Analytical and Semi-Analytical Formulas for the Self and Mutual Inductances of Concentric Coplanar Ordinary and Bitter Disk Coils

Round 1

Reviewer 1 Report

Dear Editor,

This manuscript describes the self-inductance and mutual inductance between Bitter disks with inverse radial current densities. The presented expressions can calculate the mutual inductance and magnetic force with high accuracy. Good double-checking of your codes. The English are very good.

Author Response

Please find the author's responses in the attachment.

Reviewer 2 Report

Dear Author,

You have shown a detailed calculation of mutual&self inductance calculation for disc coils. You have also shown that the formula for mutual inductance can be used for self-inductance calculation as well, based on your mathematical formulation.

However, there are numerous points that are concerning regarding your work:

• English has to be improved. Just in the abstract, you have at least 4 mistakes. Please have it proof-read and corrected.
• References are wrongly enumerated in numerous places (line 141, line 169, to just name a few). Please thoroughly correct all.
• Some of the equations have errors (e.g. (5)), please correct and recheck them.
• You are comparing the results with essentially only the work from Conway, in using essentially only one of his papers. Moreover, you are pointing out that your approach is much faster when comparing the time. It is well known that the approach by Conway is extremely accurate (in terms of the extreme number of precise digits), however, it is one of the slowest available methods in terms of calculation time. Therefore, it is not used for multiple calculations (e.g. transformers). You should compare the results against other approaches in the literature.
• In what way does your approach differ from Doležel or Liang or Župan? They are all using the inverse hyperbolic functions approach and have written it in a way to be very fast (practically instantaneous), and precise. What is the novelty in this approach??
• Why are you only writing the solutions for disc coil? Practically all of your mentioned areas (transformers, generators, motors, current reactors, magnetic resonance applications, antennas, coil guns, medical electronic devices, superconducting magnets, tokamaks, electronic and printed circuit board design, plasma science,...), apart from some PCB or antenna use, cannot benefit from disc coil solution since in real life, especially when high precision is needed, all coils have a thickness (r and z coordinates). What is the point of showing a method for detailed calculations when you are neglecting one dimension? In that sense, the filament method is much easier to implement and straightforward to use.

While this is a very sound approach (practically the most logical when it comes to implementation), I have concerns regarding novelty and applicability. However, if the paper would have thick&pancake&thin solenoid (the latter two as simplifications of the first one) solutions then it would have an engineering value, especially due to the open-access of the jorunal, even though it is essentially not new.

Author Response

Please find the author's responses in the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Babic,

Please make modifications according to my comment in the attached pdf and also reproduced below:

1. In introduction, Please explain differences. Why your code is interesting for Bitter coil since you do not make any difference with radial and azimuthal current density...?
2. Bitter is avery interesting system to study but I think our code is not able to calculate such a coil...
3. Please detail with diagrams specific behavior of such a coil and explain the assumptions used. J(r) along utheta...
4. Are the CPU compared with on the same computer? otherwise it does not make sense.
5. Please draw figures for each different examples!
6. Please compute at least, the inductance and mutual of one realistic Bitte coil configuration such as NHMFL type ?

BR,

The reviewer

Comments for author File: Comments.pdf

Author Response

Please find the author's responses in the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thank you for the revision. Unfortunately, I haven't seen any big changes, that were required, mainly:

• showing the difference between the mentioned other works, which are practically the same (only Conway, which is not applicable from an engineering perspective). Incorporating the comparison of the results against other approaches in the literature.
• broadening to incorporate both solenoid, pancake and thick

I do not consider that mentioning the number of your references for your other papers (in the same field) would be sufficient for publishing this paper. This is completely irrelevant and I would recommend not to mention it in the future correspodence.

I would still urge you to revise the paper as stated in the first review.

Author Response

I send you my answers.

Slobodan Babic

Author Response File: Author Response.pdf

Reviewer 3 Report

The author explained what he did by only citing his work in the response document and saying that everything was fine but did not make the requested changes.

In Bitter coils the current is always azimuthal and not radial but has a variation according to r, which is different. The authors should specify that J Bitter = J(r) u_theta and show the current density J(r) in the Bitter coil.

If the Bitter coils allow to produce an intense field, and the article deals with the case of Bitter coils but the formulas proposed in THIS article do not apply to realistic cases, then it is completely useless and inappropriate to talk about application for Bitter coils... This application and the references to Bitter coils should be deleted.

The author must ask the question and the reader must know if any Bitter coils with concentric coplanar discs exist?

The CPU time comparison is not fair and should be removed. Just point out that this calculation is immediate!
I was always taught that a figure always speaks more than 100 words. That's why the figures representing the coil geometries, their positioning and the direction of the current is mandatory.

My remarks do not affect the formulas that are proven, but to be of any use, the remarks mentioned here must be taken into account.

Author Response

I send you my comments,

Slobodan Babic

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Dear Author,

Thank you for a detailed revision of the manuscript. In this form, I consider it highly interesting for a broad engineering audience, especially young researchers in the field. It will be of great help to them.

Congratulations!

Reviewer 3 Report

Thank you for improving your work based on the suggested comments.