated density is $1\times {10}^{18}{\mathrm{m}}^{-2}$ between 2.5 and 3.5 s. The spectrum of high energy HXR from 2.50 to 3.5 s is shown in figure 5(c), wherein counts are measured at 5 MeV, which indicates that the highest electron energy is greater than 5 MeV. Thus, the 1–120 MHz oscillations can be excited by energetic electrons via anomalous doppler and Cherenkov resonances. The spectrum of magnetic signal is shown in figures 5(a) and (b), wherein high-frequency oscillations are observed. Oscillations between 18 and 22 MHz (figure 5(b)) exhibit frequency chirping.

Figure  4.  Time traces of (a) plasma current, (b) line integrated density, (c) hard x-ray, and (d) loop voltage.

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Figure  5.  RF magnetic fluctuations for EXL-50 obtained from high-frequency magnetic diagnostic. Spectra between 3.1 and 3.4 s (a), 3.337 and 3.344 s (b), and HX spectrum between 2.5 and 3.5 s (c).

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Figure 6 depicts a case of decreasing integrated thermal electron density $n_{\mathrm{el}}$ (B_t is approximately constant). An intensity pulse of high-frequency oscillations is observed, and the oscillations exhibit significant frequency chirping (figure 6(c)). These observations are consistent with the results of the energetic particle-driven instability with an increased drag effect predicted by the Berk–Breizman model [33–36]. Moreover, the center frequency of oscillations in the experiment matches $n_{\mathrm{el}}^{-0.56}$ (figure 6(d)), which is consistent with the experimental results observed for the DIII-D runway discharge [22].

Figure  6.  Time evolutions of (a) the integrated thermal electron density ($n_{\mathrm{el}}$), (b) raw signal measured by the probe, and (c) magnetic fluctuation power spectra. (d) Variation of mode frequency with the integrated thermal electron density and best fit at constant B_t.

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3.2   Candidate instabilities

Three density profiles (figure 7(a), with an Alfvén wave (AE) frequency for s ＝ 0, where s is the radial mode number), m ＝ 0, and n ＝ 1 ($f＝v_{\mathrm{A}}/2\pi R$) are assumed (m and n are the poloidal and toroidal modes). Figure 7(b) shows that the AE frequencies are approximately 1–30 MHz. Moreover, the center frequency of oscillations in the experiment matches $n_{\mathrm{el}}^{-0.56},$ which is close to a typical Alfvén dependence $f\propto n_{\mathrm{e}}^{-0.5}.$ Therefore, the high-frequency electromagnetic oscillations observed are likely Alfvén waves excited by the energetic electrons (l ＝ 0 or −1).

Figure  7.  Radial profiles of (a) B_t and $n_{\mathrm{el}}$ (assumption), (b) Alfvén wave (AE) frequency (s ＝ 0, m ＝ 0, n ＝ 1).

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4.   Conclusion

A high-frequency magnetic probe was designed and installed on the EXL-50 to investigate the instability caused by energetic particles. An RF limiter was utilized to protect the acquisition system and prevent high-intensity radiation during steep current drops. Multiple high-frequency oscillations, most likely Alfvén waves with chirping frequency excited by energetic electrons, were observed with the high-frequency magnetic probe. In future experiments using the EXL-50, the plasma density and toroidal magnetic field will be scanned to determine the dispersion relation of the oscillations and understand the effect of the oscillations on the energetic electron confinement and instability.