Figure
1.
The configuration of the CO2-DI.
| Citation: |
Haiying LI, Jiachen TONG, Wei DING, Bin XU, Lu BAI. Transmission characteristics of terahertz Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab[J]. Plasma Science and Technology, 2022, 24(3): 035004. DOI: 10.1088/2058-6272/ac3ad7
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The transmission of terahertz (THz) Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab is investigated by using a hybrid method of cylindrical vector wave functions (CVWFs) and Fourier transform. On the basis of the electromagnetic boundary conditions on each interface, a cascade form of expansion coefficients of the reflected and transmitted fields is obtained. Taking a double Gaussian distribution of the plasma density as an example, the influences of the applied magnetic field, the incident angle and polarization mode of the incident beams on the magnitude, OAM mode and polarization of the transmitted beams are analyzed in detail. The results indicate that the applied magnetic field has a major effect upon the polarization state of the transmitted fields but not upon the transmitted OAM spectrum. The incident angle has a powerful influence upon both the amplitude profile and the OAM spectrum of the transmitted beam. Furthermore, for multiple coaxial vortex beams, an increase of the maximum value of the plasma density causes more remarkable distortion of both the profile and OAM spectrum of the transmitted beam. This research makes a stable foundation for the THz OAM multiplexing/demultiplexing technology in a magnetized plasma environment.
Measuring and controlling the electron density are essential for plasma equilibrium reconstruction, stability, transport, and confinement studies in magnetically confined fusion devices [1, 2].
Interferometry is one of the fundamental plasma diagnostics on fusion devices to provide the line-integrated electron density [3]. However, the mechanical vibrations cause measurement errors for the interferometer and a fringe jump error leads to uncontrollability of the density. The principal advantage of dispersion interferometers (DIs) lies in their insensitivity to variations in geometric path length, thereby minimizing the occurrences of 2π phase jumps that need to be tracked. Obviously, this inherent feature will enhance the system’s reliability.
The first application of dispersion interferometry to measure the line-integrated electron density in a fusion device was at the GDT [4]. At the TEXTOR tokamak, a dispersion interferometer was developed for measuring higher density and was also the first one to use dispersion interferometry for density feedback [5]. The data recording system used fast analog-to-digital converters (ADCs) to record the photodetector and modulator signals and field-programmable gate array (FPGA)-based digital units of dataflow processing to calculate the line-integrated electron density in real time [6]. At the Large Helical Device (LHD), a dispersion interferometer was operated next to the far-IR interferometer, and a new offline phase extraction method was developed based on phase-locked-loops, which employs a true quadrature detection scheme [7, 8]. The DIII-D tokamak tested the ITER toroidal interferometer and polarimeter (TIP) system, which is a two-colour system, for primary density feedback control [9]. This is accomplished by using a four-channel digital phase demodulator (DPD), constructed with an FPGA coupled to high-speed ADCs [10, 11]. A new quadrature phase reconstruction method has been developed specifically for dispersion interferometers at the Wendelstein 7-X. This method is capable of real-time density feedback control based on an FPGA [12, 13]. A synchronous demodulation system is proposed and deployed for CO2-DI on HL-2A. Based on the FPGA, the phase adjustment (PA) method was used to synchronize the electronics with the interferometer signal [14–16].
In the first half of 2022, the CO2-DI was successfully installed on EAST, and the raw data was collected by a data acquisition (DAQ) system and subsequently subjected to offline processing. The data from the CO2-DI was confirmed with the data from the solid-state source interferometer (SSI) and POlarimeter-INTerferometer (POINT) [17]. Based on the need for experimental operation and real-time feedback, real-time processing of data is extremely important [18], for which a dedicated electronic system capable of performing digital signal processing has been developed.
This paper introduces the real-time data processing system for the CO2-DI on EAST. Section 2 specifies the real-time data processing method and functional modules. Measurement results are presented in section 3, which includes measurement results from both the bench tests and EAST experiment campaign. Finally, section 4 provides a comprehensive summary and outlook.
The configuration of the CO2-DI is illustrated in figure 1. It mainly consists of a CO2 laser, two nonlinear crystals, a photoelastic modulator (PEM), an optical filter, an infrared detector, and the real-time data processing system [7, 19].
The plasma electron density can be obtained from the ratio of intensity signals, represented as,
| ¯neL=−2ω3cp{tan−1(IωmI2ωm)−φ0}. | (1) |
In the equation, ωm denotes the modulation frequency of the PEM, cp is a constant, L represents the optical path length in the plasma, Iωm and I2ωm denote the intensity signals extracted by the lock-in amplifier, and φ0 represents the initial phase [20].
The detected data of Iωm and I2ωm signals are extracted by the lock-in amplifier from the output signals of the detectors and the reference signal is provided by the PEM. Iωm and I2ωm are then fed into the real-time data processing system for calculations. This real-time data processing system calculates the density mainly based on equation (1).
The DI system is placed in a laser room on the first floor of the basement in the EAST experimental hall. As shown in figure 2, the detector receives the signal and transmits it to the lock-in amplifier (LIA) for further processing. The real-time data processing system calculates the signal extracted from the LIA. The flowchart of the data processing system is illustrated in figure 3. The data processing system includes three key modules which are the ADC, FPGA, and DAC. The ADC module performs real-time high-speed sampling of Iωm and I2ωm signals and translates the signals to digital waveforms. Then, digital signals are processed within the FPGA, which includes a trigger module, a ‘calculations of a coordinate rotation digital computer’ (CORDIC) module [21], a correction of ‘zero’ module, and an unwrapping module. As a reconfigurable device, the FPGA offers rapid prototyping capabilities for constructing digital processing systems [22, 23]. It also enables high-speed, real-time, multichannel, parallel processing of the signals outputted by the infrared detectors. Finally, the DAC module outputs analog electron density values. After, the DI system is capable of outputting electron density information to the plasma control system (PCS) for density feedback.
(1) ADC module
The ADC module establishes a correspondence between the voltage signal and the digital signal. The Iωm and I2ωm signals from the LIA are converted from analog to digital signals through a 12-bit ADC. The FL9627 is used on the ADC module to complete four-channel ADC synchronous acquisition, with an accuracy of 12 bits and a maximum AD sampling rate of 125 million samples per second (MSPS). The 125 MHz system clock is adopted in the entire logic.
(2) Triggering module
The trigger signal is sent out by the PCS at 2 s before discharge. It is edge triggered and connected to the development board via an IO pin. The trigger is sampled using the internal clock. When the rising edge of the trigger signal is detected, the real-time calculations start to be performed.
(3) Four-quadrant CORDIC module
The four-quadrant coordinate rotation digital computer (CORDIC) algorithm performs iterative rotations and vectoring operations to approximate the mathematical functions like the arctangent [21]. The two 12-bit digital signals from the ADC are expanded to 16 bits and converted into complement format. The system uses VIVADO software to generate FPGA logics and uses the generated four-quadrant CORDIC IP core for arctangent calculation.
(4) Correction of ‘zero’ module
The correction of ‘zero’ module makes the calculation result start from zero. Since the interferometer system has a fixed phase difference generated by the optical setup, the initial value calculated by the real-time data processing system is non-zero.
The initial phase tends to drift over time and cannot be predicted; therefore, it is necessary to acquire the offset before every shot. When the trigger signal arrives at t = −2 s, the average value of all unwrapping phases within the setting time is acquired and removed as the phase offset. In the recent EAST experiment campaign, we tested various set values including 0.1 ms, 1.0 ms, and 2.0 ms. The test results did not exhibit discernible differences. Consequently, given the prevailing signal levels on EAST, a setting value of 0.1 ms was identified as capable of achieving zeroing functionality.
(5) Unwrapping module
The unwrapping module implements a method for correcting the fringe jump caused during calculation. The fringe jumps could be observed in the experiments, as shown in figure 4(a). Due to the presence of the initial phase, the CO2-DI has a fringe jump at relatively low density. The phase signal generated by the four-quadrant CORDIC algorithm is wrapping at 2π, i.e., jumping from +π to −π for a continuously increasing phase [24, 25].
To address this issue, a real-time unwrapping algorithm was deployed in the data processing system. When the absolute difference between consecutive data is greater than or equal to the specified threshold, the locations of phase jumps are identified. Each segment of data is compensated by 2nπ (n = 1, 2, 3, …) to correct the phase angle in radians by ±2π [26].
The result after phase jump correction is shown in figure 4(b). The accuracy of the corrected density results validates the effectiveness of the unwrapping algorithm when a fringe jump occurs.
(6) DAC module
The DAC module converts the digital signal into an analog signal and outputs the voltage value. The DAC module is based on the AD9767 chip, which supports independent dual-channel, 14-bit, 125 MSPS digital-to-analog conversion. After the phase jump correction, the data is taken as a 14-bit output to the DAC. The DAC has an output range of ±5 V. In the case of the EAST device, the H-mode density can achieve levels of up to (0.8–0.9)nGW [27], where nGW (1020 m−3) is the Greenwald density limit. Therefore, it is sufficient for the achievable densities in EAST.
The phase represented as voltage output by the DAC is supplied to the PCS system. The PCS system then converts the voltage back into phase and multiplies the phase by the factor 2ω3cp according to equation (1) to get the density value.
Figure 5 shows the real-time data processing system. The lower left in figure 5 shows the ADC module, which is connected to the LIA and receives the signals of Iωm and I2ωm for analog-to-digital conversion. The upper part of the figure shows the FPGA development board model AX7325, which is connected to the ADC module model FL9627 and DAC module model AN9767. It calculates and corrects the signals from the ADC module and outputs the result to the DAC module. The lower right part shows the DAC module, which can be connected to the PCS.
To verify the accuracy and reliability of this real-time data processing system, a test-bench experiment in the laboratory was first conducted. In the 2022 autumn experiment campaign, the CO2-DI system calculated the electron density offline and stored the intensity signal data extracted from the LIA, which we used for the laboratory bench test of the real-time data processing system.
For the bench testing in the laboratory, the results calculated by the real-time data processing system are compared with the results calculated offline by MATLAB, where the results of a stable plasma discharge (#120485) are shown in figure 6. From the figure, it can be observed that the real-time calculation is consistent with the offline calculations.
As for electron density diagnostics on EAST, the vertical-viewing 0.65 THz SSI has been installed for line-integrated density measurements on EAST [28] and the POINT system [29] operates at a wavelength of 432 μm and a modulation frequency of 850 kHz for density measurement. They have consistently delivered density feedback for experiments conducted on EAST. Therefore, density obtained through them can be used to confirm the accuracy of CO2-DI measurements.
Figure 7 presents the density measurement results from the CO2-DI [30], SSI [28], and POINT [29] systems during a stable plasma discharge (#120531) in the EAST experiment. The difference between the measurement results of three systems in this figure is about 0.1×1019 m−3, which is reasonable due to their setup differences on EAST. Specifically, the SSI and DI systems utilize a vertical chord, whereas the POINT system employs a horizontal chord, leading to small differences in the measurements obtained. The DI’s path length inside the last closed flux surface (LCFS) is 1.2 m, while the SSI’s path length is 1.3 m, which is proximal to the DI’s. Meanwhile, the path lengths of the horizontal 11-channel POINT system are 0.64, 0.72, 0.79, 0.84, 0.87, 0.88, 0.87, 0.84, 0.79, 0.73, and 0.65 m [30]. Moreover, it should be pointed out that the ‘density wiggles’ in figure 7 are a result of the density feedback system puffing to maintain a density. Therefore, based on the general trend of the measurement results and the puffing effects within a narrow range, it can be inferred that the real-time data processing system of the CO2-DI provided electron density that was consistent with the measurements of POINT and SSI in a long-pulse discharge period of 60 s.
It is crucial that the real-time data processing system can respond accurately to the phase changes when the density changes rapidly. In the shot #120598, between 23 s and 27 s, due to a carbon impurity burst as shown in figure 8, the density could change over 1×1019 m−3 within 0.1 s, and the system clearly shows the density change. Therefore, it can be observed that the reliability of real-time system computation and data transmission has been validated under conditions of rapid density changes.
As shown in figure 9, the rapid density change caused by disruption during the current ramp-down phase happened near 11 s, where the real-time data processing system responded more accurately compared to the SSI during these conditions. In brief, the real-time data processing system working with the CO2-DI showed preferable reliability during disruptions.
In summary, the system can extract accurately the real-time density from the CO2-DI optical parts, and the density results can serve the feedback requirements of the EAST PCS system.
A real-time digital signal processing system based on a Xilinx FPGA has been designed and implemented for the CO2-DI on EAST device. After benchtop validation in the laboratory, the system was installed on the EAST device and successfully operated in last EAST experimental campaign. The feasibility of utilizing a CO2-DI for reliable line-integrated density calculation in real-time was demonstrated. The stability and reliability of the system have also been validated in long-pulse and high-density experiments. In the future, we plan to integrate the lock-in amplifier as a digital module into the data acquisition system. This fully digital system will improve the signal-to-noise ratio and integration of the overall system.
This work was supported by National Natural Science Foundation of China (Nos. 62171355, 61801349, and 61875156), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2020JM-192), the Stable Support Project of Basic Scientific Research Institutes (Nos. A131901W14, A132001W12), the Science and Technology Foundation of State Key Laboratory of Electromagnetic Environment, and the 111 Project (No. B17035).
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