Dear Reviewer 1

Thanks for the kind review and constructive comments for the manuscript. 

Main comment:

Under what environmental conditions were the field experiments conducted? Specifically, do you expect your customized heatsink to perform as effectively as the standard one in extreme conditions, such as during a heatwave?

The experimental data presented in the paper was acquired outside of the laboratory under calm conditions and an ambient temperature of about 15^oC. We will add a comment about this to the revised paper. 

However, this is not the full answer to this question. Much more importantly, since this manuscript was submitted, our instrument with the customized heatsink has been successfully used for extensive field work in, e.g., Senegal. Here, more than 100 soundings have been conducted at temperatures above 30^oC and more than 50 soundings have been conducted at temperatures above 40^oC. We can therefore now safely conclude that the performance of the customized heatsink is good. We will add a comment on our field experiences to the concluding remarks of the manuscript.

Specific comments

1.    notations on p.7: $T_j$ and $T_p$ are confusing. Use capital `T` for temperature (T_j) and `t` (t_p) for time (even if it is a time period).

 

We will revise the manuscript according to these instructions.

2.    The way to reference the figures is not homogeneous. Sometimes it is entitled "Fig." while other times it is "Figure". Authors need to check the manuscript. Also, the references are not actual active links.

The journal instructions states that: The abbreviation "Fig." should be used when it appears in running text and should be followed by a number unless it comes at the beginning of a sentence, e.g.: "The results are depicted in Fig. 5. Figure 9 reveals that..." We have checked the manuscript, and we will correct one instance where we depart from the requested formatting. Regarding the actual links in the manuscript, we have used the LaTeX bibliography style from the editor. We will of course ensure that all references are properly formatted in the revised manuscript.

3.    On Section 5, line 228, you state that "The temperature essentially follows the trend obtained in the simulation with poor passive cooling". What about the other cooling methods? Could you provide a comparison between the simulation and the actual measurements for both the standard Heatsink and the customized one? I believe that it would be interesting to add some simulations results on Figure 6 to support your arguments.

It is a good suggestion, but unfortunately, we did not record useable temperature data for the standard heatsink before it was replaced with the customized heatsink. We will expand the text and add more details on the similarities and dissimilarities between the simulations and the experiments. 

4.    In Table 2, it is not clear if the values are measured ones or simulated ones. Could you explain how you obtained all critical design parameters? In particular, the values on this table are difficult to link with the results on Figure 5.

These are simulated values. We will update the caption, so this is immediately apparent. Second, the wording used in the text, i.e., “critical design parameters” will be changed. As such, the only design parameter is the thickness of the heatsink. The other values are then either computed directly, e.g., the mass, or found from the simulations, e.g., the temperature at the junction.

5.    In Table 2, it would be important, for reproducibility purposes, to specify what "Extreme Test Conditions" are.

The extreme test conditions correspond to continuous pulsing at 93 A for 3000 s. In reality, we never pulse continuously at the highest current for more than 60 s. The text will be revised to make this point clear.

6.    Figure 8 is hard to read, and particularly Figure 8a. The negative time must be removed. As previously, adding the comparison between the measurement and simulation for 10mF (i.e. plotting the simulation with the measurements) would back up your statements.

The negative time will be removed and the text surrounding Figure 8a will be improved so it better guides the reader in understanding the figure. Please note that Figures 8a and 8b are plotted on the same time axis, so the time to stabilize the current can be directly compared between the simulations and the measurement. However, the simulations and measurements are not plotted on the same panel as the initial and final currents do not match perfectly. Importantly, we can’t expect them to match perfectly as, e.g., the DC supply for the capacitor is assumed an ideal source – which it is not.

7.    Figure 10 is referenced before Figure 9.

This is a simply latex copy-paste error, and it will be fixed in the revision.

8.    Figure 9b is only showing the first intensity (~70A) compared to Figure 9a (~70A & ~20A).

This is a deliberate choice made to avoid having an excessive number of panels on the figure. The variations in the amplitude of the ~20 A pulses are similar to the variations in amplitude of the ~70 A pulses, so we only show the high amplitude results. We will add a comment about similar variations in the low amplitude pulses to the revised manuscript.

Dear Reviewer 2

Thanks for the kind review and constructive comments for the manuscript. 

Specific comments:

Do you really need the TEM part in the introduction?

Yes and no. This paper is certainly not about TEM, but we have more and more field work where the acquisition of both TEM and NMR data allows us to draw much firmer conclusions than if data was collected with either TEM or NMR alone. We have therefore decided to keep the few lines on TEM to address this fact.

L.33: To me, relaxation time is only indirectly controlled by porosity. It is controlled by the pore size and mineral components of the pore walls. The amplitude is more closely connected to porosity because of: NMR amplitude -> (mobile) water content -> porosity

The text will be revised to “…relaxation time of the NMR signals is controlled by the host material, e.g., pore size and mineral composition,…”

L.57: Isn't the 5s argument not a bit stretched? This strongly depends on the T1 of your subsurface and I can rarely remember ever seeing T1 above 500ms in the field. So maybe it is more fair to link the experiment time to the T1 time of the subsurface?

The wait time is limited by the need for re-magnetization, but obviously this time is not known at the time of measurement. Further, the wait time can also be affected in some instruments by the need to recharge capacitors. The sentence will be revised into “…a wait time of typically several seconds…”

L.60-68: I totally agree on your point about the new steady-state approach and the massive SNR enhancement. Yes, this helps us to get better data to estimate water content (and therefore porosity) but still lacks the possibility to infer proper relaxation times, right? Or at least comparable to the standard FID measurements. So without the relaxation time, we only get half of the picture. Don't get me wrong, the half we are getting with steady-state is very good but a short hint/comment on the relaxation time issue would be nice (and objectively fair) I guess.

We would like to stress that steady-state surface NMR is sensitive to amplitude as well as relaxation time. See for example the inversion results in this paper: M. P. Griffiths, D. Grombacher, L. Liu, M. Vang, and J. J. Larsen, Forward modelling steady-state free-precession in surface NMR, IEEE Transactions on Geoscience and Remote Sensing, DOI 10.1109/TGRS.2022.3221624, 2022.

L.90: Maybe it is worthy to explain the term "drooping"? I have no electrical engineering background and I could basically infer from the context what it means. So maybe to an inexperienced reader a short explanation would be quite helpful?

This is a good point. We will modify the text to “…consistent current drooping (the current amplitude decreases during the pulse) within ..”

Fig.1: I don't know what the policy of the journal is but I personally like to have the figure explained to me in the text also and not just in the figure caption. I can live with it as it is but maybe this is a point to reconsider?

We will move the majority of the caption text to section 2, “Challenges in steady-state surface NMR”.

L.125-L.130: You use the letter "T" for temperature (T_j) and time (T_p). This is bad practice. Consider maybe using also the letter \tau for time related variables (with the obvious exception of T1 and T2) like you do in eq. 2.

This was also pointed out by reviewer 1 with an almost identical suggestion. We will update the notation to according to the reviewer 1 suggestion.

L.148: As you are already referring the Fig.8b (also a bit of bad practice), the caption says  (c) instead of (b)

This will be fixed in the revision.

Paragraph 5.1: I guess it is clear but you could explicitly mention that Fig. 5 shows only simulations.

This will be explicitly mentioned in the revision. Please also see our response to reviewer 1 on this.

L.235: Technically, you could merge Fig.7 into Fig.4 so that the reader already there gets an impression of the decreased dimensions of the customized heatsink.

This is indeed a possibility, but we would prefer to keep them as separate figure as they have different scope. Figure 4 is a picture of the experimental setup, whereas Figure 7 shows the “before and after” result.

L.252: Description of Fig.8b: Can you comment on the variability of the pulse amplitude after the initial drooping. So from about 3s onward. Why does the intra-pulse drooping in the Apsu is much more pronounced compared to the simulations for 10mF (Fig.8a)?

This is a sampling artefact. In the experiments we use pulses with a 2127 Hz Larmor frequency. The duration of the pulses and the time between pulses are defined by the Larmor period. As this doesn’t match well with the sampling rate used to measure coil current data for this figure, we are essentially sampling the current at different times during each (drooping) pulse. This gives rise to the observed variations of about 1 A after 3 s. The right way to assess the stability of the pulses after the initial drooping is the analysis presented in Figures 9 and 10.

The most obvious reason for the discrepancy between simulations and experiments is that the simulations are based on an ideal DC supply feeding the capacitor bank, but the DC supply used in practice is not ideal. 

We will add comments on both these questions during the revision.

Paragraph 5.3: Maybe Fig.10 should come before Fig.9 as your explanation also starts with Fig.10?

This is a simply latex copy-paste error, and it will be fixed in the revision.

L.316: I like the beginning of last sentence ("We foresee") but would rather take it with the wink of an eye.

It is indeed a speculative comment. Time will tell if we are right.

Technical corrections:

L.29 - Earth's magnetic field (also in L.161)

L.39 - are of small amplitude or have a small amplitude

L.43 - have been very

L.63 - standard one

L.159 - contain instead of containing

L.175 - vary from

L.316 - and has been

These will be fixed in the revision process.