Development of double-foil soft X-ray array imaging (DSXAI) diagnostic on HL-2A tokamak

1.   Introduction

Since SXR emission from plasma, primarily bremsstrahlung emission, depends on electron temperature (T_e), density, and impurity levels, SXR diagnostics utilizing tomographic reconstruction can obtain 2D emissivity maps and reveal internal plasma behaviors. These behaviors include magneto-hydrodynamic (MHD) activities, magnetic topology, sawtooth crash, particle and heat transport, turbulence, and disruption [1, 2]. SXR diagnostics have been widely implemented in tokamaks such as JET [3], EAST [4], J-TEXT [5], and HL-2A [6], as well as in reversed field pinches (RFPs) like RFX [7] and MST [8]. Furthermore, using the double-foil technique [9], tomographic T_e can be calculated by taking the ratio of tomographic SXR emissivities from the same plasma location through two foils of different thicknesses (typically Be foils). This enhanced SXR diagnostic method, known as double-foil soft X-ray array imaging (DSXAI), has been successfully implemented on EAST [10], RFX [11], and MST [12, 13] to measure T_e.

A 100-channel DSXAI diagnostic system has been designed and installed on the HL-2A tokamak to measure SXR emission and T_e. The DSXAI system consists of five photocameras mounted at two different poloidal cross-sections and three different poloidal locations, providing excellent spatiotemporal resolution. This high resolution allows the observation of high-frequency physical phenomena using the DSXAI photocameras. By applying tomographic reconstruction and the double-foil technique, 2D tomographic SXR emissivity and T_e have been successfully reconstructed. Additionally, the compact and cost-effective nature of the DSXAI diagnostic makes it ideal for future fusion reactors, such as ITER.

This paper presents the principles of the DSXAI diagnostic in section 2. Section 3 introduces the design of the DSXAI system, while section 4 describes the bench tests of the DSXAI system. Section 5 showcases the results of 2D tomographic reconstructions of SXR emissivity and T_e on HL-2A. Finally, the summary is given in section 6.

2.   Principle of DSXAI diagnostic

When a plasma satisfies the conditions of the electron velocity distribution being Maxwell-Boltzmann and the measured SXR emission being primarily bremsstrahlung radiation, the T_e can be calculated using the double-foil technique. Be foils are used to isolate bremsstrahlung radiation from the plasma. Thus, the SXR emissivity (ε) as a function of energy (E), measured by the DSXAI photocamera through the Be foil, primarily bremsstrahlung radiation, can be expressed as:

where K is a constant for a given energy range E, A(E) is the absorption function of the detector, T(E, d) is the transmission function of the energy E and the thickness d of Be foil, Z_eff is the effective atomic number, n_e and T_e​ are the electron density and temperature, respectively.

In experiments, five photocameras measure SXR emission from the plasma poloidal cross-section along multiple lines of sight. Therefore, the measured SXR brightness f(L), which is the line-integrated SXR emissivity ε along the line of sight L, is given by:

By applying tomographic reconstruction techniques [3, 14, 15], two tomographic SXR emissivities ε₁ and ε₂ from the same poloidal cross-section can be reconstructed from two sets of brightness measurements f₁(L) and f₂(L), obtained by using two Be foils with different transmission functions T₁(E, d) and T₂(E, d), respectively. Then, a 2D tomographic T_e can be calculated by taking the ratio R of these two tomographic SXR emissivities ε₁ and ε₂. The relationship between R and T_e is as follows:

3.   Experimental setup design of DSXAI diagnostic

The DSXAI diagnostic system on HL-2A consists of five photocameras (DSXR01 to DSXR05) with a total of 100 channels, which are located at two different poloidal cross-sections, separated by 15° toroidally. Three of the photocameras (DSXR01 to DSXR03) are mounted at one poloidal cross-section at poloidal positions of −45°, 0°, and 45°, while the remaining two photocameras (DSXR04 and DSXR05) are mounted at the other poloidal cross-sections at positions of −45° and 45°. Figure 1(a) shows a picture of the DSXAI photocameras on HL-2A, and figure 1(b) provides a schematic diagram of the experimental layout.

Figure  1.  (a) Picture of DSXAI photocameras on HL-2A and (b) schematic diagram of experimental layout.

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To tomographically reconstruct the m $\leqslant$ 1 profile of the plasma, at least two photocameras are installed on one poloidal cross-section. To gather more emission information, the lines of sight can cover almost the entire plasma region of the poloidal cross-section (r < 0.9a, where a = 0.4 m is the minor radius of HL-2A).

The interior structure of each photocamera (shown in figure 2) contains two identical sets of optical systems and a pre-amplifier PCB. The lines of sight for each optical system are defined by the placement of an aperture slit and a photodiode array (AXUV20ELG, manufactured by Opto Diode Corp.). The two sets of optical systems are placed compactly side by side along the toroidal direction of HL-2A, with each aperture slit covered by a different Be foils. These two sets of optical systems are positioned close enough to almost share lines of sight, and a light barrier is installed between them to prevent light from one side from affecting the other. All optical and electronic systems are housed in a non-magnetic stainless steel box to reduce electromagnetic interference.

Figure  2.  Schematic of the interior structure for each photocamera.

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The dimensions of the aperture slit (0.5 mm × 10 mm), the distance between the aperture slit and the photodiode array (8 mm), and the distance between the aperture slit and the center of the poloidal cross-section (492 mm) are optimized to achieve high spatial resolution (approximately 8 cm in the plasma core), a good signal-to-noise ratio, and wide poloidal coverage (r < 0.9a). Be foils are used not only to select bremsstrahlung radiation from the plasma but also to implement the double-foil technique. For this technique, 25 μm and 50 μm Be foils are chosen to cover the two aperture slits of each photocamera. The E_c,50% values for the 25 μm and 50 μm Be foils are approximately 1.6 keV and 2 keV, respectively (E_c,50% is the cutoff energy at which the SXR transmission is 50%). According to formula (3), the ratio R versus T_e curve can be obtained, as shown in figure 3.

Figure  3.  The ratio R versus T_e curve for 25 μm and 50 μm Be foils.

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Due to its compactness, 100% internal quantum efficiency (QE), fast rise time of 200 ns, and good response to the SXR energy range, the AXUV20ELG photodiode array is chosen as the detector to measure SXR emission. Each photodiode array consists of 20 elements; however, only the odd-numbered elements are used to eliminate crosstalk between adjacent elements. The active area of each element is 0.75 × 4.1 mm², and the active thickness (S_i) is 35 μm. Additionally, the AXUV20ELG photodiode array demonstrates a good and stable response to SXR emission with a responsivity of approximately 0.27 A/W.

The custom pre-amplifier, designed to convert the weak current output from the photodiode array to an appropriate voltage, has a bandwidth of 500 kHz and a transimpedance of 1 × 10⁶ V/A. The voltage signals are synchronously acquired with a sampling rate of 1 MHz.

4.   Bench test of DSXAI diagnostic system

A bench test has been designed to ensure that the bandwidth and geometry of the DSXAI diagnostic system meet the specified requirements. To determine the bandwidth, we utilize a light-emitting diode (LED) as the light source and apply a sinusoidal voltage with an appropriate DC bias to ensure that the LED operates within its linear range. The frequency of the sinusoidal voltage ranges from 1 kHz to 500 kHz, and the light emitted by the LED is measured using a DSXAI photocamera. The amplitude bandwidth of the DSXAI diagnostic system, defined as the frequency at which the amplitude-frequency response curve drops to −3 dB, is approximately 390 kHz. The phase bandwidth of the system, defined as the frequency at which the phase shift reaches 90°, is approximately 230 kHz. Generally, the lower frequency, 230 kHz, is used as the bandwidth of the DSXAI diagnostic system, which corresponds to a temporal resolution of about 4 μs.

To calibrate the geometry of the DSXAI diagnostic system, we reproduce the experimental setup of a poloidal cross-section, as illustrated in figure 4(a). The black circle in the figure represents the poloidal cross-section of the HL-2A with a minor radius of 0.4 m. A photocamera is positioned to ensure that the distance between the apertures and the center of the poloidal cross-section is 492 mm. A linear guideway, controlled by a stepping motor, is aligned along a diameter of the poloidal cross-section. Additionally, a cold cathode fluorescent lamp (CCFL) is mounted on the linear guideway and is moved from one end to the other over a distance of 1.2 m. Figure 4(b) displays a typical result from the geometry test for an array of photocameras, with the actual detection ranges of 10 lines of sight presented. All channels perform correctly, with no overlap between adjacent channels. The average full width at half maximum (FWHM) of all lines of sight is approximately 5.5 cm, representing the sampling width of the DSXAI diagnostic system. Furthermore, the average spacing between adjacent lines of sight is about 8 cm, indicating the spatial resolution of the system.

Figure  4.  (a) Schematic diagram of the geometry test, (b) result of the geometry test for one photocamera ( p is the perpendicular distance from the center of poloidal cross-section to the line of sight, and the positive and negative values of p represent that the lines of sight are near to the top and bottom, respectively).

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5.   Experimental results and discussions

Figure 5 shows the discharge waveforms for shot No. 38557 with neutral beam injection (NBI) heating on HL-2A. NBI heating, with a power of approximately 500 kW, is initiated at 900 ms. During this period, the stored energy W_E increases significantly from 10 kJ to 20 kJ. The plasma current I_p remains stable at around 160 kA from 200 ms to 1100 ms, exhibiting minimal variation before and after the NBI heating phase. In contrast, the electron density n_e rises to 2.5 × 10¹⁹ m⁻³ from the start until 900 ms and maintains a high level throughout the NBI heating. Figure 5(c) presents the SXR emission intensity measured by DSXR04. It is evident that the emission intensity signals exhibit distinct behavior before and after the initiation of NBI heating, with a pronounced sawtooth oscillation observed during NBI injection. Figure 5(d) provides a detailed view of the DSXR04 signals from 900 ms to 1100 ms at various radial positions: −170 mm (grey), −66.9 mm (red), 47.6 mm (blue), 155.7 mm (green), 244.6 mm (pink), and 252.5 mm (brown). The sawtooth oscillation period is clearly around 22 ms, and the reversed sawtooth is detected by multiple channels compared to the blue curve (47.6 mm), including the black curve (−170 mm), red curve (−66.9 mm), and green curve (155.7 mm). We are now working on tomographically reconstructing a 2D map of SXR emissivity and T_e during one sawtooth oscillation period using the DSXAI diagnostic.

Figure  5.  Discharge waveform of shot No. 38557: (a) plasma current I_p and electron density n_e, (b) stored energy of plasma W_E and power of NBI heating P_NBI, (c) emission signals measured by DSXR04, (d) detailed view of the DSXR04 signals from 900 ms to 1100 ms at various radial positions.

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We select a sawtooth oscillation period from 1024 ms to 1045 ms and choose five time points for tomographic reconstruction: 1024 ms, 1030 ms, 1038 ms, 1044.364 ms, and 1045 ms, as shown in the first row of figure 6. The second and third rows of figure 6 present the 2D tomographic SXR emissivities for 25 μm and 50 μm Be foils, respectively, reconstructed using the Cormack-Bessel technique [3, 14, 15] based on DSXR04 and DSXR05 signals. The results indicate that SXR emission is predominantly localized in the plasma region where r < 0.2 m, with the emissivity of the 25 μm Be foil significantly higher than that of the 50 μm Be foil. The 2D tomographic emissivity maps of both 25 μm and 50 μm Be foils reveal the sawtooth oscillation process, showing an increase in emissivity from 1024 ms to 1038 ms. As the sawtooth crash occurs, the 2D SXR emissivity profiles change significantly, and the radiation intensity in the plasma core decreases markedly, as shown in 2D tomographic emissivity from 1044.364 ms to 1045 ms.

Figure  6.  The first row shows a sawtooth oscillation period of the SXR signals under NBI heating conditions (left) and its magnified view (right). Points A to E represent the five time points during this sawtooth oscillation period (1024 ms, 1030 ms, 1038 ms, 1044.364 ms, 1045 ms). The second and third rows illustrate the evolution of 2D tomographic SXR emissivities at five time points (A to E), reconstructed by the 25 μm and 50 μm Be foils, respectively. The fourth row shows the evolution of 2D tomographic T_e at the same five time points (A to E).

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Further, the 2D tomographic T_e is obtained by taking the ratio of two 2D tomographic emissivities using the double-foil technique, as shown in the fourth row of figure 6. Due to the low emissivity at r > 0.2 m, the error in T_e calculated from the emissivity ratio can be significant. Consequently, only the tomographic T_e for r < 0.2 m is presented here. Nevertheless, the sawtooth oscillation process is still observable in the 2D tomographic T_e from 1024 ms to 1045 ms. During the sawtooth ramp-up phase, the T_e in the plasma core gradually increases from 1024 ms to 1038 ms. In the subsequent sawtooth crash phase, the core T_e significantly decreases, accompanied by radial outward heat transport. These results are consistent with the typical sawtooth oscillation model.

To further verify the accuracy of the T_e measurements obtained from the DSXAI diagnostic, we compared these results with those from the Thomson scattering (TS) diagnostic, as shown in figure 7. The blue circles in the figure represent the T_e at five time points (A to E) measured by the DSXAI diagnostic, ranging from 470 eV to 670 eV. In contrast, the T_e measured by the TS diagnostic ranges from 720 eV to 790 eV. On average, the DSXAI diagnostic underestimates the T_e by about 24% compared to the TS diagnostic. Notably, the evolution of the core T_e at the five time points (A to E) measured by the DSXAI diagnostic effectively reveals the entire sawtooth oscillation process. During the sawtooth ramp-up phase, the core T_e increases, and it sharply decreases during the sawtooth crash phase. However, the core T_e measurements from the TS diagnostic do not show the decrease during the sawtooth crash, indicating that the DSXAI diagnostic has better temporal resolution.

Figure  7.  Comparison of core T_e measurements between the DSXAI diagnostic (blue circle) and the TS diagnostic (red triangle) at five time points (A to E).

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6.   Summary

A 100-channel DSXAI diagnostic system has been developed for the HL-2A tokamak to measure SXR emission and T_e using tomographic reconstruction and the double-foil technique. The diagnostic system comprises five photocameras positioned at two distinct poloidal cross-sections, with a 15° toroidal separation. Three of these photocameras are installed at one poloidal cross-section, with poloidal angles of −45°, 0°, and 45°, while the remaining two are positioned at the other cross-section with poloidal angles of −45° and 45°. Bench tests have been conducted to evaluate the temporal and spatial resolutions of the DSXAI diagnostic system. The results indicate that the system achieves a temporal resolution of approximately 4 μs and a spatial resolution of about 8 cm. Initial experimental results obtained on HL-2A demonstrate the system’s effective performance. Additionally, successful reconstruction of 2D tomographic emissivity and T_e has been achieved.

The T_e measured by the DSXAI diagnostic is approximately 24% lower than that obtained from the TS diagnostic, and the DSXAI diagnostic shows better temporal resolution. The DSXAI diagnostic system is compact, non-invasive, and cost-effective, and the successful application on HL-2A provides a strong foundation for its future use in fusion reactors.