2.1. Experimental setup of the diagnostic system

The KTX is a new RFP device with a major radius of R=1.4 m and a minor radius of a=0.4 m.^[9,11–13] The materials of the first wall and limiter are stainless steel and molybdenum, respectively. The height of the poloidal and toroidal molybdenum limiters is 2 cm. The diagnostic is the most basic and important of all diagnostics operating on the KTX at present.

Figure 1 shows the schematic of the detector, which is cylindrical in shape with 45 mm diameter and 300 mm long. As shown, it consists of an aperture slit, protective glass, interference filter, photodiode array, and a preamplifier, all surrounded by black aluminum foil. Light from the plasma first passes through an aperture slit (0.5 mm ×10 mm) and a protective glass. A 1.5 mm thick protective glass is placed behind the aperture slit and plays an important role in stopping both plasma sputtering and strong electromagnetic radiation such as x-rays. Thus the signal quality will improve significantly because the photodiode and preamplifier inside the diagnostic system will not be affected by the strong electromagnetic radiation. And the glass of 1.5 mm thick has the light refracted but it does not affect the adjacent channels. After passing through the narrow bandpass interference filter, the light shines onto the photodiode array, and the weak photocurrent signal is amplified by the preamplifier.

Fig. 1.

	Figure Option ViewDownloadNew Window
	Fig. 1. Schematic of the detector: 1. light from the plasma; 2. aperture slit; 3. protective glass; 4. interference filter; 5. photodiode array; 6. preamplifier; 7. black aluminum foil.

When the incident angle increases from vertical incidence, the wavelengths transmitted through the filter will shift toward shorter wavelengths and can be described by the equation^[14] , where θ is the angle of incidence, is the unshifted wavelength at vertical incidence, and n_eff is the effective index of refraction, which is relative with filter, spectral feature, and polarization. For the KTX diagnostic, the maximum incident angle reaches about 37° (see Fig. 1), which makes light cannot pass through the filter used on the KTX with a center wavelength of 658 nm and a bandwidth of 20 nm. Therefore the actual design of the flexural interference filter is shown in Fig. 1 and it has a 30° bend, which ensures the angle of incidence, θ, is less than 15° for each channel. According to the formula above, a 15° angle of incident will give about 1% change in wavelength, which is nearly 7 nm for the line. On account of the bandwidth of 20 nm for the filter, thus the detector can receive light for each channel. The AXUV20ELG photodiode array from IRD is chose as the light detector, because it has nearly 100% internal quantum efficiency (QE), includes a sensitive area of 3 mm² per element, has a rise time of 200 ns, and has a minimum shunt resistance of 100 at 25 °C. This 20-element photodiode array also retains a stable response after exposure to high energy radiation with the responsivity of about 0.35 A/W at 656.3 nm. To avoid the impact of the crosstalk between adjacent photodiode elements, only all the even number elements in the array are selected to detect the ten-channel signals. The preamplifier has a frequency bandwidth of 500 kHz with a high current-to-voltage conversion factor of 10⁶ V/A, and it is connected with a data acquisition card.

The entire diagnostic system is installed in a 2 mm thick cylindrical aluminum cylinder to reduce the influence of electromagnetic interference. Black aluminum foil, BKF12 from Thorlabs,^[15] with a reflectance of only 5% in the visible and near-infrared (VIS NIR) waveband, is attached to the interior surface of the aluminum shielding cylinder and effectively eliminates the reflected light inside the device. The detector is placed on port GU of the KTX, which is a vertical top port with an inside diameter of 47 mm. An aperture slit has been employed instead of an optical lens to increase the spatial resolution because of the limited port size. Figure 2 shows the experimental layout of the diagnostic system on a round poloidal cross section of the KTX. As shown, the 10 chords cover almost the entire poloidal cross section.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. A poloidal cross section of the KTX, showing the experimental layout of the detector.

2.2. Laboratory tests of the diagnostic system

The frequency bandwidth of the diagnostic system is 300 kHz, as obtained by laboratory tests. We use a high-frequency (100 MHz) wide spectrum light emitting diode (LED) as the visible light source and it is biased with a DC voltage to ensure that it is operated in the linear I–V range. The oscillations added onto the DC bias voltage vary from 1 kHz to 1 MHz. Figure 3 shows the output amplitude and phase shift of the system. As shown, the amplitude of the output signal remains roughly constant with increasing frequency up to about 50 kHz, and it decreases to half the value at 50 kHz at a frequency of 400 kHz. The phase shift increases to 180° when the frequency is 300 kHz. Thus, the diagnostic system has a frequency bandwidth of 300 kHz.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. Calibration of the amplitude and phase shift frequency response of the diagnostic system.

The geometrical parameters of the diagnostic system were also tested, including the chord positions and the overlap between two neighboring channels. Figure 4 shows a schematic illustration of the spatial geometry used for the calibration. The dashed circle represents the poloidal cross section of the KTX vacuum vessel. The geometric position of the diagnostic system in the laboratory test setup is the same as that in the experimental device. The 420 mm distance shown in the schematic is the actual distance from the aperture slit to the center of the KTX vacuum vessel. As shown, the linear actuator based on the stepping motor technique is placed crossing the center of the poloidal cross section for the laboratory test. A cold cathode fluorescent tube (CCFT) is used as an isotropic light source having a slender shape, and it is mounted vertically on the linear actuator. During the test, the CCFT moves along the linear actuator over a total distance of 800 mm, which equals the diameter of the poloidal cross section of the KTX. The test results are shown in Fig. 5 and these data in Table 1 are obtained from the results. Table 1 shows a list of the full width at half maximum (FWHM) of the channels, and the maximum FWHM is about 40 mm. The degrees of overlap between the channels listed in Table 2 are each about 3%, based on these test data. For each column in Table 2, which shows vs. , overlap rate 1 refers to the former and overlap rate 2 to the latter. Here, the overlap between the 8th and the 9th channels is higher than others, which may be the crosstalk defect between these two elements of the photodiode array.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. Schematic of the spatial geometry used for calibration.

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. Results of the laboratory tests. The r axis is the perpendicular distance from the center of the vacuum vessel to the chord.

Table 1.

Table 1.

Table 1. FWHM for each of the 10 channels. . Channel FWHM/mm 20 24 32 36 40 40 37 33 25 21

Table 1. FWHM for each of the 10 channels. .

Table 2.

Table 2.

Table 2. Overlap between adjacent channels. . Channel vs. vs. vs. vs. vs. vs. vs. vs. vs. Overlap rate 1/% 4.1 3.0 2.9 2.5 2.4 3.2 3.1 14.5 2.2 Overlap rate 2/% 3.4 2.6 2.7 2.4 2.5 3.5 3.2 17.3 2.8

Table 2. Overlap between adjacent channels. .

Because of the smooth surfaces of the metals at the inner wall of the vacuum vessel on KTX, the effect of reflection on the signals has to be considered. To assess the proportion of the reflection, a two-dimensional model is constructed according to ray tracing equation , , where r is the minor radius of the KTX. In the model, the geometric positions of every part, including the ports, slit, detector elements, and so on, are the same with the real experimental geometry. The number of rays from the plasma we used in the model is 4000. The ray direction vector is spherical and the number of rays in wave vector space is 150. The source power per unit thickness is from the emissivity profile. And some other main parameters we used are as follows: the refractive index of a vacuum, n = 1; wavelength, 656.3 nm; plasma minor radius, m. In the model, when the rays from plasma strike the detector element, the detector element will record the power of the incident rays. On KTX, the material of the first wall is stainless steel, the reflection coefficient of which is from 0.55 to 0.65. According to the smoothness of the KTX first wall, we chose a reflection coefficient of 0.6 in the model. The transmitted ray power recorded by the detector elements was obtained with the reflection coefficients of 0.6 and 0, respectively. In this way, the proportion of reflection can be estimated in the signals. Firstly, we use the experimental data to obtain emissivity profile by the Abel inversion without the reflection. Then the emissivity profile is inputted into the numerical model and the proportion of the reflection can be roughly estimated in the signals. Afterwards, in the case of wall reflection, the results are used to calculate a new emissivity profile and estimate a new proportion of the reflection. Finally, the optimal results can be converged by repeated iterations.

The ultra-low q discharge^[9] is the typical discharge on the KTX. For an ultra-low q discharge, Figure 6 shows the waveforms of the plasma current I_p, loop voltage V_loop, and 10-channel signals. As shown by the locations of the different -signal channels, the level of emission is currently strong in the center of the KTX. Since is the first spectral line of the Balmer series (with a wavelength of 656.3 nm), the intensity of the emission is proportional to the neutral hydrogen density in the atomic energy level p = 3.^[16] Because the KTX plasma is currently in a low temperature state of about several tens eV, the neutral hydrogen cannot be ionized rapidly and the recombination of hydrogen ions occurs easily to form neutral atoms, so it maintains a high density in the p = 3 excited state in the core plasma. The relative level of the emission will be lower in the plasma center when the plasma is heated to a higher temperature,^[16] e.g., to 500 eV.

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. Waveforms for an ultra-low q discharge on KTX: (a) plasma current Ip; (b) loop voltage Vloop; (c) ten-channel signals.

To demonstrate the frequency response of the diagnostic system, the signals with obvious MHD activity are shown in Fig. 7 in a tokamak discharge.^[9] The MHD activity oscillates with a frequency of about 10 , as observed in the cross-power spectrogram of and . Oscillations at about 10 kHz are confirmed by the cross-power spectrogram of and , which are differential poloidal in vessel magnetic field signals at the poloidal angles of and , respectively. Moreover, the 2nd and 3rd harmonic peaks of the MHD activity also can be seen clearly from the cross-power spectrogram in the high frequency region. Thus, with its high-frequency response and good spatial resolution, this diagnostic is capable of providing more detailed analysis of the physics of RFP plasmas.

Fig. 7.

	Figure Option ViewDownloadNew Window
	Fig. 7. Waveforms for a tokamak discharge on KTX: (a) plasma current Ip; (b) two-channel signals ( and ); (c) cross-power spectrogram of and (d) two-channel differential poloidal magnetic field signals ( and ); (e) cross-power spectrogram of and .

3.1. Relationship between neutral density and emission

The emission originates from neutral hydrogen when an electron undergoes a transition from energy level p = 3 to p = 2. The main mechanism for the emission is electron–neutral collisions. Hence, the neutral density has a direct relation to the intensity of the emission. An approximate expression for the neutral hydrogen density is given by^[16] 1 Here is the emissivity of , is the energy of an photon, and A₃₂ is the Einstein spontaneous emission coefficient for . The quantities and are numerical coefficients given in Ref. [17], which vary with the electron temperature and density, where 3 indicates the atomic energy level p = 3. The quantities and are the Saha-equilibrium population densities in atomic energy levels 1 and 3, respectively; they are given by^[17] , where is the ionization energy for atomic energy level p, and is assumed to be equal to the electron density. The expression given by Eq. (1) agrees closely with the ADAS simulation code,^[18] although it becomes incorrect at low electron temperatures and densities. The comparisons between the neutral density calculated using a fixed emissivity of 0.1 MW/m³ and the ADAS database are shown in Fig. 8.

Fig. 8.

	Figure Option ViewDownloadNew Window
	Fig. 8. The comparisons between the computed results and the ADAS database.

In a plasma, the emissivity of is a quantity that changes in both space and time. For each channel, the measured value of the local emissivity is relative to the geometrical position of the aperture optics. And the radiation of the line is assumed to be isotropic in the plasma. Therefore, the overall power of a photodiode viewing along the chord is given by 2 where T₁ and T₂ are the transmissivity of the protective glass and the interference filter, respectively; A_ap and A_det are the effective area of the aperture slit and the sensitive area per element for the photodiode; and and are the angle between the surface normal to the photodiode and the chord viewed and the angle between the surface normal to the aperture slit and the chord viewed, respectively. The d is the distance between the photodiode and the aperture slit. The output voltage from the preamplifier can then be written as , where is the responsivity of the AXUV20ELG photodiode at 656.3 nm, and is the transimpedance gain of the preamplifier. Thus, can be calculated from V_output and the emissivity can be obtained by the Abel inversion of Eq. (2):^[19,20] , where is the brightness of a chord in units of . Finally, the neutral density profile in the plasma can be calculated from Eq. (1) using the results for .

Figure 9 shows the time evolution of I_p and the signals for an ultra-low q discharge on KTX. We use the data for the emission at 3.8 ms, when the plasma current reaches its peak value (see Fig. 9). The proportion of the reflection is estimated by numerical simulation with the emissivity profile of , and the results of multiple iterations are shown in Table 3. The considerable proportion of the reflection in the simulated results suggests that the effects caused by the reflection of the vacuum vessel should not be ignored. The profiles of electron density and temperature at 3.8 ms are shown in Fig. 10 by the blue-dashed and red-dashed lines, respectively. The profiles of these plasma parameters are measured with a radially movable Langmuir probe at the mid-plane. The blue and red solid lines are fittings to the measured data. The quantities , , , and in Eq. (1) can be obtained with the profiles of electron density and temperature. The brightness for 10-channel signals and the emissivity profile at 3.8 ms are shown in Figs. 11(a) and 11(b), respectively. The brightness is about and the emissivity profile is not hollow at 3.8 ms. Figure 11(c) shows the profile of neutral density obtained from Eq. (1) using the data for the emission and the fittings to the profiles of electron density and temperature at 3.8 ms. In this ultra-low q discharge, the neutral density in the core plasma is about , and at the edge it is about . Based on the ideal gaseity equation and the breakdown pressure , the background neutral density is about at normal temperature. The red dashed line at r = 0.38 m in the figure indicates the position of the limiter on KTX.

Fig. 9.

	Figure Option ViewDownloadNew Window
	Fig. 9. (a) Time evolution of the plasma current Ip and (b) the signals for the ultra-low q discharge.

Fig. 10.

	Figure Option ViewDownloadNew Window
	Fig. 10. Profiles of the electron temperature and electron density at 3.8 ms, as obtained using the Langmuir probe.

Fig. 11.

	Figure Option ViewDownloadNew Window
	Fig. 11. The ultra-low q discharge on KTX at 3.8 ms: (a) the brightness for 10-channel signals; (b) profile of emissivity (c) profile of neutral density .

Table 3.

Table 3.

Table 3. The proportion of the reflection in the signals. . Channel % 23.8 23.2 23.4 24.6 24.7 24.7 24.6 23.4 23.2 23.8

Table 3. The proportion of the reflection in the signals. .

Figure 12 shows the experimental data for I_p and the signals for a tokamak discharge on KTX. The plasma current reaches its peak value at 4.0 ms. Figure 13 shows the profiles of electron density and electron temperature at 4.0 ms as measured by the Langmuir probe. Figure 14(a) and 14(b) show the brightness for the 10-channel signals and the emissivity profile, respectively. The brightness is about 40 and the emissivity profile has a peak value at the plasma center. With the low electron temperature in KTX, the emission mainly comes from the center rather than the edge of the KTX, thus the plasma facing components do not contribute a major impact. As a result, the radiation would be approximately symmetric on KTX. In the same manner as above, the profile of neutral hydrogen density is obtained at 4.0 ms (see Fig. 14(c)). In the tokamak discharge, the neutral density in the core plasma is about , and at the edge it is about . The background neutral density is about with a breakdown pressure at normal temperature. The neutral hydrogen density in the tokamak discharge is currently higher than that in the ultra-low q discharge, because the KTX plasmas are in a lower temperature state in the tokamak discharge. Also, due to the lower plasma temperature, there is a higher bump at the edge of the poloidal cross section in the profile of neutral density in the tokamak discharge.

Fig. 12.

	Figure Option ViewDownloadNew Window
	Fig. 12. (a) Time evolution of the plasma current Ip and (b) the signals for a tokamak discharge.

Fig. 13.

	Figure Option ViewDownloadNew Window
	Fig. 13. Profiles of electron temperature and electron density at 4.0 ms from the Langmuir probe.

Fig. 14.

	Figure Option ViewDownloadNew Window
	Fig. 14. The tokamak discharge on KTX at 4.0 ms: (a) the brightness for 10-channel signals; (b) profile of emissivity (c) profile of neutral density .