Evaluation of Spatial Profile of Local Emissions from W17+–W23+ Unresolved Transition Array Spectra
, Izumi Murakami 2,3, Daiji Kato 2,4, Hiroyuki A. Sakaue 2, Hayato Ohashi 5, Shivam Gupta 6, Chihiro Suzuki 2,3, Motoshi Goto 2,3, Yasuko Kawamoto 2,3, Tomoko Kawate 2,3, Hiroyuki Takahashi 1 and Kenji Tobita 1Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors present new work on identifying emitting W ions in space-resolved spectra collected from LHD after tungsten pellet injections into its plasma. The abstract describe the work correctly but it needs a small clarification. See below. The introduction and experimental method sections are well referenced and provide sufficient background for readers to follow and understand the results. Some minor corrections can be made to these for clarity. Again, see below. The results and discussion and conclusion sections are well presented and discussed. Again, some minor modifications are suggested below.
Overall, the work will be of considerable interest to colleagues who have an interest in tungsten impurities in magnetic confinement devices. Indeed, there is a need for new spectroscopic data on tungsten. I can approve publication of this paper once the comments that I list below are attended to.
Abstract:
a) I suggest that the authors mention the electron temperature range studied in the abstract.
b) Line 25-26 in the abstract, the phrase "in the region where the electron temperature decreases locally" needs to be improved. For instance, "in a radial region, reff = 0.38 m, where the local electron temperature decreases by 30% to 40% with respect to more central and outer temperatures."
c) line 27: Rather than "in our previous study", the authors should consider including the reference
Experimental Setup:
Figure 1, caption. Change to "Large Helical Device"
Page 3, line 78. The authors should include the tungsten pellet injection or arrival time in the text.
Figure 2: I suggest that the authors shade the time interval, 5 to 5.3 s, in which spectra are recorded (at least for b, c, d and e).
The term "EUV Short2" is sometimes written as "EUV short2". Please ensure consistency.
Figure 3. Please indicate in the caption what the black vertical arrows represent in this figure.
Page 5, Line 141. I cannot understand what the authors want to express in the text "The line-of-sight passes a long length through a specific reff to snatch the magnetic surface". Please rewrite.
The caption of Figure 5 should include more details about this figure. What do #1, #50 represent?
Page 7: Line 170: The phrase "The UTA spectrum around 200 Å contains emissions from multiples states at the same wavelength". Maybe it should be "line emissions from multiple states with very similar wavelengths.".
In Figure 7, experimental and synthesized spectra are shown around 200 Å. I imagine that the experimental spectrum contains detector readout noise, bremmstrahlung, etc. The authors should mention this in the text or caption.
Figure 8. The authors should define ZR3600 (mm) in the caption or in the text. Also, change the text in the caption to "... EUV spectra for (a) " and "The blue vertical spectra represent the ..... ".
Figure 9. Please include in the caption the time when the TS profile is obtained.
Conclusions:
The authors write, lines 254 and 255, that "In this study, tungsten pellet injection experiments were conducted in LHD to understand the transport process of tungsten impurities". However, in the last phrase in the previous section, they write "Future studies should reveal the transport process that determine these processes." The authors should rewrite the former phrase to reflect better the work in this paper. A similar phrase in found in the abstract "to understand the impurity transport process". Again, this should be modified to reflect better the work presented here.
General question: The authors note that spectra were recorded between 5 and 5.3 s with 0.1 s integration time. Also, they note that during the period, 5 to 5.3 s, the Te0 falls from 0.8 keV to 0.3 keV. In order to support their findings, the authors should indicate more clearly the narrow time interval (0.1 s) and if Te0 is constant during this integration time. If not, then they should provide a Te0 range.
Comments on the Quality of English LanguageOverall the English is correct but with some minor errors.
Soem are included above. Additional comments are
Page 1, line 35. Change to "... penetrate into high-temperature plasma".
Page 1, line 39. Change to "... in fusion plasmas with ..."
Page 2, line 56. Change to "In our previous study, an Unresolved Transition Array (UTA) spectrum ..."
Author Response
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Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsPlease check the attached file.
Comments for author File: Comments.pdf
Please check the attached file.
Author Response
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Reviewer 3 Report
Comments and Suggestions for AuthorsThe study of spectra of multiply charged tungsten ions is of great applied interest, since this metal, firstly, is a structural metal for plasma installations with magnetic confinement, and, secondly, is one of the main impurities in thermonuclear plasma. Energy losses, both radiation and those occurring during ionization of tungsten ions, depend on the charge state of the ions, the density and temperature of the plasma. Therefore, studies of the charge state of impurity tungsten ions in various spatial regions of magnetically confined high-temperature plasma are very relevant. In the work under consideration, a method is developed that allows estimating the spatial profiles of tungsten ions with charges of the order of 20, using the results of observations with spatial resolution of emission plasma spectra in the wavelength ranges of (180 -240) Å and (24 – 38) Å.
The manuscript is clear, and is presented in a well-structured manner. The cited references are relevant. The paper is scientifically sound and is based on the experimental study. The manuscript’s results reproducible based on the details given in the section 2.3 “Method to Evaluate Impurity Spatial Profile”. The conclusions are well founded.
Comments for author File: Comments.pdf
Author Response
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Reviewer 4 Report
Comments and Suggestions for AuthorsReferee report on the paper
Evaluation of Spatial Profile of Local Emissions from W17+–W23+ 2 Unresolved Transition Array Spectrum 3
Ryota Nishimura 1, *, Tetsutarou Oishi 1, Izumi Murakami 2,3, Daiji Kato 2,4, Hiroyuki A. Sakaue 2, Hayato Ohashi 5, 4 Shivam Gupta 6, Chihiro Suzuki 2,3, Motoshi Goto 2,3, Yasuko Kawamoto 2,3, Tomoko Kawate 2,3, Hiroyuki 5 Takahashi 1 and Kenji Tobita 1 6
The paper is devoted to the spatially resolved observations of tungsten (W) spectra with the spatial emissivity profiles of W ions with charge q =17-23 (W17+ -W23+) in the Large Helical Devise (LHD) facility. The determination of W spectra in a magnetically confined system is of particular interest due to the application of W material in future fusion device designs. Indeed, to ensure stable reactor operation, it is necessary to develop our understanding of the behavior of this heavy plasma impurity, in particular, to measure and study its distributions both spectrally and charge-radially. Huge radiative losses from plasma are due to low-ionized tungsten ions, which are mainly concentrated in the regions with rather low temperatures. Therefore, the choice of W17+ -W23+ ions presented in this work is quite reasonable.
The authors applied original method of impurity observations based on the application of two kinds of spectrometers which can catch the spectra regions of 24.2-37.8 A and 183.7–234.3 Å. The observed spectra have a very complex structure due to the strong overlapping of enormous number of radiative transitions belonging to the W ions with the different ionization degree. Such kind of quasi-continuous spectra were called Unresolved Transition Arrays (UTA) along with the proposed model approaches to describe them using special approximate statistical averaging of calculated synthetic spectra. Evidently the theoretical treatment of such complex spectra is very complicated since its rigorous theoretical description was not developed yet.
In this work the synthetic spectra which were further used in UTA approach were calculated with the FAC code combined with collisional- radiative model (CRM).
The authors also utilize an original interpretation of chordal intensity measurements by partitioning the plasma chord cross section into effective annular zones k=1, 2, ..., N, in cylindrical geometry proportional to their area and, respectively, to the square of the effective radius of plasma column. The description of chordal intensities along lines of observation is discretized and reduced to the use of a lower triangular matrix formed by chord segments along lines of observation. This leads to a justified radially nonlinear description: to relatively large sizes of the zones in the plasma core and densification of the zones at the periphery depending on the number N, since it meets the conditions of an equiprobable representation of ring intervals with a constant local emission of impurities inside each zone.
However, the proposed description could not distinguish between the emissivity contributions of the total impurity density, nW, and the charge state distributions (or ion fractional abundance Wq+), 
, which are represented through the emissivity of charge states via UTA, but determined only by the ratios of ionization-recombination rates of W (see, e.g., [1, 34, 35]).
Hence, a number of questions and comments arise to the methodology of this work claiming to provide information on tungsten transport.
1) The general expressions for the local emissivity 
are necessary in our opinion, but not presented in the paper, except for the fitting expression. Therefore, it remains unclear what physical factors determine the impurity emission? How it depends on nW, ne and PECs (photoemission coefficients) and on the charge state distribution, ?
In the absence of data on total density profiles and 
for their subsequent use in emissivity analysis, it is questionable to directly assert that
“The result suggests that the UTA spectrum observed around 200 Å contains 5s2-5s5p satellite lines of around W20+. It is also inferred that the tungsten ions around W20+ are densely concentrated in the region where the electron temperature decreases locally.”
2) It is not clear from the paper how the profiles 
can be related to the proposed study of tungsten transport and what kind of transport is it: charge-radial or only radial 1D diffusive-convective particle transport for total density?
In particular, how do the authors imagine the relation of the measured local emissions to particle transport?
The thing is that from the point of view of standard codes, measurements of tungsten density profiles appear to be transport-free, i.e., either they do not provide information on impurity transport in principle or it is a qualitatively different nature of transport compared to that assumed in standard 1D codes. Further clarification of the stated motivation for the transport study is required.
Indeed, it has long been established that “within the existing uncertainties in the ionization and dielectronic recombination rate coefficients the heavy impurity ions are in ionization equilibrium.” (TFR Group. 1980. Plasma Phys. V. 22, P. 851). The parameter describing density profiles is the ratio of ionization rates to recombination rates (Breton C., et al. 1983. J. Phys. B: At. Mol. Phys. V. 16, P. 2627).
It is also noted, e.g. in [34], that “the ion abundance ratios in the radial transport model implemented using the STRAHL code are consistent with those in the model without transport”. Therefore, in the case of tungsten the standard 1D transport codes can be used only for the calculation of impurity charge state distributions being transport-free.
This is also found in [1] and then postulated in Pütterich T, Neu R, Dux R, Whiteford A and O'Mullane M 2008 Plasma Phys. Control. Fusion 50 085016 in the calculations of the ionization balance of tungsten.
All recent works on the observations of tungsten emissivity only confirm the long-standing discovery of the ionization balance of heavy impurities in the quasi-stationary plasma from the TFR Group. Its utilization is devoted to the works from the proposed list [1, 11, 12, 34, 35]. But in none of these works the connection of charge state distributions with impurity transport is indicated.
So, the lack of such a connection is asserted everywhere, but this directly contradicts the original transport motivation of this paper and its conclusions.
3) The Gaussian form of the approximation of the tungsten radial emissivity profiles (formulas (2)) is also used in the paper Daiji Kato et al 2021 Nucl. Fusion 61 116008, where, in addition, it was correctly noted that
“the temporal behavior of each ion density is entangled with those of total tungsten density 
, and each ion fractional abundance Wq+, nq as 
.”
Physically it means that last two variables describe two qualitatively different, statistically independent, but joint plasma processes: the transport of particles and the transport of their charge states due to ionization and recombination. Then it is complex 2D charge-radial transport of impurity, but not the particles only (as in 1D STRAHL code). Therefore, when studying impurity transport, it is necessary to distinguish two main processes: radial dynamics and kinetics of charge states of impurities. Moreover, due to the incompatible representation of the radial dynamics and charge kinetics of impurity charge states, the standard approach of 1D impurity transport codes (e.g., STRAHL) and the results obtained are mostly erroneous (see V.A. Shurygin. 2024. Plasma Physics Reports. V. 50, P. 911).
In our view, the Gaussian spatial distribution is a direct consequence of the discrete Gaussian charge state distribution nq (see, e.g., in A.V. Demura et al, Atoms 2015, 2, 162-181)
Their relations must be explained together using expressions (2).
4) The cross-correlation coefficient designations k > 99.5% in Figure 6(a) and the numbering of emission zones k=1, 2, ..., N are the same and may be confused. This should be corrected.
Finally we recommend to include more references of the other authors on the subject under consideration since the list of references contains practically totally only the Japan authors in the field. Indeed, the detailed investigations of the complex ion spectra that deserves to be cited in context of the work under review are presented in the publications, itemized below:
*A.V. Demura et al. Statistical model for quasicontinuum of heavy ions in hot plasma. Plasma Phys. Rep. 46, 241–251 (2020), where UTA spectra of W ions are described within the atomic statistical theory;
*S.S. Churilov et al. EUV spectra of Gd and Tb ions excited in laser-produced and vacuum spark plasmas. Phys. Scr. 80, 045303 (2009), where the experimental data on spectra of complex rare elements are presented;
*V.A. Shurygin. Diffusive-Convective Model of Impurity Transport in Quasi-Stationary Plasma: Criticism and Alternative. Plasma Phys. Rep. 50, 911 (2024), where a new point of view on impurity transport was suggested.
After the requested corrections, comments and additions in the text and in the list of references, this paper could be recommended for publication in Atoms.
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Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsI appreciate the effort of authors for this revision and answer sheet except the reference citation. Anyway, I believe that the paper is sound and can be published in Atoms after the correction of the reference. The self-citation rate is too high in the revised version. For example, Refs 11~14, only one of them is enough. Refs 21,30,37,38 can be removed since these references are used to surpport the same thing as those suggesed to be kept.
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