Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have prepared a very well-executed study of a wide range of viable candidates for fusion system shielding. This is a highly important topic that will require additional research and the authors have done well to address the beginning stage of the investigation. The methods and presentation are sound but I have a couple suggestions that may be incorporated into this or a future study.

1) In all nearly all of the figures, attention should be given to the scale. In many cases, an excessive number of decades are presented in the lag scale. In other cases, a linear scale is used when a log scale may be more enlightening to the reader. To be clear, all figures are acceptable, however a conscious review of these decisions may improve the impact of the paper.

2) I'm curious if the radiation transport in this study could be reduced to a 2-D problem to improve statistics. The simplified geometry used could be taken one step further. This may or may not be of value in future studies.

3) I think more attention could be given to the impact of the material density on the attenuation of prompt and secondary gamma-rays. Some information can be extracted from the figures but this was not discussed in as much detail as I would hope for.

4) I observed in Figure 10 that there are distinct advantages in the neutron spectrum impacts between borides and hydrides and indeed the authors indicate this as well. I'm curious if a combination shield (layered) would be able to further utilize this impact. I will go on to suggest a follow-on study that would examine the effectiveness of a combined H2Ti / B2W shield. The H2Ti would moderate the neutrons for the B2W to absorb. The higher density of B2W would also decrease the prompt and secondary gamma-ray dose. A different boride may be more appropriate, I simply suggested B2W because of it's density compared to the others in this paper.

Overall this is a very well-done study and I highly recommend it for publication with or without the implementation of my recommendations. 

Author Response

Reviewer 1 report

The authors have prepared a very well-executed study of a wide range of viable candidates for fusion system shielding. This is a highly important topic that will require additional research and the authors have done well to address the beginning stage of the investigation. The methods and presentation are sound but I have a couple suggestions that may be incorporated into this or a future study.

Response: we sincerely thank the Reviewer for his comments and suggestions, which have helped us improve the clarity, quality, and completeness of the manuscript.

Comment: 1) In nearly all of the figures, attention should be given to the scale. In many cases, an excessive number of decades are presented in the lag scale. In other cases, a linear scale is used when a log scale may be more enlightening to the reader. To be clear, all figures are acceptable, however a conscious review of these decisions may improve the impact of the paper.

Response: We thank the Reviewer for this constructive comment. In response, we have revised Figures 10a and 10b by narrowing the axis ranges to avoid presenting an excessive number of decades, and we have also indicated more clearly the use of logarithmic scale in Figures 7 and 9 by changing the grid lines style.

Comment: 2) I'm curious if the radiation transport in this study could be reduced to a 2-D problem to improve statistics. The simplified geometry used could be taken one step further. This may or may not be of value in future studies.

Response: We thank the Reviewer for this useful suggestion. For the present work the chosen geometry is simple enough that we did not encounter issues with statistical convergence, owing in part to the computational performance of our simulation tools. Nevertheless, a 2-D reduction could indeed be useful to improve statistics in large parametric studies, or if available computational power is limited.

Comment: 3) I think more attention could be given to the impact of the material density on the attenuation of prompt and secondary gamma-rays. Some information can be extracted from the figures but this was not discussed in as much detail as I would hope for.

Response: We thank the Referee for this helpful comment. The primary aim of this paper was to highlight which binary compounds would be most suitable as shielding materials in compact fusion reactors, rather than to perform an exhaustive study of the relations between shielding performance and material properties. For this reason, we did not include a detailed analysis of the relationship between material density and attenuation of prompt and secondary gamma rays. However, our analysis indeed allows investigating also such effects, as shown in the figure below.  
We agree that this is an important aspect, and as such we think it deserves a dedicated work (which is however beyond the scope of the current manuscript, where we prefer to keep the discussion focused on the goal). Meanwhile, we have added a brief statement to the manuscript (page 7, lines 204-208):

«It is worth noting that the gamma-ray flux decreases exponentially with increasing density of the compound, as confirmed by our results; however, a detailed analysis of the influence of material density on gamma attenuation is beyond the scope of the present study.»

Comment: 4) I observed in Figure 10 that there are distinct advantages in the neutron spectrum impacts between borides and hydrides and indeed the authors indicate this as well. I'm curious if a combination shield (layered) would be able to further utilize this impact. I will go on to suggest a follow-on study that would examine the effectiveness of a combined H2Ti / B2W shield. The H2Ti would moderate the neutrons for the B2W to absorb. The higher density of B2W would also decrease the prompt and secondary gamma-ray dose. A different boride may be more appropriate, I simply suggested B2W because of it's density compared to the others in this paper.

Response: We thank the Reviewer for this insightful suggestion. We observed the complementary spectral behaviour of hydrides and borides reported in Figure 10, and we agree that layered composite shields could exploit this effect. We will consider a dedicated follow-up study to evaluate the effectiveness of combinations such as H2Ti / B2W and of the other promising candidates that emerged from this study.

Overall this is a very well-done study and I highly recommend it for publication with or without the implementation of my recommendations. 

Response: We are grateful to the Reviewer for the very positive assessment and for the helpful suggestions. We have addressed the comments by correcting typographical errors throughout the manuscript, improving the clarity of the figures, and adding targeted clarifications where needed to improve readability and interpretation. We believe these revisions have strengthened the paper.

Reviewer 2 Report

Comments and Suggestions for Authors

Please read the attached pdf.

Comments for author File: Comments.pdf

Author Response

Reviewer 2 report

The authors carried out large-scale simulation to optimize the compound used in shielding structure. The workflow is clear and the results are comprehensive. I would recommend for publication if the following concerns are adequately addressed by the authors.

Response: we sincerely thank the Reviewer for his comments and suggestions, which have helped us improve the clarity, quality, and completeness of the manuscript.

Comment: 1) For the void line indicated from Fig.2 to Fig. 4, the flux ratio is 0.8. Does NFR=0 indicate perfect shielding and NFR=1 indicate absence of shielding? Why would an empty shielding yield non-unity NFR? The author should explain this more specifically. For some data points from   Fig. 2 to Fig. 4, the NFR ratio is larger than 1, is it normal? What does it mean?

Response: We thank the Reviewer for pointing out this clarity issue, that is very important for the whole manuscript.
We have defined the NFR as the ratio of the neutron flux densities (n cm^-2 s^-1), and not of the neutron fluxes (n s^-1). Despite both these quantities often identifies as “flux” in the literature and community, they are different and this caused the misunderstanding. Indeed, the difference between the inner surface area and outer surface area of the neutron shield dictates that if no interactions happen inside (void, or absence of shielding) and all the neutrons can pass freely, the NFR value is 0.802 due to the increased (outer) surface over which the flux density is calculated.
The NFR can exceed this value (and for extreme cases also the value of 1), when the material acts as a neutron multiplier rather than a neutron shield due to the abundance of (n, 2n) and  (γ, n+2α) reactions.
We have added a clarification of the definition of NFR used and a concise discussion above Figure 2 (page 4) that describes the “void” reference line and explains the origins of NFR values above the “void line”.

«The horizontal dotted line, corresponding to NFR = 0.802, denotes the reference case (i.e., the absence of shielding material) and highlights the flux density reduction attributable to purely geometrical effects. In that case, although the total number of neutrons is conserved, they are spread over a larger exit surface area; consequently, the void reference value differs from 1. Thus, a value of 0 denotes perfect shielding, while an NFR = 0.802 corresponds to no shielding: the outgoing flux equals the incoming flux, and the material does not contribute to the flux density decrease. Moreover, materials above this line increase the neutron flux relative to the void case due to neutron multiplication driven by their nuclear cross sections.»

Comment: 2) As seen in Fig. 3 and Fig. 4, there appears a linear correlation between PDD and Flux Ratio, this is also evident in Fig. 2. I suggest the authors address the underlying physics.

Response: We thank the Reviewer for this comment. We acknowledge that we did not sufficiently emphasize some of the features revealed by these plots. The reason lies in the fact that the stronger is the interaction (and in the case of inelastic ones, the larger the deposited power in the material) the higher is the shielding performance and therefore the lower the NFR.
To address this, we have added a brief discussion of the mechanism underlying the linear correlation observed in Figures 2–4 (see page 4), which we hope addresses the Reviewer’s suggestion.

«Another interesting observation from the figure is that most of the data present a linear dependence of NFR on PDD. This behavior is readily explained: a lower NFR corresponds to a stronger neutron interaction, and therefore (if the interaction is inelastic) to a larger amount of power deposited in the material.»

Comment: 3) On page 5, in attempt to clarify the lack of correlation between shielding effectiveness and the atomic mass of heavier element. The author wrote ”this highlights the importance of the specific properties of each element...”. I would welcome more detailed analysis on this issue. Besides, atomic mass is one inherent property of atoms. The delivery of message is not strictly accurate.

Response: The Reviewer is correct; the delivery of the message was not accurate. The phrase “atomic mass” was wrong – we intended to refer to the atomic number. In the revised manuscript we have (i) corrected this terminology and (ii) expanded the paragraph to clarify the “specific nuclear properties” we meant: specifically, the nuclear configuration of the heavier element. We also clarified the link between these properties and the occurrence of peaks associated with nuclei having neutron numbers near magic numbers. We believe that these changes improve both the accuracy and clarity of the discussion.

«The behaviour observed in this plot indicates that there is no straightforward correlation between shielding effectiveness and the atomic number of the heavier element, rather highlighting the importance of other specific nuclear properties, such as the nuclear configuration of the element. In this sense, we can observe peaks of low neutron absorption that can be attributed to the enhanced nuclear stability (e.g., nuclei whose neutron numbers are close to magic numbers).»

Comment: 4) Why is Gamma Rays Flux taken as an indicator? This may appear trivial for experts, but should be better explained for general readers.

Response: We thank the Reviewer for this useful comment. To make the manuscript accessible to a broader readership, we have added a brief explanation of why gamma-ray flux is reported and its relevance for fusion applications (see pages 6 – 7): a high outgoing gamma flux can strongly contribute to heating nearby components. This is particularly important for the current cause since behind the shielding layer the magnet cryostat will be positioned, with an operating temperature of the superconducting magnet of about 20 K or below.

«Thermal issues can also arise from gamma-ray production. Large emissions of this radiation can cause severe overheating of nearby components (potentially critical on the magnet system near the shielding layer that needs to be kept at 20 K or below), while also posing safety issues for the personnel and complication in remote maintenance. For these reasons, it is desirable to investigate and minimize such emissions.»

Comment: 5) In the discussion section, the author includes ”some borides” to ”offer wider range of options”. What are the criteria for adding these extra compounds? Since lots of efforts have been made to exclude possible candidates. Moreover, since the number of final candidates in Table. 1 is finite, I would suggest the author to explicitly specify the name of the added compound at the beginning.

Response: We thank the Reviewer for this helpful question. In the revised manuscript we have clarified the rationale and criteria used to add extra boride compounds to the final subset of candidates.
First, on page 5 we added a brief justification for emphasizing borides, which notes their widespread use in nuclear applications and the higher level of practical safety and robustness that motivates their consideration.

«This choice is also motivated by their widespread use in nuclear applications: hydrides give the best NFR values, whereas borides are widely used as control materials and are valid alternatives if one wants to avoid hydrogen-rich materials in nuclear facilities.»

Second, in the discussion (page 7) we now make explicit that NFR is not the sole selection metric: PDD and other practical considerations are also important in engineering applications, and these additional criteria guided the inclusion of extra compounds.

«[…] borides generally exhibit lower levels of PDD and can be preferred in some neutron control application, as mentioned before.»

Finally, the specific reasons for adding ZrH₂ are now described at the beginning of the discussion section (page 7), and we have moved ZrH₂ to the top of Table 1 to make its inclusion immediately apparent.