Emission spectroscopy of He lines in high-density plasmas in Magnum-PSI

Helium (He) line emissions have been utilized to measure the electron density ( n e ) and temperature ( T e ), and validity checks have been conducted in various linear devices. In this study, we performed optical emission spectroscopy (OES) of He line emissions in the linear plasma device Magnum-PSI, where the used density range was 1–8 × 10 20 m − 3 , which was much higher than those used until now. We observed nine line emissions in the wavelength range of 388–728 nm and deduced n e and T e based on comparisons with a collisional radiative model. From the variation of the difference between the experiments and calculations, the joint probability distribution of n e and T e was deduced. We will discuss the effect of radiation trapping, in particular, based on comparisons between OES measurement results and Thomson scattering measurements.


I. INTRODUCTION
Helium (He) line emissions from fusion edge/divertor plasmas provide important information for plasma diagnostics. A line intensity ratio method using several He line intensities has been utilized to measure the electron density, ne, and the temperature, Te, in various fusion devices including TEXTOR, 1 JET, 2 LHD, 3 ASDEX Upgrade, 4 and JT-60U. 5 In some cases, a thermal He-beam has been used for diagnostic purposes; 1,6 because He atoms are produced by the nuclear fusion reaction of deuterium and tritium, the emissions will be available even without an additional injection of He atoms from outside in future fusion devices.
Feasibility studies have been mainly conducted in linear devices: NAGDIS-I, 7 MAP-II, 8,9 NAGDIS-II, 10,11 and PISCES-A. 12,13 It has been revealed that radiation trapping is an important effect to understand the population distribution of He atoms. Here, radiation trapping is mainly caused by the re-absorption of resonance lines (1 1 S-n 1 P), where n is the principal quantum number. However, the density range used in the linear devices was mainly less than 10 19 m −3 , which was lower than the actual fusion conditions.
In this study, we performed optical emission spectroscopy (OES) of He lines in the Magnum-PSI device, 14 where the plasma density can be higher than 10 20 m −3 . After describing the experimental setup, we show two typical cases to make a detailed comparison with the collisional radiative (CR) model. For the two cases, it is shown how the difference in the population distribution between the CR model and OES results alters when changing ne and Te used for the CR model. The joint probability distribution will be deduced from the difference between the CR model and experiments. Then, using the joint probability distribution, ne and Te from the OES are compared with those measured by laser Thomson scattering (TS) measurements.

A. Setup
Experiments were conducted in the Magnum-PSI device. We used pure He discharges in the present study; helium gas was fed from the source region for discharge and additional He gas was also introduced from the downstream. Figure 1 shows a schematic of the experimental setup. Magnum-PSI has a TS system, 15 which can measure the radial distribution of ne and Te with a single laser shot.
Recently, a collective TS system was developed to measure the ion temperature and the flow velocity. 16 The laser passed through the vertical windows, and TS signals were observed from a transversal direction. There are other optical ports at the same axial position, and the OES was performed at the same location. A lens collected the emission from the plasma, and the light was transferred to the spectrometer through a mirror and optical fibers. A Czerny-Turner type monochromator was used in the spectrometer. We observed nine line intensities shown in Table I in the wavelength range of 388.9-728.1 nm. The corresponding optical transitions were from the upper states with n = 3-5 to the lower states with n = 2. The spectrometer can cover a wavelength range of ∼150 nm with an exposure; one image covered 667.8 nm, 706.5 nm, and 728.1 nm with an exposure, and another image covered the other lines. The plasma was produced in a steady state. When scanning parameters, we first measured spectra as scanning the plasma parameters at one of the grating positions, and, then, measured remains at the other grating position as scanning the plasma parameters again. It is noted that the reproducibility of plasma condition is very good in the Magnum-PSI

B. Examples
Figures 2(a)-2(c) show the emission profiles, the profiles of intensities normalized to those at the center, and the profiles of ne and Te measured with the TS system, respectively. The discharge current was 80 A, and the neutral pressure, P, was 0.3 Pa. This is a typical low-density and low-pressure case. We call this as case (i) (low-density case) in this study. The emission region was about 5 mm in radius, and ne ≈ 10 20 m −3 and Te ≈ 1.5 eV at the center of the plasma column. It is seen that 501 nm (3 1 P) line has a clear wing, and 728 nm (3 1 S) and 668 nm (3 1 D) also have a small wing at radii >10 mm. This was the same tendency observed in PISCES-A. The phenomenon was well explained by the excitations of radiation from

ARTICLE
scitation.org/journal/adv the plasma column as the effect was simulated qualitatively using ray tracing calculations. 13 Figures 3(a)-3(c) show the emission profiles, the profiles of intensities normalized to those at the center, and the profiles of ne and Te under a different condition: the discharge current of 160 A and P of 3.1 Pa. This corresponds to a typical high-density and highpressure case, and we call this as case (ii) (high-density case) in this study. Intensities do not decrease sharply in radius, and the emissions are strong even at r > 10 mm. The peak density is 6 × 10 20 m −3 and decreases with radius to 0.5-1 × 10 20 m −3 at r = 10 mm; the low temperature (<1 eV) plasma existed around the region. In Fig. 3, different from the low-density case, it was likely that the plasma expanded and the plasma column size became wider. The plasma widening in low-temperature plasmas has been observed in PISCES-A 17 and NAGDIS-II 18 together with an enhancement of fluctuation, suggesting that similar phenomena also occurred in Magnum-PSI.

C. Comparison with CR model
Population distribution of He atoms is compared with the CR model that was developed by Goto. 19 In this study, we used the so called formulation II in Ref. 19, where the quasisteady-state approximation is applied for all the states, including the two metastable states (2 1 S and 2 3 S). Although the importance of the transport of metastable states was discussed in the NAGDIS-II device recently, 20 we neglect the effect in this study, because the plasma density is much higher in Magnum-PSI.
To calculate the population distribution using the CR model, the optical escape factor (OEF) is used to consider radiation trapping. The OEF in cylindrical geometry with Doppler broadening is defined as follows: where R OEF is the radius of the spatial distribution of the excited atom (OEF radius) and κ 0 is the absorption coefficient at the center of the spectrum having a Gaussian profile. 21 In the formulation II of the CR model, the population of the p state, n cal (p), is expressed by the summation of two terms as 19 where ni is the ion density, n(1 1 S) is the ground state density, and R 0 (p) and R 1 (p) are reduced population coefficients, which can be calculated by solving a set of rate equations and have ne and Te dependences. In this study, we assume ni = ne. and 4(d) correspond to the cases at the column center and 10 mm from the center, respectively. To compare the relative population distribution, we offset the calculation results from n cal (p) to n ′ cal (p) = Bn cal (p), where B is a coefficient, and B is chosen so that the following relation is satisfied:

A. Population distributions
Here, nexp(i) is the i state density obtained experimentally, and the summation should be taken for all the used states. Markers represent experimentally obtained population densities at y = 0 mm and 10 mm, where y is the radial distance from the center of the plasma column. The densities for each state were deduced from the calibrated line emission intensities divided by the photon energy and the Einstein A coefficient for the corresponding transitions. Four cases from the CR model calculations are shown: calculated population distributions using ne and Te from TS at r = 0 mm and 10 mm with R OEF = 0 mm and 10 mm for each r value. From Figs. 4(a) and 4(b), it is seen that the population distribution at y = 0 mm was quite different from that at y = 10 mm. The populations in 3 1 P and 3 1 S states were significantly enhanced AIP Advances in a relative manner. This can be explained by the radiation transfer from the center of the plasma column. 13,22 Although it is rather easy to explain the effect of radiation trapping at the center of the plasma column by using the OEF, it is not so simple to assess the effect at the periphery of the plasma column because of the existence of the radiation from the center. In Fig. 4(b), the experimental results at y = 0 mm and 10 mm did not differ so much. This was probably because the size of the plasma column became wider. The population distribution agrees well with the calculation, in particular, with ne and Te at r = 0 mm and R OEF = 10 mm, respectively. Details will be discussed in Sec. III C.

B. Joint probability distribution
We use the same error function for the optimization used in Ref. 20, which is defined as Here, the function ρ(p) is the normalized density written as where the summation of n(i) represents the sum of the upper states of the line emission used for the analysis, and ρexp and ρ cal in Eq. (4) correspond to the values from the experiment and the CR model calculation, respectively. Because ρ cal is a function of Te and ne, f also depends on Te and ne. for cases (i) and (ii), respectively. Here, we assume that R OEF = 10 mm and n(1 1 S) is spatially uniform and can be determined from the measured P. Thus, ne and Te are the sole parameters, which determine the f value. Note that this joint distribution can be computed as where C is a coefficient and σ = f (n For the five and nine-line cases, n opt e was consistent with ne from TS at the center, though Te was slightly lower. One of the ambiguities in our assumptions is in the neutral density/temperature. In the above two cases, the neutral density deduced from the measured pressure is 7.8 × 10 19 and 7.6 × 10 20 m −3 , respectively, which is lower than or comparable to ne. The ground state density can be decreased by, for example, an ionization process or transportation to the outer region after charge exchange process. In addition, although we assumed that the neutral temperature is at the room temperature, the temperature could be higher. A decrease in the neutral density influences the population distribution in two ways; it can effectively change R OEF and also the ratio between the ionizing and recombining components, which are the first and second term of Eq. (2), respectively. An increase in the neutral temperature decreases R OEF effectively as well. 12 In Figs did not change so much at 0.5 × P, while n opt e significantly shifted to a higher density region at 0.2 × P. In case (ii) [Figs. 6(c) and 6(d)], n opt e shifted to a lower density region, and the high probability region slightly expanded to the high-temperature direction. Although, it is difficult to see what the best choice for P is, the results show that n opt e and T opt e can be altered by the neutral density, and it can be an important factor to assess the joint probability distribution.
It seems from the joint probability distribution maps that the five lines are at least necessary to deduce appropriate Te and ne, and the usage of the nine lines is better than the other sets. Next, setting aside which lines should be chosen in a practical sense, we will make comparisons between TS and OES methods using all the nine lines. r = 10 mm. First, let us take a look at the OES without radiation trapping, namely, R OEF = 0 mm (blue open circles). The density was always assessed to be higher than TS values (dotted lines). When taking into account the radiation trapping with R OEF = 10 mm (closed circles), ne became plausible values. They were in between TS values at r = 0 mm and 10 mm almost in all the cases, except for several cases that were presented with a gray color. When 0.2 × P was used for the neutral pressure (green triangles), similar to the cases shown in Fig. 6, these points became consistent with the TS values within the error range.

C. Comparisons
When it comes to Te, it was also overestimated in many cases without considering the radiation trapping; in several cases, underestimation also occurred. When considering the radiation trapping effect with R OEF = 10 mm, the overestimation was well compensated when Te > 1.1 eV. However, for the underestimated cases, the temperature became further lower, and the discrepancy increased. In addition, when 0.3 < Te < 1.1 eV, the overestimation was not compensated. Green triangles show the cases when the radiation trapping was taken into account with 0.2 × P. The underestimation was mitigated, and the values with error bars were marginally overlapped with TS values at 10 mm. One of the typical underestimation cases corresponds to case (i) (the low-density case), which has been discussed in Fig. 2. Although the mechanism to cause the discrepancy is not clear, because the population distributions at y = 10 was quite different from that at y = 0 mm, as shown in Fig. 4(a), it maybe of importance to take into account the radial emission profile. Concerning some overestimation cases in the range of 0.3 < Te < 1.1 eV, the discrepancy could not be compensated even when changing R OEF . Although not shown in Fig. 7(b), the difference could not be entirely explained even with higher R OEF such as 20 mm. In the NAGDIS-II device, fluctuation was enhanced and the fraction of the non-Maxwellian component increased when the temperature became lower than ≈1 eV. 24 For the plasma conditions investigated, no apparent non-Maxwell component has been identified in the high quality TS spectra measured in Magnum-PSI. However, to get a more accurate picture of the influence of fluctuations and the existence of small non-Maxwell components, advanced signal averaging techniques can be applied in the future.

IV. CONCLUSIONS
We performed OES of He line emissions in high-density plasmas in the Magnum-PSI device. The typical density and temperature ranges were 1-8 × 10 20 m −3 and 0.3-3.5 eV, respectively. Line intensity ratios have been used to deduce ne and Te; we deduced the joint probability distribution from the difference between the CR model and OES results using three lines (λ = 667.8 nm, 706.5 nm, and 728.1 nm), four lines (the three lines + λ = 501.6 nm), five lines (the four lines + λ = 447.1 nm), and all the measured nine lines (the five lines + λ = 388.9 nm, 492.2 nm, 438.8 nm, and 402.6 nm) in two typical high and low-density cases. The deduced ne and Te from the joint probability distribution were quite different from TS values in the three-line and four-line cases. The five-line and nine-line cases were close to each other.
We used the nine lines to measure Te and ne from OES and compared with TS values. Without taking into account the effect of radiation trapping, ne was always overestimated and Te was contradicted with the TS measurements. When taking into account the radiation trapping using the optical escape factor, ne was almost consistent with the TS value; one can say that the radiation trapping is essential to understand the population distribution in the high-density regime as well. The optical escape factor has sensitivity to the neutral density, temperature, and R OEF . Because there are ambiguities in the neutral density and temperature, we discussed the sensitivity as changing R OEF by assuming that the neutral density is spatially uniform and the temperature was at the room temperature. In this study, because the emission profile expanded in the radial direction and the measurements could not cover the whole area especially when the temperature was ≪1 eV, it was difficult to use Abel inversion; we used line-integrated emission intensities. In some cases, R OEF = 10 mm was too much, probably because of a higher neutral temperature or a decrease in the neutral density at the plasma center. Concerning Te assessment, when taking into account the effect of radiation trapping, Te from the OES was in between the TS values at 0 mm and 10 mm, except for ten cases out of 24 conditions, as shown in Fig. 7 with green markers. In five out of the ten cases, the difference was not well explained with the variations in ARTICLE scitation.org/journal/adv R OEF and/or neutral density. The mechanism has yet to be understood well; considerations of the radial emission profile using Abel inversion/tomographic reconstruction, plasma fluctuation, and electron energy distribution function may be necessary. It is of interest in the future to investigate the mechanisms that cause the discrepancy in a detailed manner.