Improved Line Intensity Analysis of Neutral Helium by Incorporating the Reabsorption Processes in a Helium Collisional-Radiative Model
Round 1
Reviewer 1 Report
The manuscript discusses the accuracy of the collisional-radiative model for low-pressure helium plasma. In this paper, the authors developed a helium collisional-radiative model considering the optical escape factor from the ground state to n1P states. They determined the electron density and electron temperature of the LHD helium plasma with 8 emission lines, where they applied the bias and variance analyses to the determination. The bias-variance analyses is an interesting method. However, many researchers already reported improvement in the accuracy of the helium collisional-radiative model when the considered transition lines increased. So, I think that several points about this article should be clarified and improved before publication.
Many researchers already reported improvement in the accuracy of the helium collisional-radiative model when the considered transition lines increased.
- S. Kajita et. al., Rev. Sci. Instrum. 82, 023501 (2011)
- S. Kajita et. al., Phys. Plasmas 25, 063303 (2018)
- K. Sawada et. al., Plasma Fusion Res. 6, 1401010 (2011).
- W. Lee et. al., Phys. Plasmas 25, 113504 (2018).
- M. Goto and K. Sawada, J. Quant. Spectrosc. Radiat. Transfer 137, 23 (2014)
What is different from these papers? The authors should explain the differences.
The authors compared 8 transition lines of helium to determine electron temperature and density, where 8 lines are in the range of 380nm-730nm. I think that they calibrated their all optical systems. So, they should be explained their calibration method (including absolute calibration or relative calibration) in the experiment section.
At 118 lines in page 5, the authors claimed that “However, the escape factor was introduced …”. However, S. Kajita and co-workers already evaluated the re-absorption effect from the ground state to 21P, 31P, 41P, and 51P state.
- S. Kajita et. al., Rev. Sci. Instrum. 82, 023501 (2011).
So, the authors should revise the relevant contents including this sentence.
At 121 lines in page 5, the authors claimed that “The escape factors can be roughly evaluated assuming that …”. However, Iida and co-workers already suggested the complete analytic expression of the optical escape factor in cylindrical geometry.
- Y. Iida et. al., Phys. Plasmas 17, 123301 (2010).
So, the authors should revise the relevant contents including this sentence.
In Eq. (3) and (8), the authors assumed the LHD geometry as an infinite plane-parallel slab, and they applied the optical escape model for the slab model to the analysis. The authors should explain the validity of OEF for the slab model to apply the model to LHD.
In Eq. (9) and (10), the authors explained the interior point method. However, I think the method is basically the same to the methods of S. Kajita and W. Lee.
- S. Kajita et. al., Rev. Sci. Instrum. 82, 023501 (2011)
- W. Lee et. al., Phys. Plasmas 25, 113504 (2018).
- K. Sawada et. al., Plasma Fusion Res. 6, 1401010 (2011).
The authors should explain the difference from the reported papers.
In Eq. (9) and (10), the authors used the bias-variance analysis to determine electron temperature and density. However, their explanation is not sufficient. The authors should add the advantages of the bias-variance method, they should explain the reason why they selected the method.
At 234 lines in page 10, they wrote that “The escape factor for state 31P was in between those for states 21P and 41P …”. The re-absorption effect is proportional to Einstein A coefficient because the effect is the stimulated absorption process. Therefore, it is natural that the OEF for 31P state is in between those for 21P and 41P. So, the authors should revise the relevant contents including this sentence.
In this manuscript, the authors claimed that they improved the accuracy of helium collisional-radiative model and they suggested some normalized intensities. If the authors suggest the reproduced spectra by the collisional-radiative model and compare them with the experiment data, the authors can present their improvements more intuitively.
In Figure 9, the OEF decreased when electron density increased. However, the authors did not explain the characteristics. The authors should suggest a physical explanation for the experimental result.
Author Response
Please see attached.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Please find detailed comments in attached file.
Comments for author File: Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have covered my comments to a satisfactory level. Thank you for the effort and detailed answers. I believe that the paper can be published.
However, I have a question about the revised manuscript.
When the authors calculated the absorption coefficient, they assumed the Doppler broadening is the most dominant in line 165. So they didn’t consider any other spectral line broadening. However, the authors explained the increase of the escape factor as like “The rise of the escape factor in the high line …” at line 289. If the increase of Stark broadening is not negligible, the measured spectral line shape is changed, and Eq. (6) is not valid anymore. But, the authors did not suggest any experimental data, such as the change of spectral line shape. So, the authors should suggest experimental data for their claim, and they should check the validity of Eq. (6).
Minor issue.
- Table 1, figure 3,and figure 9 span two pages.
- There are some typos, such as T’e,’ in line 201. Please, check the whole manuscript.
Author Response
Please see the attachment. Concerning the minor comments, we corrected all of them as suggested.
Author Response File: Author Response.pdf
Reviewer 2 Report
Response to Authors, Rev. 2
General Comments
I appreciate the authors for clarifying the text. The discussion is now more tractable, even though a few points remain that require some elaboration. I believe I would be able to accept the paper after the following points are addressed.
Detailed Comments
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1) The explanation of the experimental setup is now discussed in more detail. However, how the measurements are taken is not elaborated upon. The authors mention in Section 3.2, lines 210- 212 that 40 spectra are recorded over a period of 0.4 s, and yet Figures 3, 8, 9, and 11 contain many more than 40 data points for each of the plotted quantities (be they ratios, n_e or T_e). This reinforces my view that the data acquisition is not sufficiently described. The authors are advised to add such a subsection to Section 2.
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2) A discussion on the line-averaged electron density is warranted, which would address why that value, determined by laser interferometer, is inappropriate for comparisons against computed values.
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3) Given that no experimental measurement of the electron density and temperature are made, the claim that the presented method determines them is inappropriate, and there are several instances of it, even in the abstract. The language used should be softened to say they are ‘computed’, or something like that.
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4) The authors were kind enough to post their atomic model in the cover letter. I do not believe it is necessary to include in the manuscript, but a short discussion would be beneficial. For instance, they could say that the model is term-resolved up to n=7, and extends up to n=26, or 99.9% of the ground state ionization energy.
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5) It would be worth mentioning that the selected lines are not subject to optical depth effects, as they do not decay to the ground state, and so no escape factors are needed for them in Eq 1.
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6) The units of the emissivity on lines 90-91 are incorrect. The emissivity is defined per unit volume, so its units should be mˆ-3, instead of -2. Then the Phi quantity on Eq. (2) has the same units as in Eq. (1).
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7) The authors did not address my previous comments on the equations of Section 3.1. Once again:
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From Eqs 4 and 8, it is obvious that k*D/2x is the optical depth, t_0. Please explain what x is, and why it appears in the denominator.
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The Doppler profile in Eq 6 is incorrect, as it peaks at 0 Hz. It would be better expressed with the central frequency appearing in the numerator in the exponential so it reads (nu-nu_0).
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The Doppler width in Eq 6 is incorrect: the ratio in the square root ought to be the inverse of what is written. As written, higher temperatures lead to sharper profiles.
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Typos
Line Change
74 a wavelength of approximately 520 nm -> a wavelength range of. . .
89 Phi_t -> Phi_p,q
112 is first suggested -> was first suggested
146 persuasive -> (delete)
201 T_e’,‘-> T_e’, (drop the extra prime)
Author Response
Please see the attachment. Concerning typos, we corrected them as pointed out.
Author Response File: Author Response.pdf
Round 3
Reviewer 1 Report
The authors have covered my comment to a satisfactory level. Thank you for the effort and detailed answers.
I think that this paper needs one minor correction.
The authors applied the infinite plane-parallel slab model with thinkness D=0.01m at 172 line. However, the length of line-of-sight and LHD size is larger than D=0.01m. Please, add the explanation for the difference.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
