Experimental investigation on high heat flux plasma parameters of HIT-PSI device in argon discharges

1.   Introduction

One of the paramount challenges to steady-state magnetic fusion reactor operations is the performance of plasma-facing materials/components (PFMs/PFCs), which is required to withstand the extreme conditions encountered in advanced tokamaks [1–4]. These materials and components must endure intense particle flux and significant heat flux, as their durability and effectiveness crucial to achieve long-duration, high-performance operations in future fusion devices [2–4]. PFMs/PFCs must cope with the significant heat deposition and high particle flux impact generated by the plasma, necessitating materials/components capable of rapid heat dissipation over prolonged periods [3, 4]. Additionally, the continuous particle bombardment results in sputtering and material erosion, adversely affecting their lifetime and functionality, and posing significant challenges to the long-term capability of these materials/components. The thermal protection materials on spacecraft must also exhibit excellent thermal resistance in high heat flux and high enthalpy plasma environments, for key performance indicators including ablation rate, thermal conductivity, and structural integrity [5–7].

Various international facilities have already been employed to test material performance under high heat flux environments, each offering unique advantages and technical characteristics. MPEX [8, 9] in the United States utilizes a helicon wave source, with multiple plasma heating methods and superconducting magnets to achieve high particle and high heat fluxes, and for testing neutron-irradiated materials. Magnum-PSI [10, 11] in Europe employs a cascaded arc source, operating with strong magnetic fields (up to 2.5 T) and a high-performance vacuum system to simulate the heat and particle fluxes in ITER divertor region. It is the only linear plasma device in the world capable of delivering over 40 MW/m² of continuous heat flux for several hours with hydrogen, offering an optimal platform for studying material surface interactions and thermal fatigue. The NASA Ames Arc Jet Complex [12] has over 40 years of experience in thermal protection systems and has seven test bays. It can generate and control various high-temperature gas flow conditions to simulate the extreme heat flux encountered during spacecraft reentry. It focuses on simulating high-temperature gas flows, validating spacecraft designs and testing the thermal resistance and ablation performance of thermal protection materials [13]. These advanced facilities, with their capabilities to handle high heat and particle flux, offer critical support for testing materials performance and assessing durability in extreme conditions, thus driving advancements in fusion energy research and aerospace technology.

The Plasma-Surface Interaction Research Platform at Harbin Institute of Technology (HIT-PSI) [14] has been developed, aiming to generate plasma beams with stable heat flux to effectively replicate the operational conditions in divertor region expected in future tokamaks and for thermal testing of spacecraft surface materials. The design of HIT-PSI follows the technical approach of Magnum-PSI [15]. Comparatively, we have adopted a compact design characterized by low cost, low energy storage for superconducting magnets, and comparable heat flux level to provide a valuable complement in PSI research. One can expect its contributions to the development of fusion-related technologies by offering a versatile and efficient platform for PSI studies. Besides the primary research areas of HIT-PSI in fusion studies, argon discharges in HIT-PSI can still provide a flexible and valuable environment and reference for heat flux testing of relevant materials in other areas, such as aerospace materials tests and surface modifications by irradiations. This paper presents the preliminary results of argon discharges in HIT-PSI, which may be used to support irradiation experiments with high heat and particle fluxes while also facilitating fundamental plasma physics research under strong magnetic fields. Here in this work, we have utilized a water-cooled probe specifically designed for high heat flux environments to measure argon plasma parameters over a wide axial range under a magnetic field of up to 2 T. Critical information such as potential and electron energy probability functions in this range has been obtained. Additionally, the infrared camera has also been utilized to quantify the heat flux resulting from beam bombardment on the graphite target. Combined with emission spectroscopy data, the transport characteristics of the argon plasma beam have been analyzed. The research results can assist in understanding the transport characteristics of argon beams in strong magnetic fields and provide valuable references for studying high heat flux plasma environments.

The layout of the paper is as follows. After introduction, experimental setups for HIT-PSI and diagnostic equipment are presented in section 2. Then in section 3, feature measurement results are shown and discussed. Finally, the paper concludes with a summary in section 4.

2.   Experimental setup

As shown in figure 1, HIT-PSI is equipped with a single-channel cascaded arc plasma source, combined with a superconducting magnet to produce a steady magnetic field of up to 2.5 T, with a uniform magnetic field region extending over 1 m. The details of the HIT-PSI design can be found in reference [14], and the newly upgraded two-dimensional movable target support platform is assembled to adjust the position of the substrate downstream, and can move to any axial position beyond 25 cm from the plasma source outlet. The vacuum chamber has an inner diameter of 0.35 m and a total length of over 2.6 m. A screw pump and a dual Roots pump set with pumping speed of 2500 L/s maintain the vacuum chamber conditions, and the relationship between the chamber neutral pressure and the argon gas flow rate is shown in figure 2(a). The typical magnetic configurations for experiments in this study are shown in figure 2(b) as Condition 1 with coil current of 230 A (C1) and Condition 2 with coil current of 170 A (C2). Correspondingly, the central magnetic fields of C1 and C2 are 2.0 T and 1.5 T, respectively. A mass flow controller is applied to regulate the gas flow rate at 1.4 L/min, with the corresponding pressure of 3 Pa, measured by an Inficon CDG025 capacitance diaphragm gauge with a full scale of 13.3 Pa.

Figure  1.  The schematic diagram of HIT-PSI.

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Figure  2.  (a) The relationship between argon gas pressure and argon flow rate, (b) two typical magnetic configurations used for experiments.

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To diagnose the plasma parameters, a water-cooled planar Langmuir probe is used with the full-tungsten design similar to ITER divertor Langmuir probe (DLP) by Southwestern Institute of Physics, China (detailed in reference [16]). The probe head has a diameter of 2 mm, combined with water cooling to withstand heat flux exceeding 10 MW/m². Additionally, a 100 mm×100 mm tantalum plate is installed in front of the probe, connected to a water-cooled copper block to protect the probe circuitry and cooling system from the heat flux impact. The tantalum plate and water-cooled copper block, which are fixed on the two-dimensional movable target support platform, are both connected to the chamber and grounded. Their range of movement is from 25 to 121 cm from the outlet of the source, spanning between Window 1 (W1) and Window 2 (W2). The infrared camera used to measure the heat flux is located at W1, and the specific parameters of the infrared camera and experimental settings are installed as in reference [17].

The optical emission spectrum is collected by a Princeton Instruments spectrometer SP-2750, paired with an ICCD (MAX4 1024i). Two diffraction gratings are utilized, including a groove density of 1200 grooves/mm with a blaze wavelength of 500 nm and a groove density of 2400 grooves/mm with a blaze wavelength of 240 nm. The optical fiber is a UV-VIS (ultraviolet-visible) fiber bundle, model LG-455-020-3, while the lens is a fused silica plano-convex type with a diameter of 50.8 mm and a focal length of 200 mm. Wavelength is calibrated by calibration light source AvaLight-HAL-CAL-Mini. Intensity calibration is conducted using the intensity lamp of the IntelliCal® System (> 400 nm) and the AvaLight-DH-CAL (< 400 nm). The spectral acquisition positions are at W1 and W2, perpendicular to the flux transport direction and the magnetic field. The radial position of 0 cm for optical fiber collection is the center of the observation window.

3.   Results and discussion

3.1   Diagnosis by Langmuir probe

The steady-state heat flux capacity of HIT-PSI is fairly high, which poses significant damage risks even when using a water-cooled probe. To protect the probe, measurements are taken approximately 5 s after ignition, once the discharge has essentially reached a stable state. Also, the measurements are only conducted in the core of the plasma beam, and an extensive scanning voltage range is avoided, especially at W1. Compared to the 2 mm probe diameter, the electron and the ion cyclotron radii are in the order of 10⁻² mm and 10 mm, respectively, presenting a typical strongly magnetized case. The ion current can then be described as [18]

where k = 0.49, e is the elementary charge, A_s is the projection of the effective area of the collecting probe aligned with the magnetic field line, m_i represents the ion mass, and T_e is the electron temperature. A strong magnetic field alters the motion of charged particles within the plasma, leading to partial distortion of the electron flux. Electron temperature is derived using a four-parameter fitting model as follows [19]

where I is the probe current, I_s is the ion saturation current, R is a parameter for the variation in ion collection area with voltage, V_f is the floating potential, V is the applied probe voltage, and k_B is the Boltzmann constant. Among them, I_s, R, V_f, and T_e are the fitting parameters. Electron energy probability function (EEPF) in the strongly magnetized plasma can be obtained by using the first derivatives of current and voltage formulas [20]

where m_e is the electron mass, L is the characteristic length scale of the probe, R_Le is the probe radius, and dI_e/dV is the derivative of the electron current with respect to the probe voltage. During the differential process, appropriate smoothing of the data to avoid notable discrepancy in calculating the derivation was applied.

Figure 3 shows the current-voltage (I-V) characteristics curves at a typical condition, C1, with a discharge current of 130 A at W1 and W2 (a), and its corresponding first derivative (b). At W1, as the scanning voltage continuously increases from negative values, the electron current exhibits a remarkable increase. The I-V curve deviates early from the exponential form and almost increases linearly. At W2, the ratio of nearly saturated electron current to the ion current is ~ 5, whereas at W1, the electron current is still increasing, and the ratio has already exceeded this value. This indicates that in regions with higher electron density and temperature, more electrons are collected by the probe. It should be noted that this type of probe directly obstructs the plasma beam, leading to a considerable difference for the plasma state in front of the target compared to the free beam. As illustrated in figure 1, the plasma exhibits a noticeable color change in front of the target, complicating the determination of whether the observed growth in the electron current is attributable to localized perturbations or alterations in the probe sheath. The expansion of the probe sheath, especially the radial expansion perpendicular to the magnetic field and the probe surface, will clearly alter the effective collection area of the probe. According to the flush probe theory, the lateral expansion of ions is $\delta \approx 0.25{\lambda _{\text{D}}}|V{|^{3/4}}/\sqrt {\sin \theta }$ [21], which varies with the potential difference between the plasma and the probe. However, there is currently no definitive and comprehensive model for electrons.

Figure  3.  Typical I-V characteristics (a), first derivative (b), and EEPF (c) at W1 and W2 with C1 at 130 A.

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It can be observed from figure 3(c) that the measurements in the high-energy range of C1 at W2, with a discharge current of 130 A, show an upward trend. Due to the large particle flux and heat flux, it is challenging to distinguish energetic electron fluctuations from noise. While at W1, electrons are non-Maxwellian, indicating a lower population of energetic electrons. The subsequent spectroscopic measurements can provide an explanation. Neutral gas enters the plasma source from the outside, followed by arc discharge between the cathode and anode within the plasma source. The pressure inside the plasma source channel could be high to reach a level up to several thousand Pascals [22]. Intense collisions occur within the channel, with most energetic electrons participating in ionization and collision excitation, resulting in remarkably strong ion lines in spectroscopic measurements near the source exit. As the transport develops, electrons undergo more collisions, leading to energy reduction and equilibration. Consequently, the electron energy distribution approaches the Maxwellian distribution.

The water-cooled probe is moved along the axis to diagnose the electron temperature and density over a length of nearly 1 m, and results are shown in figure 4. Both the electron temperature and density decrease along the transmission direction. In the upstream region near the outlet of the source, due to higher electron temperature, diffusion and collision losses are more severe, and the plasma pressure gradient is large, resulting in more rapid decline in the first half. As the current increases at the same magnetic field, the electron temperature and density slightly rise. Under stronger magnetic fields, both parameters increase further. This is also reflected in the output power of the discharge power supply, which is higher with increased magnetic field strength and current. The energy loss of the beam is more effectively suppressed with a strong magnetic field, as it more effectively confines the plasma, reduces radial diffusion perpendicular to the field direction, and decreases the collision frequency with background neutral particles, thereby better maintaining the beam energy.

Figure  4.  Probe measurements of the electron temperature (a) and density (b) at different axial positions using four-parameter fitting.

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Based on the plasma parameters measured by the probe, we can roughly estimate the characteristic frequency [23, 24]. The neutral gas density is set to 10¹⁹–10²⁰ m⁻³, and the gas temperature is set to 5000 K (obtained by fitting the actual measured OH spectral lines in the range of 304–314 nm, approximately 6000 K at W1 and 4500 K at W2, and 5000 K is chosen for estimation here). The electron-atom elastic collision cross-section, obtained from reference [25], is 4×10⁻²⁰ m². The collision frequency parallel to the magnetic field is approximately ${\nu }_{\mathrm{e}\mathrm{n}}=n\sigma {v}_{\mathrm{t}\mathrm{h}}\sim 1{0}^{5}\;\mathrm{H}\mathrm{z}$. The cross-section for collisions between argon ions and neutral particles is selected from reference [26], ${\nu }_{\mathrm{A}{\mathrm{r}}^{+}\mathrm{n}}=n\sigma {v}_{\mathrm{t}\mathrm{h}}\sim 1{0}^{6}\;\mathrm{H}\mathrm{z}$; the electron-ion collision frequency is ${\nu }_{\mathrm{e}\mathrm{i}}\sim \dfrac{{Z}^{2}{e}^{4}{n}_{\mathrm{i}}{\mathrm{ln}\Lambda }_{\mathrm{e}\mathrm{i}}}{{\left(4{\text{π}}{\epsilon}_{0}\right)}^{2}{m}_{\mathrm{e}}^{1/2}{T}_{\mathrm{e}}^{3/2}}\sim 1{0}^{9}\;\mathrm{H}\mathrm{z}$. It is apparent that electrons collide with ions far more frequently than with neutral particles, thus engaging in frequent energy transfer to the ions, resulting in a minimal temperature difference between the two. It has been reported that the ion temperature is slightly lower than the electron temperature [27], which is beneficial for the maintenance of the heat flux. The elastic collisions between neutral gas and ions have higher heat transfer efficiency, and the energy loss of the beam mainly originates from this.

In figure 5, the plasma potential and floating potential measured by the probe are shown. Results are very close to the data measured in reference [28] , where V_f is close to zero, and taking the zero-point of the first derivative as V_p, it is positive. This shows a significant difference compared to the potential of hydrogen plasma, where V_f is typically negative by several tens of volts [29, 30]. It is possibly due to that a detachment-like state may have formed between the argon plasma beam and the target probe. The floating potential V_f gradually increases from the proximal to the distal end. Undoubtedly, the overall electron temperature and density should decrease during transmission. Then, the increase in V_f is likely indicative of an increase in the energetic electron component. Under the C2 magnetic field, the floating potential changes from negative to positive. The increase of energetic electrons indeed causes V_f to rise [31]. The measured V_p is positive and higher at positions closer to the source, which is quite unexpected and contrary to the predicted cathode source plasma potential. The cathode of the plasma source is at a negative voltage, while the distant end (chamber, target probe, etc.) can be considered grounded. According to this model, the plasma potential should gradually increase from the source to the distant end, but the measured values are the opposite. As shown by the results of the I-V characteristic curve, a more reasonable explanation is that the electron current near the probe is quickly attracted due to sheath expansion and other reasons, causing V_p to shift towards positive voltage. This may also be a primary source of probe error, namely the applicability of the sheath expansion model under such high particle and heat flux.

Figure  5.  Floating and plasma potentials with discharge current of 130 A at different axial positions respectively, while the plasma potential is taken as the maximum value of the first derivative of the I-V curve. The left axis represents V_p, and the right axis represents V_f.

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The plasma parameters measured by the probe allow for the estimation of the heat flux. At C1 and W1 conditions with a discharge current of 140 A, ${n}_{\mathrm{e}}\approx 1.21\times 1{0}^{21}\;{\mathrm{m}}^{-3}$, ${T}_{\mathrm{e}}\approx 4.0\;\mathrm{e}\mathrm{V}$, and assuming T_e = T_i, particle flux can be calculated as [32, 33]

where c_s is the ion acoustic velocity. When graphite serves as the target material, heat flux can be calculated by the following expression [32, 34]

where ${\delta _{\text{e}}} = {(2.72)^2}\dfrac{{{E_0}}}{{{E_{\max }}}}\exp \left[ { - 2{{\left( {\dfrac{{{E_0}}}{{{E_{\max }}}}} \right)}^{1/2}}} \right]{\delta _{\max }}$ is the coefficient of secondary electron emission (SEE) yield, with $E_0=-0.5k_{\text{B}}T_{\text{e}}\ln\left[\left(2\text{π}m_{\text{e}}/m_{\text{i}}\right)\left(1+T_{\text{i}}/T_{\text{e}}\right)\right]+0.7k_{\text{B}}T_{\text{e}}$, and ${\delta }_{\mathrm{m}\mathrm{a}\mathrm{x}}= 1.0$, ${E}_{\mathrm{m}\mathrm{a}\mathrm{x}}=300\;\mathrm{e}\mathrm{V}$. Also, it is very sensitive to surface conditions and topography, and likely to undergo considerable changes during operation of a plasma device. Furthermore, $\varepsilon_{\text{pre}\text{.sh}\text{.}}=0.5k_{\text{B}}T_{\text{e}}$ is pre-sheath voltage drop, ${R}_{\text{iE}}$ and ${R}_{\text{eE}}$ are ion and electron energy reflection coefficients of argon to C for the energy at 10 eV (while no values are available for energies below 10 eV), ${\chi }_{\mathrm{i}}$ and ${\chi }_{\mathrm{r}}$ are ionization and dissociation energy of argon, and ${R}_{\text{iN}}$ is the neutral reflection coefficient for the surface material.

Simultaneously, the two-dimensional heat flux distribution of the deposition heat flux of the argon beam irradiating graphite at W1, under C1 and C2 magnetic fields with discharge currents of 120 A and 140 A, measured by the infrared camera, is shown in figure 6. The pattern of the beam is irregular, primarily influenced by the irregular shape of the nozzle after prolonged discharge and the uneven polishing of the graphite surface. At C1 magnetic field, a faint beam afterglow can be observed to the right of the heat flux spots, attributed to the infrared light emitted from the plasma captured by the infrared camera. In general, the heat flux increases with the magnetic field and discharge current, to a level around 4 MW/m², showing a significant discrepancy from the heat flux estimated with the parameters measured by the probe mentioned above. In comparison, with the same magnetic field and current, the heat flux of helium plasma discharge measured by the infrared camera can exceed 20 MW/m² [17].

Figure  6.  Typical two-dimensional heat flux distribution at the C1 and C2 magnetic fields with discharge currents of 120 A and 140 A. (a) 120 A at C2, (b) 140 A at C2, (c) 120 A at C1, (d) 120 A at C1.

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The sheath heat transmission coefficient is introduced to quantify these differences. Based on the plasma temperature and density obtained from the probe measurements, and by substituting the heat flux calculated at the probe (q_probe) with the heat flux measured by infrared (q), the sheath heat transmission coefficient is calculated using the following formula [32]

The relevant parameters for the four discharge conditions corresponding to figure 6 are shown in table 1. The sheath heat transmission coefficient $\gamma$ calculated from the plasma parameters of the argon plasma beam, as measured by the probe, is 3–4 times higher than the value derived from the heat flux loaded on the target obtained through infrared camera measurements. This result is in close agreement with the findings in reference [35], where plasma parameters were measured 17 mm in front of the target using Thomson scattering. Due to the effect of plasma sheath, the actual measured boundary conditions of the probe in our experiment are of certain similarity to the cases in reference [35], and differ from that of the graphite target surface, and thus, great discrepancies are observed between the heat flux estimated by probe and that measured by infrared camera. In fact, factors such as surface charge accumulation, surface potential distribution, particle reflection and sputtering, and SEE profoundly impact the sheath structure, directly affecting heat flux deposition. As discussed in reference [35], differences in sheath transmission coefficients may be related to several factors, including the secondary electron emission coefficient, ion-neutral particle momentum exchange, and neutral gas pressure. Additionally, as indicated by the probe measurements above, a detachment-like state probably exists between the plasma beam and the graphite surface, which could also be a reason for the reduced heat flux deposition on the material surface.

Table  1.  Relevant parameters for the four discharge conditions.

Parameters	C2 120 A	C2 140 A	C1 120 A	C1 140 A
ne (m−3)	7.75×1020	1.0×1021	1.15×1021	1.21×1021
Te (eV)	3.396	3.560	3.867	3.980
$\Gamma$ (m−2s−1)	1.80×1024	2.38×1024	2.86×1024	3.06×1024
qprobe (MW/m2)	13.15	18.55	23.58	25.70
${\gamma _{{\text{probe}}}}$	13.84	13.64	13.32	13.22
q (MW/m2)	3.43	3.82	4.26	4.52
$\gamma$	3.50	2.81	2.41	2.30

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3.2   Diagnosis by optical emission spectroscopy

Typical emission spectra in the wavelength range of 400–850 nm at W1 and W2 under C1 with a 130 A discharge current in HIT-PSI are shown in figure 7. The two spectra nevertheless show different patterns. At the position of W1, the spectrum in the short wavelength (high frequency) regime between 400–500 nm is exceptionally intensive, primarily concentrated in the lines of Ar II, such as 4p–4s, 5s–4p, 4p–3d, and 4f–3d transitions, with the energy level differences of ~ 3 eV. Atomic lines are rare and weak in intensity, with only faint W I 420.39 nm and W I 821.02 nm lines observed. At W2, the ion lines are weakened and even essentially disappear. Ar I emissions primarily consist of very strong 2p–1s radiative transitions (atomic energy levels indicated by Paschen notation), along with weak np–1s transitions. The difference in spectra can also be seen easily in the visible discharge color, of bluish-violet at W1 and pink at W2. This indicates a significant change in electron energy between W1 and W2 during the transport process, with the beam energy decreasing rapidly.

Figure  7.  The typical spectra and discharge photos at W1 (a) and W2 (b).

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3.2.1   Zeeman effect

As shown in figure 8, spectral line of Ar I at 696.54 nm is measured at W2 under a strong magnetic field. The line clearly shows a pronounced Zeeman effect, resulting in the splitting of the energy levels, with $\mathrm{\Delta}\lambda_{\mathrm{H}}=0.062\pm1\; \mathrm{n}\mathrm{m}$ for the high field C1, and $\mathrm{\Delta}\lambda_{\mathrm{L}}= 0.047\pm1\; \mathrm{n}\mathrm{m}$ for the relatively lower field C2.

Figure  8.  The measured spectral line of Ar I 696.54 nm. Please note that the relative intensity is undisputed.

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The energy level information is listed in table 2 for this line, with the Landé g-factor measured experimentally [36]. Theoretically, at a strong magnetic field, this line should be split into 9 lines with g₁m₁−g₂m₂ of (0, ±0.123), (1.255, 1.378, 1.501), and (−1.255, −1.378, −1.501) respectively. However, the three lines in each group are very close together, to be experimentally recorded as a single line and assumed to consist of three, to allow the magnetic field to be deduced from the split wavelengths by

Table  2.  Parameters for the 696.54 nm line of Ar I.

$\lambda$ (nm)	E1–E2 (eV)	Configurations	Terms	J1, J2	g1, g2
696.54	11.55–13.32	4s–4p	2[3/2], 2[1/2]	2, 1	1.501, 1.378

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where $\mu\mathrm{_B}$ is the Bohr magneton, $B$ is the magnetic field strength, $g_1$ and $g_2$ are the Landé g-factor for two states, $m_1$ and $m_2$ are the magnetic quantum numbers corresponding to the two states. By applying this formula, we can calculate that the magnetic field in the region where the spectral lines were collected in figure 8 is 1.825 T and 1.383 T, which are in reasonably good agreement with the experiment settings.

3.2.2   Line ratio

The Ar I lines at 415.86 nm, 420.07 nm, 696.54 nm, 738.40 nm, 794.82 nm, and 801.48 nm were to calculate the excitation temperature by the Boltzmann plot method. The selected radiative line at W1 exhibits a typical non-Boltzmann distribution. In contrast, the line at W2 exhibits an approximate Boltzmann distribution, as shown in figure 9(a). The line-averaged electron excitation temperatures at different radial positions at W2, calculated using the Boltzmann slope method, are shown in figure 9(b). Electron excitation temperatures are quite close to the electron temperature measured by the probe at W2, indicating that as the beam transports, the plasma gradually approaches local thermal equilibrium state due to collisions [30].

Figure  9.  (a) Boltzmann plot of selected Ar I spectral lines at W1 (black squares) and W2 (red stars), (b) the line-averaged electron excitation temperatures at different radial positions at W2.

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The argon discharge emission spectrum shown in figure 7 contains a number of ion and atomic lines. Spectral line formation is a complex process influenced by various factors. Thus, by analyzing the line ratios in the spectrum, we can deduce specific processes. When excitations are dominated by electron collisions, the line ratio can be expressed

where, I₁ and I₂ are the intensities of two spectral lines, A₁ and A₂ are the Einstein coefficients of spontaneous emission (transition probability) in respective transitions, g_j and g_k are the statistical weights of energy levels j and k, respectively. R_0j(T_e) and R_0k(T_e) are excitation rates from the ground state (or a reference state) to the energy levels j and k, respectively, depending on the electron temperature T_e, and n₁, n₂ are the number density of particles in the ground state (or the reference state). The ratio of spectral lines excited by electron-atom collisions indicates the trend of electron excitation temperature, while the ratio of spectral lines excited by electron-ion collisions to those excited by electron-atom collisions indicates the trend of electron density when n_e = n_i.

Figure 10(a) shows the radial variation of the 811.5 nm/751.5 nm line ratio. The lower value at the core may be due to a slight offset between the 0 cm position of the observation window and the center of the beam. The line ratio does not directly depend on electron density but is primarily influenced by high-energy electrons, indicating the concentration of metastable state atoms. At W1, the line ratio decreases with increasing radius, suggesting that the plasma is well confined, resulting in a smaller beam radius. At a larger radius of W2, the line ratio increases, indicating the expanded beam radius. Clearly, the edge electron temperature is lower, and the increase in metastable states indicates that electron collision excitation processes have become more prevalent. This increase is likely due to more frequent recombination in this region, which promotes a higher number of high-energy electrons and an enhanced concentration of metastable states.

Figure  10.  Intensity ratios of (a) 811.5 to 751.5 nm lines, (b) 476.5 to 750.4 nm lines.

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Figure 10(b) shows the Ar II 476.5 nm to Ar I 750.4 nm ratio at W1, which can be used to infer changes in the ion-to-atom density ratio. Ion density decreases sharply with increasing radius. The ratio of excited ions to excited atoms increases remarkably at high discharge current, indicating an enhancement in the ionization rate and an increase in density. Combined with probe results, even in the upstream near the source outlet, a stronger magnetic field can still provide better confinement for the plasma, and this effect is very significant.

Recombination features can have a substantial effect on the discharges of different working gases. In the argon plasma discharges analyzed in this work, recombination reactions are mainly the ion-electron and three-bodies as [37]

with ${k}_{\mathrm{r}\mathrm{c}}$ the volume recombination coefficient. In the experiment, a relatively intuitive manifestation is the increase in the intensity of the Ar I spectral line. At W1, the electron density and temperature in the plasma column are relatively high, leading to a lower recombination rate, with the recombination mainly close to the beam edge due to the lower electron temperature. As the beam transmits, the electron temperature and density drop markedly at W2, which makes recombination the primary plasma loss mechanism. Based on the reaction rate, ion-electron recombination and three-body recombination involving argon atoms gradually become dominant. For hydrogen discharges, however, the collision cross-section and rate of the recombination reaction are remarkably different from those in argon discharges [38]. Thus, better vacuum control is required, which should be considered in future hydrogen discharge plans.

3.2.3   H_β broadening

At W1, there are intensive Ar II lines around 486.13 nm, reliable measurement of H_β is not feasible, while measurements at the W2 are more accurate. With a strong external magnetic field, the broadening of H_β is also affected. The impact of the Zeeman effect can be assessed using the following formula [39]

where n is the principal quantum number, n_e is the electron density per cm³, and B is the magnetic field magnitude. The Stark-Zeeman effect, which is the influence of magnetic fields on the perturbed electric field in a plasma, makes the line broadening process exceptionally complicated. By the methodology described in section 3.2.1, and assuming that the broadening effects are similar to each other, the magnetic field caused broadening is calculated. Given g = 2/3 or 4/3, and g = 1, $\mathrm{\Delta }m=\pm 1$, the broadening at 1.824 T and 1.383 T is approximately 0.0201 nm and 0.0152 nm, respectively. Such line broadening follows a Lorentzian line shape [40]. The gas temperature, measured with OH of 306–314 nm and fitted by LIFBASE spectroscopy tool, is approximately 4500 K. By Voigt fitting, the line average densities at C1 and C2 are shown in figure 11(b). The overall trend correlates well with the electron density measured by the probe. At high magnetic fields, the line-averaged density is considerably higher, indicating that the high magnetic field effectively confines the plasma and limits beam diffusion.

Figure  11.  Voigt fitting is performed on H_β (a), and the line-average densities at different radial positions are calculated (b).

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4.   Conclusion

Experiments of argon plasma parameter measurements, both upstream and downstream, have been carried out on HIT-PSI at various magnetic fields and discharge currents. The results can be summarized as follows.

(1) At a high magnetic field of 2 T, the electron density of the argon plasma beam can reach a high level of 10²¹ m⁻³, with the electron temperature up to 4 eV. Thus, the particle flux exceeds 10²⁴ m⁻²s⁻¹, and achieves a heat flux around 4 MW/m² loaded on the target surface. The floating potential measured by the probe is only a few negative volts, which may indicate a detachment-like state for argon plasma beam before reaching the target.

(2) Overall, the electron temperature and density have increased with the magnetic field strength due to the enhancement of the cascaded arc source power, but rapidly decreased during the transport process caused by collision and diffusion. In the upstream region near the outlet of the source, electrons exhibited a non-Maxwellian distribution with a lower population of high-energy electrons, likely due to their involvement in ionization and excitation processes. As the plasma beam has been transported downstream, the energy distribution has gradually approached a Boltzmann distribution.

(3) Significant differences in the emission spectroscopic distribution profiles corresponding to the upstream and downstream regions have been observed, indicating a significant variation in the electron temperature as well as the corresponding collision excitation/ionization processes. Notably, the spectral line of Ar I 696.54 nm has exhibited significant Zeeman splitting, by which the local magnetic field could be calculated accurately in reasonably good agreement with experimental measurements. The variation in line ratios predicted the diffusion of the beam during the transmission process, along with a decrease in ionization degree and electron temperature.

As the starting point for HIT-PSI’s high heat flux beam research, the argon discharge marks a crucial first step and lays a solid foundation for subsequent experiments. In the next phase, HIT-PSI will gradually expand its research scope to investigate high heat flux processes involving gases such as hydrogen (H) and deuterium (D). Additionally, HIT-PSI will focus on developing more advanced diagnostic methods to further improve measurement accuracy and experimental efficiency.