Role of Simple Spatial Gradient in Reinforcing the Accuracy of Temperature Determination of HED Plasma via Spectral Line-Area Ratios

Round 1

Reviewer 1 Report

In their article entitled "Role of simple spatial gradient in reinforcing the accuracy of temperature determination of HED plasma via spectral line-area ratios", Riggs et al. present the simulation of temperature gradients in tamped NaFMgO foils, heated and backlit by Z-pinch dynamic Hohlraum radiation. The tamped foils were heated and ionized by the Z-pinch and the X-ray absorption spectrum was recorded in the interval [7-15 Angstroms]. 

The work relies on several assumptions, which may be questionable:

- Local thermodynamic equilibrium is assumed, and determined by Griem's criterion. The hypothesis of the latter criterion should be briefly explained (Griem has proposed several criteria). Additionally, such an approximation may be questionable here, since the radiation of the field is probably not perfectly Planckian.

Moreover, it is worth mentioning that other criteria exist, see for instance :

M. Numano, Criteria for local thermodynamic equilibrium distributions of populations of excited atoms in a plasma, J. Quant. Spectrosc. Radiat. Transfer 43, 311-317, 1990, 

which gives a higher critical electron density and thus a more severe condition for complete LTE than Griem's criterion. 

- The system is assumed 1D for simplicity.

The authors should explain why they believe that such an assumption is realistic.

- Only bound-bound transitions are considered!

The authors should comment on the way they deal with continuous (bound-free and free-free) absorption.

- The gradient model is simply based on a three-parameter scheme: two temperatures Te1, and Te2, and a length ration L2/L1 (under the constraint that L=L1+L2 is constant). 

The authors should explain more clearly why they posit the existence of a thin, hot layer on the pinch facing side of the target-foil plasma.

The expression "length of the interval containing electron temperature Te,k" sounds a bit strange. This should be reformulated ("length of the interval in which the temperature is assumed to be constant equal to Te,k" for instance, ...).

- The line shapes are modeled by simple Voigt functions. As is well known, He-like lines have a more complicated structure, and a proper treatment of Stark effect may impact the conclusions. This should be discussed in the manuscript. In addition, the plasma is a mixture of Na, F, Mg and O, which brings additional issues, related to the determination of a microfield distribution for a mixture, which is a rather difficult problem.

The conclusion is somewhat puzzling. The authors find that a temperature spatial gradient is inconsistent with experimental data, and conclude that this justifies a posteriori their neglect in [1,10]... This needs to be qualified, in the sense that the conclusion should more reasonably be that, provided that the way the spatial gradients are modeled in the present work is realistic, the latter should not affect much experimental data. 

Although the work relies on a few questionable assumptions and belongs more to engineering than science, the paper is clearly written. 

The results are presented in a honest way (the authors have clearly improved their analysis technique and changed their previous conclusions) and the assessment of 2D maps of line-area ratio as functions of the two temperatures T1 and T2 is rather convincing.

For these reasons, I recommend the paper for publication in Atoms, provided that my comments/queries above are properly addressed.

Typo : conclusion : "... a spatial gradient... their neglect in [1,10]".

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Temperature diagnosis of high energy density plasmas is a challenging work in experiment. In this work the authors investigated the role of simple spatial gradient in determining temperature of dense Plasma via Spectral Line-Area Ratios. They compared the simulated spectroscopy of a collisional-radiative model with the measured x-ray absorption spectra collected on Sandia National Laboratories’ Z Pulsed Power Facility. They showed that a negligible gradient in electron temperature is consistent with experimental data.

 From my experience, there are some studies on the temperature determination, but the study presented in this work is rather rare. I consider the topic is original. As a result, I think it address a specific gap in the field.

Compared with other published material, it added further details on the effect of spatial gradient on the accuracy of temperature diagnosis. Actually, direct measurement of temperature of high energy density plasmas is a challenging work. The conclusions are consistent with the evidence and arguments presented and they did address the main question. At last, the references are appropriate for the topic.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The present manuscript concerns a spectroscopic analysis method allowing to improve the evaluation of the temperature of photoionized plasma gathered from the Z pulsed power facility at Sandia National Laboratory. The title and the abstract of this manuscript are sufficiently clear. The scientific objectives are well underlined. It’s a interesting and clearly written manuscript. This manuscript is suitable for publication.

Three minors corrections :

- Page 2 : line 61 : “flouride” need to be corrected

- page 5 : line 110 : “...of the data, each...” could be replace by “ ...of the experimental data, each...”

- Page 6 : Figure 5 : it’s very difficult to distinguish between the white color and the gray color

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have properly taken my comments on board.