Heat Diffusion in High-C_p Nb₃Sn Composite Superconducting Wires

Round 1

Reviewer 1 Report

The invited article by Barzi et al. for the special issue on Applied Superconductivity for Particle Accelerator(s) covers the topic of Nb3Sn wires engineered to have a high specific heat for the purpose of controlling quench in high-field accelerator magnets. The link between the material and the scope of the journal ("studies related to the design and applications of instruments, apparatuses, and experimental techniques") is tenuous, but this would appear to be an issue for the editors rather than the authors, and they have made their decision by choosing to issue the invitation.

The paper presented is a high-quality work of novel importance and, in my view, fully merits publication. The writing is good, the level of background material is appropriate to the likely readership, and the study is well-conceived, competently conducted and properly presented (although a lack of consistency in the formatting of graphs is regrettable). The paper is suitable for publication as is, but I offer the authors the opportunity to make the following changes prior to publication should they choose to do so.

Line 30: "Another source of magnet training are..." should be "Other sources..."

Line 38: "The number of quenches is proportional to magnet length." Is this true? The actual magnet length, not the length of wire in the magnet or the magnet volume?

Throughout: Are subscripts formatted correctly? Is this the style of the journal? It looks rather as though small text has simply been used in place of properly subscripted text.

Line 56: Bc20 is an unusual symbol for the upper critical field. Is something intended to be indicated by the zero? If so, it is not explained. (Similarly the zero on Tc0, although this is a more commonly-used symbol.) Also, should it be a superscripted zero to avoid confusion with the number 20?

Line 68: It would be helpful to the discussion to define bronze as Cu-Sn.

Line 101-102: "...in short lengths down to 0.7 mm..." "...at a wire size of 4.1 mm." The way this is expressed is confusing. I'm assuming that the quantities refer to diameters, but conflating them with lengths and nonspecific "sizes" makes the meaning unclear. If I'm right, diameter should be specified in the first case, and used in place of size in the second.

Line 107: "Sn-in-Tube" is used when "Tin-in-Tube" has previously been used. The authors should pick one and stick to it.

Line 183: "Reference system" should probably be "coordinate system".

Line 194: It would be preferable for the reader if the table were compressed to fit on one line. There appears to be enough empty space to accomplish this.

Line 201: "Rule of mixture" should be "rule of mixtures".

Line 205: Subscripts and superscripts are incorrectly formatted on the y-axis label of the graph.

Lines 277, 294 and 297: Tables 2, 3 and 4 should be improved. The "Min. MQE" and the "Max. MQE" are each identical throughout each table. Enumerating them individually in this fashion is unnecessary and confusing. Instead, the approach should be much more clearly described, and instead of heading the meaningful columns "I/Ic Min. Dev." and "I/Ic Max. Dev." which are themselves confusing descriptors (particularly when I-tilde has been defined in the text, but remains unused in the tables), these can be labelled "I/Ic dev. at 320 uJ MQE" and "I/Ic dev. at 2300 mJ MQE", etc. This would be far clearer, and would again enable each full table to fit on a single line. This would help in avoiding the present situation where the display items become progressively more and more out of step with the text, making life difficult for the reader and resulting in several figures appearing after the conclusions. If this cannot be done, display items should be repositioned to better align with the text that refers to them. Furthermore, in the variations listed in the first column, a + symbol should be used to indicate a positive variation.

Line 317: On the figure, one data set is labelled "standard wire" but the legend reads "normal wire". A consistent descriptor should be used. The undefined abbreviation "APDL" is used on the legend when it should read "experiment" (or "data") and "model". Ideally either a legend or direct labelling should be used, not both.

Line 334: Additional numbers are required on the x-axis, otherwise it is not possible to determine the scale.

Author Response

Response in attached file.

Author Response File: Author Response.pdf

Reviewer 2 Report

Overall the concept of this paper and the experiments and modeling presented therein is quite good. This is a research topic that is of important interest within the HEP accelerator community, and having a clear understanding of the effects of adding high C_p materials to Nb₃Sn wires could result in a significant improvement in magnet technology, for accelerator and, perhaps other applications.

That said, there is one important deficiency in the work presented here, plus a few minor issues with legibility of the figures.

The significant issue I have with this work is that, when looking on the scale of quench in a single wire, the problem is not 2D but 3D. That is why the concept of Minimum Propagating Zone (MPZ) has such significance when looking at issues of premature quenching and training. I can see that authors also recognize and appreciate this since they mention that MPZ must be considered for a better study of training in the first paragraph on Page 11. Axial heat conduction is at least as food as radial conduction. Taking axial heat transport into account is, of course, much more difficult experimentally, but perhaps less difficult when using FEM simulations. I am not asking the authors to do that analysis here, but I think it would help if they can introduce the MPZ issue earlier in the paper when describing the 2D model and its limitations, and then better explaining how a 3D model/experiment might change these results. My  intuition tells me it might not change the results qualitatively but certainly quantitatively.

There are a few specific comments I would like to make.

• Page 2, first line, 45. “The idea to reduce the MQE by inserting high…”. Shouldn’t reduce actually be increase?
• Page 3, first paragraph. This is a good discussion of the reason for adding Gd₂O₃ to the wire. When first reading it made me want to see a plot or table about the different Cp and other properties of the materials discussed. Reading further, I see that comprehensive tables are included. This is good, but you might want to alert the reader earlier that the data is here in this paper.
• Page 5, lines 167 and 171 that have the two I equations. I think it would be clearer if they were expressed as:

I(T₀) = I_c(T₀, f(I))

and

I(T₀+T)  I_c(T₀, f(I))

• Page 5, line 184, first word: “Figure”? Should this be Fig. 4?
• Page 6, Fig 4. This figure needs improvement. In the copy I am reviewing I cannot see the x-y axes, I cannot really see the FEM mesh (too small) and there are no labels. For example, it took me a while to figure out that the blues zone represents Stycast. I think!. It could also just be ANSYS model background. I would also like to see the heater location and angular spread. Alternatively, just show a clearer Fig. of the ANSYS model.
• Page 6, Table 1. The table could be improved somewhat by adding a column for thermal diffusivity of these materials because it succinctly combines both thermal conductivity and specific heat, and it might make it clear the roles of the different materials in the thermal modeling.
• Page 8, Line 22: The subscript text is too small to read in the first item in the line.

Author Response

Response in attached file.

Author Response File: Author Response.pdf