Measurement and Simulation of Demagnetization in a Prototype Halbach Array Quadrupole

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This  manuscript describes  unexpected difficulties in the design and manufacuring of quadrupoles magnets for electrons accelerators. Of particular interest, albeit not emphasized by the authors is the degradation of perfomances following dismantlement and rebuilding of the quadrupole.  This article is interesting and deserves publication, after the authors have answered the following questions and requests:

1. In Fig.10,  how are the measurements carried out? Was it done  as in Fig.8? From another point of view, it is surprising that the difference between the magnetization  of ID09 and ID24 on the one hand and ID04 on the other hand  is a few degrees only. Is this consistent with Fig.6? 

2. Can you please detail the process resulting in the graphs in Fig.11, maybe with the help of an additional  figure ? The given explanations are not easy to understand for people lacking expertise  in numerical simulations.

Author Response

The authors would like to thank all three reviewers for their time and effort in reading and reviewing our manuscript in detail. We have read their insightful and highly constructive comments and we have made several edits and expansions to the manuscript to address their comments. These are detailed below, alongside our additional responses to some comments. We are pleased with the feedback that suggests that the work is of current relevance and interest, and we hope that this edited manuscript addresses the reviewers concerns sufficiently to reach the point of suitability for publication.

In specific response to Reviewer 1, we thank the reviewer for their positive comments and their indication that they are willing to sign the report is appreciated. The reviewer has raised two key questions, both of which we agree highlighted areas where the manuscript lacked detail and as such, we have edited the manuscript to address these.

Point 1 stated that: “In Fig.10,  how are the measurements carried out? Was it done  as in Fig.8? From another point of view, it is surprising that the difference between the magnetization  of ID09 and ID24 on the one hand and ID04 on the other hand  is a few degrees only. Is this consistent with Fig.6?”

Our response: The data in this figure was taken in the same manner as the data in figure 8, we have added a sentence to the manuscript to state this (lines 234-236) - "The two unused blocks shown in Figure 11 were measured in the same manner by scanning the Hall probe over the individual blocks as for the data shown in Figure 9". This comment also helped us to notice a mistake in the paper, the 4^th panel was labelled as the angle being in degrees, this was a mistake, it should have been labelled as radians. This has been corrected and the caption has been edited to clarify that measurement (Figure 11 and caption, page 11).

Point 2 stated that: “Can you please detail the process resulting in the graphs in Fig.11, maybe with the help of an additional  figure? The given explanations are not easy to understand for people lacking expertise  in numerical simulations.”

Our response: We agree that this could have been expanded upon, and as such we have added new content to section 6 of the manuscript to add more detail and explain the process in a step-by step fashion. Two new figures illustrating intermediate steps have been included to reinforce this expanded explanation (multiple significant changes on pages 11-13, new figures as Figs.12 and 13.)

Reviewer 2 Report

Comments and Suggestions for Authors

The paper is well written. However, there are several areas for improvement. Please refer to the attachment for details.

Comments for author File: Comments.pdf

Author Response

The authors would like to thank all three reviewers for their time and effort in reading and reviewing our manuscript in detail. We have read their insightful and highly constructive comments and we have made several edits and expansions to the manuscript to address their comments. These are detailed below, alongside our additional responses to some comments. We are pleased with the feedback that suggests that the work is of current relevance and interest, and we hope that this edited manuscript addresses the reviewers concerns sufficiently to reach the point of suitability for publication.

Reviewer 2 made  a number of detailed and constructive comments and in response we have made multiple edits. Our response to each point is as follows:

Point 1 stated that: "The selection of VACODYM-745-TP as the permanent magnet material, despite its relatively low coercivity, is questionable given the high field strengths involved. The authors mentioned this in hindsight but do not provide a comparative analysis of alternative materials that could have mitigated demagnetization. A more thorough discussion of material selection trade-offs,including higher coercivity alternatives, would improve the paper."

Our response: The reviewer makes  a valid point about the poor material selection. The primary focus of the design was to achieve the highest gradient, therefore the remnant field of the magnet blocks was given higher priority than the coercivity. Naturally we recognize in hindsight that this was a mistake on our part. The demagnetisation effects were of course not discovered until the magnet was assembled but the revised modelling method introduced in the paper will allow the trade-off between remnant field and coercivity to be better optimised in future magnet designs.

We have added the sentence: “This material was chosen because of its high remanent flux density because at the design stage the demagnetisation effects, which would have been mitigated by the use of a higher coercivity material, were not predicted.” (Lines 64-66)

We have also expanded the conclusion to state: “For example material grade VACODYM-806-TP has a Hcj of -1990 kA/m and a Br of 1.3 Tesla and so may be appropriate, although would require a larger volume of material to achieve the required strength. Alternatively, materials that have undergone grain boundary diffusion are also more resistant to demagnetization but are only effective in certain aspect ratios.” (lines 346-350)

Point 2 stated: "Although the experimental measurements are conducted with precision instruments, the quadrupole magnet was placed on a separate table from the vibration-isolated granite bench, which may have introduced additional measurement problem. The Hall probe methodology used to measure field gradients is known to be sensitive to probe positioning errors. While circular sweeps were performed for verification the paper lacks a detailed uncertainty quantification for the measurement process. Better experimental validation protocols would benefit the paper."

Our response: Although the magnet was on a separate table, the measurements were taken at a time when no other heavy work was being performed nearby and so external sources of vibration were limited. We do have data on the uncertainty in the Hall probe measurements as the probe also reports the standard deviation of its readings, as each reading is taken as the average of 1000 individual readings. We have expanded the caption to figure 3 (which was figure 2) to give the values (page 4). We have estimated the uncertainty in the graph showing integrated harmonics and have applied error bars on to the graph (figure 4, page 5), although they are small and so are difficult to see, especially if the page is printed. They can be seen when zoomed in on the pdf. These error bars only reflect the errors that we can directly quantify, such as the standard deviation of probe measurements. We also noticed a mistake in the graph whilst making this edit – the data had been accidentally plotted such that where real and skew harmonics had the same sign the bars were stacked, giving a slightly misleading impression of the strength of the n=5 harmonic in particular, this mistake has been corrected in the revision (Fig. 4(b), page 4).

Point 3 stated: "While the study acknowledges that Halbach quadrupoles typically exhibit poorer field homogeneity than traditional electromagnets, it does not explore potential corrective measures. Furthermore, given the significant impact of demagnetization on performance, discussing the stability of these magnets under operational conditions would be beneficial."

Our response: We did not explore such measures in this case as they were not necessary as the magnet met the required homogeneity specification. We have added a sentence to section 3 to explicitly state this (lines 133-135).

Point 4 stated: "An image of the Hybrid Halbach Quadrupole model with the magnetization vectors of each block indicated should be added to the paper."

Our response: We have added a figure showing this as requested, which is the new figure 1. (page 2)

Point 5 stated: "The paper should clearly state how the vectors are labeled and what each vector represents. Specifically, in equation (1) and line 174, is Hopp a vector or a scalar? Clarifying this would improve readability."

Our response: It is a scalar, we note that there was an accidental underline on it which showed it as a vector, this error has been corrected to remove the confusion (eqn. 1, page 8). In addition we have improved the consistency throughout the manuscript of using underlines to denote vectors (multiple changes throughout document).

Point 6 stated: "The percentage deviation of the results shown in Figure 9 should be mentioned to provide a clearer understanding of the data variation."

Our response: We agree, and so we have added a sentence to the discussion of the figure (now figure 10) stating that “Over the tip of the block, at z=0, the degradation is 3.5%.” (Line 231)

Point 7 stated: "In line (227), the values of y and z, along with the label for magnetic flux density B, should be in the index, and the vector modulus B should be labeled as shown in Figure 10 (the notation in the text is not consistent with the notation in Figure 10). Additionally in the same line, the label for the angle of the magnetization vector , should be provided in accordance with the notation in figure 10."

Our response:  We agree that the differences in notation were confusing, and we have edited the manuscript to make this much more consistent throughout the document.

The reviewer also commented: "However, future studies should incorporate demagnetization effects from the outset, rather than treating them as a post experimental correction"

Our response: We entirely agree with this statement, indeed that this is the message this publication aims to convey and it was already stated in the conclusion by the phrase “We present this as a warning in particular that designers should inspect their models for potential demagnetization effects properly, and should modify their models to simulate these effects if the potential for demagnetization is suspected.”

The reviewer also made a final comment: "Also, during the magnet reassembly phase, human errors led to the incorrect insertion of magnet blocks, resulting in additional demagnetization. This mistake highlights potential 2 weaknesses in assembly protocols and quality control that should be changed in further investigation."

Our response: We agree and so we have made some minor edits to the conclusion to remark on this fact (line 330). And we can confirm that for the four other identical quadrupoles that we are currently constructing, we have indeed developed much clearer assembly protocols.

 

 

Reviewer 3 Report

Comments and Suggestions for Authors

Please see attachment.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

 The English should be improved to more clearly express the research.

Author Response

The authors would like to thank all three reviewers for their time and effort in reading and reviewing our manuscript in detail. We have read their insightful and highly constructive comments and we have made several edits and expansions to the manuscript to address their comments. These are detailed below, alongside our additional responses to some comments. We are pleased with the feedback that suggests that the work is of current relevance and interest, and we hope that this edited manuscript addresses the reviewers concerns sufficiently to reach the point of suitability for publication.

Reviewer 3 highlighted three key areas where they saw points of uncertainty in the article where additional explanation was desirable.

Point 1 stated: "The direction and origin of the 3D axis should be clearly defined and explained before presenting the measurement data. It is preferable to include a figure illustrating this."

Our response: We have edited Figure 2 (which was originally Figure 1) to show the coordinate system used for the measurements of the assembled magnet and have updated the caption to reflect this (Fig. 2 and caption, page 3). The coordinate system for measurements of individual blocks is shown in what is now Figure 9 (which has also had a minor edit made to the caption) (Page 9).

Point 2 stated: "The structure of the proposed hybrid Halbach quadrupole magnet is understood to have a 4-fold symmetric structure. Figure 6 was estimated based on this assumption, whereas the simulation result in Figure 7 does not exhibit this symmetry. Why does the simulation result deviate from the 4-fold symmetry? The article should include an additional explanation for this discrepancy."

Our response: The symmetry is not broken, but we understand that the way that the colour overlay was presented may have been quite confusing, as the colour map overlay on the entire magnet was defined by the magnetisation relative to one blocks magnetization vector, rather than each block being mapped relative to its own magnetization vector, which would have shown the symmetry but also, in our opinion, would have been even more visibly confusing. To address this comment we have remade the image to and have re-written the caption to reflect the new image, which we hope will make it clearer what we are actually trying to show (Fig. 8 and caption, page 8).

Point 3 stated: "In the case of rebuilding the magnet (Section 7), the generated magnetic field differed from the original one, as shown in Figure 12. This result raises concerns and doubts about the correctness of the fabrication procedure for this prototype magnet. The author should provide additional explanation regarding the assembly considerations for this hybrid Halbach quadrupole magnet to prevent demagnetization."

Our response: This point was similar to one made by reviewer 2 regarding the rigorousness of the assembly procedure. We have added the statement “This result highlights the importance of a rigorous assembly procedure." (Line 312-313) In addition to some other minor edits to the conclusion in our response to reviewer 2, which also addresses this point. The reviewer also remarked that a comment should be included on why the rebuilt magnet experienced such a demagnetising force.  Some text is already included in the rebuild section, which I believe addresses the comments of the reviewer, but we have expanded that text to state: “However during the incorrect insertion these two blocks were exposed to strong fields from the neighbouring blocks in opposition to their magnetization vector which likely demagnetized them further, as well as affecting the neighbouring blocks. Rather than flux feeding from one block into another as per Figure 1, the magnetization vectors would have pushed flux at an orthogonal angle to the magnetization vector near the join between the blocks, resulting in local demagnetization followed by re-magnetization in that new orthogonal direction.  Following the rebuild a severe degradation in gradient homogeneity was also observed, even after the mistake in block positioning was corrected. This indicates that the incorrectly inserted blocks did indeed experience further permanent degradation.” (Line 296-302)

 

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is suitably revised.