Comparing simulated and experimental spectral line splitting in visible spectroscopy diagnostics in the HL-2A tokamak

1.   Introduction

Visible spectroscopy diagnostics (VSD) is used to monitor the densities of hydrogen/deuterium (H/D) and impurities (carbon C and tungsten W) in the core and edge (divertor and scrape-off layer (SOL)) regions of fusion reactors, thereby ensuring their safe operation. The acquisition of these parameters is essential for the low-confinement-mode (L mode) to high-confinement-mode (H mode) transition and fuel cycle studies. The concentration of impurities in the core region causes plasma disruption with subsequent severe thermal and current quenching. The physics parameter of the effective charge number (Z_eff) derived from VSD is used to monitor the impurity concentrations [1].

In general, physical parameters can be obtained by making suitable fits to VSD spectra [2, 3], e.g., impurity densities, transport coefficient, transport flux, effective charge number Z_eff, temperature T_i, plasma rotation velocity V, plasma current density J, safety factor q, magnetic field fluctuation (∆B), as well as deuterium/tritium (n_D/n_T) and hydrogen/deuterium (n_H/n_D) fuel ratios. These physical quantities help us understand the physical mechanism of fusion plasma confinement. VSD also plays a significant role in plasma control systems (PCSs), and it is mainly used in plasma disruption and edge local mode (ELM) studies [4–8]. VSD measures physics parameters in the core bulk plasma (0 < r/a < 0.65), edge plasma (0.65 < r/a < 0.95), SOL and the divertor regions, where r is the radial coordinate, a is the minor radius and r/a is the normalized minor radius. The magnetic confinement for fusion requires feedback that relies on VSD.

Spectral overlapping can be an issue and challenge for VSD. In particular, reflected or stray light from the vacuum chamber's walls can affect the reliability of SOL and divertor diagnostic results. The stray light from the SOL and divertor regions rather than the neutral beam-based active spectra is captured in the P-VSD system. Since the reflected light in the neutral beam region has a high Doppler wavelength shift, it can be effectively excluded in P-VSD spectra analysis. The spectra of H/D, He₃/He₄, W and neutral beam injection (NBI) with different energies (the full energy E, the half energy E/2, the one-third energy E/3, and maybe the one-eighteenth energy E/18) sometimes overlap with each other and are indistinguishable [9–12]. Reducing or eliminating the reflected stray light has become essential to VSD. The intensity of reflected light can be higher than the light that needs diagnosing, therefore affecting the diagnostic system's signal-to-noise ratio (SNR) and resulting in a diagnostics system error.

Another issue for A-VSD takes the form of spectral structures emitted after CX collisions between slowed-down fast ions that originated in the NBI systems and neutral H or D atoms injected by the same or another NBI system. A further issue to be handled and analyzed is line broadening and splitting due to the Lorentz electric field E_Lorentz, an electric field induced in beam atoms by the V_beam × B effect. It should be noted that the spectral splitting caused by the motional Stark effect (MSE) is from E=V_beam×B+E_r. The relative magnitude of the Lorentz electric field E_L=V_beam×B is derived from the D⁺ ion generated by the collision of neutral particles with the plasma during the NBI process. The rotational motion of the D⁺ ion in the bulk plasma generates a radial electric field E_r. According to Charge eXchange Recombination Spectroscopy (CXRS) diagnostics, HL-2A has a plasma toroidal rotation velocity of V_τ ≈ 10⁴ m s^-1 at the edge and 10⁵ m s^-1 in the core and a poloidal upper limit rotation velocity of V_p ≈ 10⁴ m s^-1. The beam energy is 22.5 keV amu^-1 for H, considered the full energy, with four ion sources turned on. Thus, the beam particle's velocity isV_beam ≈ 10⁶ m s^-1 (not considering special relativistic effects). According to the angle γ between V_beam and B_τ, approximately equal to 127.8 degrees, we calculated the sinγ ≈ 0.8. Thus, the ratio of theE_Lorentz to the E_r is estimated to be about 10 to 100.

As a result, the spectral splitting model did not account for the Lorentz electric field generated by the plasma rotation. In subsequent sections, we use E_L to represent the Lorentz electric field generated by NBI. However, if the plasma performance is enhanced, we must account for the radial electric field E_r generated by bulk plasma ions' rotational motion.

Spectral line splitting has been studied and qualified for VSD in many devices. For instance, Balmer line spectra (D_α, H_α, D_β, H_β, D_γ, H_γ) in the SOL and divertor showed strong Zeeman splitting in the TEXTOR tokamak [13]. Zeeman splitting was studied in the TEXTOR tokamak for ion temperatures of 0.5–1.0 eV and magnetic fields B from 1 to 1.5 T using edge passive and active charge-exchange (P-CXRS and A-CXRS) diagnostics [14, 15]. The Zeeman splitting of D_α 656.10 nm and H_α 656.28 nm in the KSTAR tokamak showed that the internal magnetic field could be determined by analyzing the circularly polarized spectral lines emitted by the plasma impurities [16]. The Abel inversion method was used to calculate the radial magnetic field B_r, the magnetic field pitch angle and the boundary impurity densities n_z [17–22] from the Zeeman splitting polarization characteristics of H_α (656.28 nm) based on calibrated light intensity [23–27].

FIDAsim [28, 29], TRANSP [30] and SOS [31, 32] codes are usually introduced to simulate the visible spectra caused by a diagnostics neutral beam (DNB). This study observes spectra measured from the midplane horizontal and vertical top windows from the line-of-sight (LOS). Based on the SOS code and the ADAS database [31–33], this study models the Stark and Zeeman spectral splitting in P-VSD and A-VSD of beam emission spectra (BES) and MSE.

In this work, the ion temperature T_i and density n_i, the electron temperature T_e and density n_e profile, the cross-section between particles $\left\langle Q_{i, j}\right\rangle$, and the central wavelength (λ) models are introduced into the simulation and experimental spectral reconstruction model. We used the magnetic field-induced Zeeman splitting spectra to distinguish the H/D spectra from different regions (divertor and SOL) and discriminated the reflected light mixed with the diagnostic spectra. Spectra were distinguished due to different magnetic fields with special Zeeman splitting characters. We set a spectral model for H/D with a warm component (< 50 eV) and a cold one (< 3 eV) in the divertor and SOL. The spectral reconstruction was performed using simulation and experimental MSE spectra [34–39], and then the safety factor q was calculated from the Lorentz angle from the reconstructed MSE spectral curve.

2.   Simulation and experimental set-up

2.1   Diagnostic layout

Figure 1 shows the HL-2A geometry of the diagnostic LOS schematic model. The LOS and electric/magnetic field (E/B) angle affect the Stark and Zeeman splitting I_π/I_σ ratio. Figure 1(a) shows the side view of the HL-2A vertical observation schematic for P-VSD, which can monitor the helium (He), tungsten (W) and H/D densities in the downwards divertor. When looking at the downwards divertor, the LOS inevitably receives reflected light from the SOL region, which should be excluded. It is also subjected to a significant stray light from the nearby (upper divertor). The first mirror (FM) generally penetrates the diagnostics port plug, equivalent to attaching a lens hood to avoid nearby stray light, avoiding being affected by stray light from the upper divertor. A shutter is used before the FM to avoid being sputtering and deposition by the plasma. Figure 1(b) shows the side view of the midplane window of the inner-wall LOS for P-VSD. The LOS spread lines change in the Z-direction (up and down). This diagnostic port plug window also integrates CXRS, BES, MSE and fast-ion D_α diagnostics (FIDA) of A-VSD in HL-2A, as shown in figure 1(d).

Figure  1.  (a) Side view of the P-VSD vertical observation LOS schematic used to diagnose the divertor region. (b) Side view of the P-VSD midplane window LOS layout used to diagnose the SOL inner-wall region. (c) Optical light path simulation of the divertor region from a top vertical view using Zemax software. (d) Top view of the midplane window observation LOS for A-VSD.

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Figure 1(c) presents the Zemax simulation by the vertical LOS. The dark horizontal line at the bottom of the figure represents the focused image plate, which includes the components facing the lower divertor, covering the magnetic field zero point (X-point) of the lower divertor, inner target board, demo board, external target board, cassette box and C-sharp block complex components. It should be noted that the focus position difference between various components is not considered in the image plane. The spatial position of various components needs to be clarified to ensure that the image plane has a slight position difference between different components. Figure 1(d) shows the top view of the HL-2A midplane window observation LOS for A-VSD. The LOS spread lines change in the X–Y plane (e_τ and e_r direction). The spatial distribution's top view of the cross-section area is presented, providing the angle between the LOS and NBI. The green beamline represents the NBI neutral beamline and the black shading is LOS.

2.2   Spectral simulation model

2.2.1   Atomic spectroscopy model

NBI can heat the plasma core region efficiently since the neutral particles can traverse through the magnetic field. However, a fraction of beam particles, D⁰, is ionized by charge-exchange collisions and becomes trapped, as shown in equation (1), where Aⁿ⁺ represents plasma ions. Active spectral diagnostics CXRS, BES and MSE are developed during the collision between neutral particles and bulk plasma. Now, since the collision cross-section, $\left\langle Q_{i, j}\right\rangle$, between beam particles and bulk plasma impurities decreases with beam energy in the range of 50–100 keV amu^-1 for hydrogen, here, i stands for a neutral beam particle and j stands for impurities (He, C, W); using a beam with such energies would result in reduced SNR. Therefore, a suitable energy DNB (< 50 keV amu^-1, for H) was developed [40, 41]. The CX process is shown in equation (1), where the intensity of the spectra is given in equation (2). We can calculate the plasma temperature T_i from the Doppler wavelength broadening λ_d as shown in equation (3), and the Doppler wavelength shifts ∆λ from the beam velocity V_beam and the angle β between the LOS and the NBI from equation (4).

where I_cx is the intensity of the CXRS, n_z is the impurity density, n_b is the neutral beam density, n_e is the electron density, T_i is the ion temperature, Z_eff is the effective charge number, E is the beam energy, Q_cx is the charge-exchange collision cross-section between neutral particles and bulk plasma impurities, ds is the light from the cross-sectional area integration, λ_d is the Doppler wavelength broadening, c is the light speed in the vacuum, and β is the angle between the LOS and the NBI, which can be obtained from the geometry of the VSD layout.

BES emissions originate from interactions between neutral beam particles (H/D) and plasma electrons, and plasma impurities (see equation (5)). The spectral intensities of BES can be determined by the formula (6).

where D means the neutral deuterium particles and Z means the bulk plasma impurities. I_BES is the intensity of the beam emission spectra and Q_BES is the BES collision cross-section coefficient.

The light from BES emissions can be analyzed in several ways. For instance, when using fast light detectors and bandpass filters, microsecond (ms) scale turbulent fluctuations can be investigated [42]. In contrast, when emission spectra are collected using, for instance, a spectrometer and a CCD camera, then the MSE structures can be extracted and analyzed to determine magnetic field quantities. Indeed, each energy component produces spectral line splitting due to the interaction of the beam atoms with the magnetic field. Moreover, the fractions of the beam energy species (E, E/2, E/3 and maybe E/18) can be determined from such spectra by the intensities of the different energy components (E, E/2, E/3 and sometimes E/18) [43]. In this work, we model the spectra of each component to find parameter settings, like the energy ratio for spectral line splitting. NBI is accompanied by a neutral cloud (halo) along its injection path. The diagnostic port plug window in the midplane is behind the NBI, as seen in figure 1(d), so spectra are red-shifted in wavelength, and FIDA spectra overlap with the MSE spectra in HL-2A. An accurate MSE spectral splitting model relies on well-modelled FIDA spectra. In HL-2A, the FIDA spectra are much lower in intensity than the MSE spectra and there are passive contributions from the edge (PCX-edge). Establishing an accurate MSE spectral splitting model is also essential for FIDA spectra analysis.

The Lorentz electric field E_L due to the NBI can be calculated from the neutral beam particle velocity and magnetic field interaction, as shown in equation (7). We use equations (8) and (9) to calculate the spectral splitting ∆λ due to the Stark and Zeeman effect.

whereE_L is the Lorentz electric field due to NBI injection, V_beam is the neutral particles' velocity, B is the magnetic field, including the toroidal B_τ and the poloidal B_p, ∆λ is the spectral line wavelength splitting, h is the Planck constant, e is the electron charge, $m_{\mathrm{e}}$ is the electron mass, λ is the centre wavelength of the spectral, g is the Lande factor, and M is the magnetic quantum number. The angle between the LOS and the E_L determine the splitting spectral intensity ratio between I_π and I_σ, which can be used to calculate the safety factor q, as shown in equations (10) and (11). We reconstruct the splitting spectral caused by E_L and calculate the q with the spatial profile.

where I_π is the intensity of the π component in the Stark splitting, I_σ is the σ component, θ is the angle between the LOS and the E_L, and the correction factor T_f is the π to σ transmission ratio for the optical chain system. We assume T_f = 1.0 here, which means that the diagnostic system has the same sensitivity for I_π and I_σ polarized light. Note that this value introduces diagnostic system errors, especially when introducing the first mirror, which we describe in detail in section 3.2. θ₀ is the angle between the LOS and E_L without the poloidal magnetic field B_p, and q = aB_τ/RB_p, the pitch angle of the magnetic field α = arctan (B_p/B_τ). Appendix A shows the safety factor q calculation process.

Magnetic fields give rise to spectral Zeeman splitting in P-VSD. Since the magnetic field strengths in the divertor, B_divetor, and at the wall, B_wall, are different, light from the SOL can be distinguished from light from the divertor by analyzing the Zeeman splitting. Figure 2 shows the Zeeman splitting testing versus different temperatures (T) and magnetic fields (B). The Zeeman splitting is more significant in the edge region with a lower temperature (B_t ≈ 2.8 T under the T_i ≈ 0.6–1.2 eV). The result shows that lower temperature and higher magnetic fields are beneficial to distinguishing the Zeeman splitting.

Figure  2.  (a) Zeeman splitting at different temperatures 0.078125–5 eV. The temperature of 0.078125 eV is approximately the HL-2A vacuum vessel baking temperature of 300 K. (b) Zeeman splitting at different magnetic field strengths 0.7–2.8 T.

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2.2.2   HL-2A parameter profile

The HL-2A tokamak has a major radius R=1.65 m, a minor radius a = 0.4 m, a toroidal magnetic field B_τ = 2.8 T, plasma current I_p = 480 kA, electron density n_e = (1–3.5)×10¹⁹ m^-3, NBI duration time 500 ms, heating power of LHCD 2 MW, ECRH 3 MW, ICRH 1 MW and NBI 1–2 MW, and the angle between the mid-plate window and the NBI is about 52.1 degrees. An optical grating of 1800 grooves per mm is used for the spectral analysis, and an optical fibre system is installed on a spectrometer that can transmit the light to the electron-multiplying CCD (DU888, 1024×400 pixels) camera. The simulation parameters are consistent with the experimental parameters [31], where the CCD quantum efficiency is 90%, F_# = 2.8, optical throughput is 0.1, integration time is 12.5 ms, slit height and width are 0.2 mm, optical grating dispersion is 0.115 A per pixel, CCD pixel area is 16 μm×16 μm, ion and electron temperatures T_i and T_e are 1.0 keV, toroidal rotational velocity V_τ=-120 km s^-1 (the negative sign means that the particle is moving away from the observer and the wavelength redshifts), and poloidal rotational velocity is V_p=0–20 km s^-1 in r/a=0.0. The NBI power is 22.5 keV amu^-1 for H, the beam (D) divergence is 15 mrad and the current I_beam = 8 A. Due to the resolution of the HL-2A poloidal diagnostics layout, the poloidal rotation velocity V_p cannot be accurately measured in the core region. Based on the experimental results of V_p in the edge of HL-2A [44] and other tokamak devices [45], the initial value of the poloidal rotation velocity V_p on the plasma magnetic axis is set to the range from 0 to 20 km s^-1. Note that this parameter can be adjusted according to experimental results.

Figure 3 shows the relationship between the physics parameters and normalized minor radius r/a. Figure 3(a) gives the I_π/I_σ ratio profile in the MSE spectra simulation, which reaches a minimum peak at r/a ≈ 0.5. Figure 3(b) gives the spectra Lorentz split profile versus r/a. This value increases with the r/a and is nearly stable at the edge region r/a ≈ 0.8. Equations (7) and (8) show that ∆λ_stark splitting is sensitive to V_beam, B and λ₀. Since the beam velocity V_beam is constant for each energy component and does not vary with penetration depth into the plasma, λ₀ is constant, and B is lower at the r/a=1.0 than that at r/a=0.0, then the angle between V_beam and B (E_L=V_beam×B), might account for the increasing Lorentz split. The E and B are perpendicular to each other, and the neutral beam particle velocity direction V can be obtained according to the injection angle of the NBI (disregarding the spread of the velocity vectors representing the injected neutral beam). The observation angle β between the LOS and V_beam can be calculated according to figure 1(d). Therefore, by calculating the angle θ between LOS andE using the I_π/I_σ ratio from equation (10), we can calculate the angle between V_beam and the magnetic field B. The geometric relationship of the angles can be obtained from appendix A.

Figure  3.  Relationship between the physics parameters versus normalized minor radius r/a: (a) I_π/I_σ ratio, (b) spectra Lorentz split, (c) BES emission doppler shift, (d) the attenuation of the NBI with the halo, (e) HL-2A beam attenuation 2D profile, and (f) 2D HL-2A halo attenuation profile.

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Figure 3(c) gives the BES doppler shift versus r/a. Doppler wavelength shift (full beam energy E) results from wavelength shift caused by relative motion to the observer. We can see from formula (4) that V_beam and λ₀=656.3 nm are constant, and the angle β can be calculated according to the observer's LOS layout and V_beam. We can see that the Doppler wavelength shift ∆λ, which is significant in the core, gradually decreases as the normalized minor radius (r/a) increases. Figure 3(d) gives the different NBI (halo) energy attenuation profiles. The NBI attenuation for different energy components (designed power fraction for E (68%), E/2 (19%) and E/3 (13%)) is also given in figures 3(d) and (e). The neutral beam particles interact with the bulk plasma ions (charge-exchange process), and the ionization density of the neutral beam increases, so the neutral beam density gradually increases as r/a decreases. The deeper into the core region, the more substantial neutral beam density attenuation, which reduces the neutral beam heating effect in the core.

It should be noted here that in figure 3(d), the region of r/a > 0.95 is the NBI position, so the density of the particle beam dropped. Figure 3(e) gives the 2D profiles of the NBI attenuation process with the density profile, and the left axis shows the divergence in the perpendicular direction. Figure 3(f) is the NBI–halo attenuation 2D profile.

3.   Results and discussion

3.1   Zeeman splitting in P-VSD

The Zeeman splitting model is adopted to resolve the overlapping issue of the divertor and SOL's reflected spectra. The SOL has a different magnetic field from the divertor. In the case of the LOS that looks downwards towards the divertor (P-VSD) in figure 1(a), reflected light comes mainly from the inner-wall (SOL). Using the Zeeman splitting model, we simulated the Zeeman splitting in the SOL and divertor regions with different B_wall and B_divertor. Different magnetic fields help distinguish the signal and reflected light. Zeeman splitting helps identify reflected light and thus provides a reference for edge P-VSD. It should be noted that the light in the divertor region is directly observed. The plasma velocity in this region is small, so there is a slight wavelength Doppler blue wing due to the observed divertor region where the plasma may be close to the viewpoint.

Given that the Doppler broadening of passive spectral lines (∆λ_Doppler < 0.214 nm for Balmer H_α and D_α) is small due to the low temperature (< 50 eV), the Zeeman splitting can be detected in the experimental spectra with better resolution. The temperature in the edge assumes a warm component (50 eV) and cold component (< 3 eV) [46, 47]. The edge spectral line parameters (wavelength broadening, wavelength shift, wavelength splitting and spectra intensity) in the divertor and SOL are modelled. Spectral reconstructions can be obtained for different particle compositions (H/D), different positions (divertor, SOL) and different temperature (cold and warm components) models.

The principle of distinguishing between different sources of reflected light is as follows: for different magnetic fields, light from the wall has a different Zeeman splitting from that from the divertor. The light from the divertor and the inner-wall reflection are marked as 'div' and 'wall'. H 656.28 nm and D 656.10 nm spectral lines in the divertor and inner wall (SOL) are used to calculate the H/D ratio. According to the Zeeman splitting models, we established the I_π and I_σ of the cold and warm components in the divertor and wall regions.

In this model, the Gaussian curve spectra are added together to form the total spectral curve, and its profile is compared with the experimental spectral curve so that the mean square error is minimized to meet the fitting accuracy. In figure 4(a), we choose a magnetic field of the divertor B in the range of 1.6–2.0 T, a edge hot component temperature of 15 eV and a cold component temperature of 0.3 eV, with H_α/D_α spectral lines. The red legend 'meas. spec' curve means the sum spectra from the hot, cold, D, H, divertor and SOL components. The left lines are the spectral lines of D 656.10 nm, and the right lines are H 656.28 nm. Figure 4(b) shows the experimental spectral reconstruction in the downward divertor of P-VSD. The experimental fitting model contains cold and warm components, divertor and wall regions, and H/D spectral lines with Zeeman splitting. They are superimposed by setting Gaussian curves to simulate different polarization components to form the sum spectral curve. The reconstructed sum curve is compared with the experimental one to minimize the mean square error. The following plasma parameters were obtained in this simulation: B_div ≈ 1.8 T, B_wall ≈ 0.675 T, H/D ratio in the wall = 5.039 and H/D ratio in the divertor = 1.632.

Figure  4.  (a) Simulated HL-2A divertor and SOL H/D spectral lines in P-VSD. Zeeman splitting of the H/D spectra and the overall edge spectral profiles are established in the divertor and wall regions with different splitting components (I_π and I_σ) according to temperatures (warm and cold), respectively. (b) Experimental HL-2A divertor H/D spectral lines in P-VSD. The reconstructed Zeeman splitting spectral line profiles of the experimental and simulation results are nearly consistent.

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It should be noted that the FIDA spectra are also included in the experimental spectra, which are mainly from the NBI heating, and the ion cyclotron resonance heating in HL-2A, as shown in figures 4(b) and 5(b). The HL-2A FIDA spectra intensity is much lower than MSE and the passive spectra (PCX in edge), so the FIDA is not considered in the simulation. Spectral splitting provides a reference for distinguishing the collected light from the divertor and the reflection light from the wall (SOL), as shown in figure 4. The relative errors are from the divertor magnetic field (0.3%), inner-wall magnetic field (5%) and hydrogen-deuterium ratio (2.9%) in the simulation. The results verify the spectral splitting model for experimental spectra reconstruction.

3.2   Stark splitting in A-VSD

The MSE diagnostic spectra are from interactions between neutral beam particles (H/D), plasma electrons and plasma impurities. It has a higher velocity related to the beam energy and thus has a significant Doppler wavelength shift. Since the observation LOS is back from the NBI, the particles are away from the observer. Thus, the observed spectra show a Doppler red wing in HL-2A (wavelength redshift, long-wavelength shift).

Figure 5(a) shows the HL-2A MSE spectral simulation in r/a=0.95. The models have included the PCX and the spectra at three energies (E, E/2, E/3). The I_π/I_σ ratio for different polarization in the Stark splitting is due to E_L. Figure 5(b) gives the experimental reconstruction of MSE spectra for #19680 track 9 (r/a ≈ 0.7), in which all spectral models used the Gaussian curve but gave variable parameters for splitting spectra models: centre wavelength (λ), spectral intensity (I_λ) and Doppler wavelength shift (λ_d). We need to superimpose all spectral lines to ensure that the difference between the sum of Gauss curves and the experimental curve is the smallest to meet the best fitting requirements and minimize the mean square error.

Figure  5.  (a) HL-2A spectral simulation of MSE in r/a=0.95. Simulation of the spectra (MSE) of neutral beam ions in the magnetic field by Stark spectral splitting. The model includes three energy components (E, E/2, E/3) splitting spectra, different splitting components (I_π and I_σ), halo spectra, and edge passive charge-exchange spectra (PCX). (b) Experimental reconstruction of MSE spectra splitting for #19680 track 9 (r/a ≈ 0.7). Combining the experimental D⁺, CII, FIDA and bremsstrahlung spectral lines, we reconstructed HL-2A experimental spectra with the MSE spectral model developed in the simulation.

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Spectra line emissions from carbon, CII (657.8 nm and 658.2 nm), FIDA spectra and bremsstrahlung radiation also appear in the experimental spectra, which were collected during discharge #19680 of HL-2A. The bremsstrahlung radiation originates in the bulk plasma due to the deceleration of electrons. Its wavelength profile, which is a continuum, is determined by electron density n_e = (1–3.5) × 10¹⁹ m^-3 in HL-2A, electron temperature T_e, and the Z_eff of the plasma (Z_eff is effective charge number and it provides a measure of impurity content in the plasma) [48]. The intensity of bremsstrahlung is much lower than the spectral intensity of MSE and edge PCX, which has little effect on the MSE results. We did not account for bremsstrahlung spectra in the MSE. However, it cannot be ignored when the electron density increases, for example, as at ITER.

The simulation code used the following monotonic fitting function for the HL-2A positive shear scenario q profile: q(r/a)=q(on axis)+[q(boundary)-q(on axis)]×(r/a)² [31, 32]. The q profile is given an initial set of parameters q(on axis) and q(boundary) by the MSE core and edge diagnostics results. Note that due to the high SNR of the core, the error is small, but due to the stray light in the edge area and the angle of the LOS, the diagnostic error is significant, and we find suitable initial setting parameters, especially for q(boundary) value. From the MSE diagnostic experiment results, we set initial q(0) to 1 and q(a) to 3.

The MSE spectra simulation model is illustrated in appendix B. Collisional radiative Marchuk MSE level population modelling gives the relative intensity ratio for the simulated q profile [49]. The relative intensity ratios included: I_σ1/I_σ0, I_π2/I_π3, I_π4/I_π3, and the I_π-total/I_σ-total, which have a close relationship with n_e and E_collision. The simulation code SOS can give the n_e radial profile, and the E_collision can be derived from E_NBI. References [31, 32] give the modelling for the component's intensity. We compare Lorentz angle θ and the total MSE spectra with the experimental one, update the q(0) and q(a) initial settings, and scan the best function curve that simulates the q profile. Figure 6 gives the simulation of HL-2A-T Lorentz angle θ versus normalized minor radius r/a, and figure 7 gives the simulation q profile compared with the experimental #19680 one.

Figure  6.  Simulation of HL-2A-T Lorentz angle θ versus normalized minor radius r/a with a simulation error bar. The pitch angle α = π/2–θ shows that the maximum pitch angle is 6° on the edge and 2° in the r/a = 0.

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Figure  7.  HL-2A experimental reconstruction of the safe factor q profile from the MSE spectra of #19680 compared with simulation results.

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The q profile for #19680 in the radial position (0.0 < r/a < 0.75) and the comparison with simulation results are given in figure 7. The relative errors between the experimental and simulation results are small for 0.0 < r/a < 0.25 but increase gradually for 0.25 < r/a < 0.75. A lower relative error is achieved in the core region because the MSE spectra have more significant Doppler shifts, which helps to distinguish MSE spectra from the edge. The LOS for the experimental MSE spectra is affected by reflection and stray light on the edge, where the spectra are integrated and have more than one reflection and stray light, which means the spectra overlap in the edge region. We tried to utilize the Zeeman splitting models to improve the accuracy of diagnostics in the edge region. However, using the Zeeman splitting model in the core region is challenging because the low spectral splitting line resolution due to the high plasma temperature induced significant Doppler broadening enhancement in the core region, as discussed in section 2. Zeeman splitting can reduce the effect of reflected light on the edge for P-VSD.

Another source of systematic error is from the I_π/I_σ ratio measurement. We assume that the diagnostic system has the same sensitivity for π and σ polarized light, T_f = 1 in equation (10). However, this assumption causes a system error [50]. The reason is that a first mirror (FM) is introduced for HL-2A MSE diagnostics and adopts aluminium (Al) as the substrate with silver (Ag) reflection film. We measured all diagnostic channels' MSE optical chain transmittance with a He–Ne laser (650 nm) R > 95%. The error mainly originates from the FM in the MSE optical chain. Since the FM is subjected to the sputtering deposition of plasma ions in a plasma environment, films or defects will be generated, resulting in a polarized light I_π/I_σ ratio change. A comparison with the measured line ratio suggests that the reflectivity of the aluminium mirror was reduced by about 24% for σ components relative to π components in pulse #19949 on the JET [51]. Measuring the change of the polarization light reflection by the FM to determine its influence on the HL-2A q profile is essential work for the future.

4.   Conclusions

We have studied the Lorentz electric (E_L) and magnetic (B) fields' influence on the VSD in the HL-2A tokamak. Spectral Stark splitting in MSE diagnostics during NBI provides an accurate physical model for the diagnostics of safety factor q in A-VSD, and the Zeeman splitting solves the influence of reflected light on P-VSD in the divertor to promote diagnostic accuracy. P-VSD primarily monitors the divertor region, but the reflected SOL region Balmer H_α (656.10 nm) and D_α (656.28 nm) spectra, which undergo different spectral Zeeman splitting and slight Doppler broadening and shift, have an impact. A-VSD concentrates on Doppler-shifted beam emissions, including bremsstrahlung, fast-ion loss emissions, MSE and impurity emission (CII) spectra.

The Zeeman effect caused visible spectral splitting in a magnetic field (B), and reconstruction spectra fitting has been studied in this work. The non-negligible reflected light from the wall (SOL) influenced the diagnostic results. We modelled the divertor and inner-wall spectra to reconstruct the spectra of different components. The relative errors of simulation and experimental results are from the divertor magnetic field (0.3%), inner-wall magnetic field (5%) and hydrogen-deuterium ratio (2.9%). The results related to the H/D ratio are consistent, which verifies the accuracy of our spectral splitting model.

The results of the q profile obtained from simulation and experiment show that the MSE model with spectral Stark splitting verifies the spectral reconstruction in the experiment. However, the simulation code did not add bremsstrahlung, FIDA and CII spectra. The relative errors of the experimental and simulated results gradually increase in the region of 0.25 < r/a < 0.75. The spectra at the edge are easily affected by reflection and stray light, which increases the experimental diagnostics error. A lower relative error is achieved in the core region because the MSE spectra have more significant Doppler shifts, which helps to distinguish such structures from passive edge structures (PCX). The results obtained by the simulation and experiment diagnostics are compared, verifying the model's reliability and providing a reference for the future diagnostics of VSD in HL-2M.

Appendix A

The solution derives the safety factor q from MSE diagnostics spatial and physical vector diagram.

Angle definitions:

α is the angle between B and B_τ;

β is the angle between LOSand V(NBI);

γ is the angle between V(NBI) and B_τ;

θ is the angle between LOSand E_L;

Φ is the angle between LOSand B;

The relationship between the angles:

where E_L and B are perpendicular to each other. LOS, V(NBI) and B_τ are in the midplane, and the B_p is in the vertical direction.

So, we have:

where pitch angle α=arctan (B_p/B_τ).

In HL-2A, β ≈ 52.1°, and γ≈127.8° in the diagnostics layout, as shown in figure 1(d), so β+γ ≈ 180°, equations (A1) and (A2) can be written as:

So, we have:

where θ₀ is the angle without the poloidal magnetic field B_p. In figure A1, V(NBI) and B_τ are both in the midplane, and the E_L0 (E_L without B_p) is in the vertical direction, so the angle between LOSand E_L0 is θ₀ = π/2. From equation (A6), the θ₀=π/2, while α=0.

  A1.  MSE diagnostics spatial and physical vector diagram.

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Appendix B

Collisional radiative Marchuk MSE level population modelling is used to reconstruct the MSE spectra [31, 32, 49].

with:

Normalization requires:

Alternatively, rewriting the equation in terms of established line ratios:

Introducing the σ-π line ratio:

or:

The normalization is rewritten as:

Therefore, the I_σ0 component can be expressed entirely in terms of the multiplet sub-level line ratio and I_π-total/I_σ-total group ratio, and R can be obtained from the Lorentz angle θ or safety factor q.