Study of Possible Frequency Dependence of Small AC Fields on Magnetic Flux Trapping in Niobium by Polarized Neutron Imaging

Round 1

Reviewer 1 Report

Dear Authors,

Thank you for your dedicated work in magnetic flux trapping in superconducting materials. Your study contains both experimental and simulation work, which would provide more convincing conclusion. There are some questions need to be addressed.

1. What is the purpose of using a offset, Boffset,  to the magnetic field? Why is it chosen to be 0 to 0.5mT?
2. Figure 3 to 6. Are those plots in equilibrium states? Will the trapped flux reach equilibrium eventually? Or the intensity of the signal at each location change with time?
3. Figure 7 and 8. Seems the experimental data is quite different from the simulation data. What is the reason for this? Is this due to the selection of the experimental data, which changes with time? Or the selection of the magnetic field in simulation? Or the error in the experiment, such as the angle of the field and sample, the design of the equipment, or the environmental noise?
4. So the summary of this manuscript is that no magnetic flux trap can be suppressed with small alternating magnetic field. So how about stronger magnetic field or higher/lower frequency? The size/shape of the superconductor? Temperature? Uniformity of the magnetic field? More study is needed to get a more convincing conclusion.

Yours Sincerely

Author Response

ANSWER TO REVIEWER 1

Thank you for your dedicated work in magnetic flux trapping in superconducting materials. Your study contains both experimental and simulation work, which would provide more convincing conclusion. There are some questions need to be addressed.

1. What is the purpose of using a offset, Boffset,  to the magnetic field? Why is it chosen to be 0 to 0.5mT?
   
   Answer:  Added to text (to clarify the text):
   The mobility of the flux lines is highest at T ~ Tc,  an alternating magnetic field applied to the sample during cooling is supposed to enhance the mobility of the flux lines and their movement in the axial direction by adding a constant field.
   
   The sample was held in a closed cycle refrigerator between two Helmholtz coils, so  that 5mT  was  the largest constant
2. field that could be generated with the Helmholtz coils.
   
   Do you mean 0.5Hz? An earlier series with 10 Hz showed no influence on the flux trap. Therefore the range 0 to 0.5 Hz was chosen as low frequency AC
   
   
3. Figure 3 to 6. Are those plots in equilibrium states? Will the trapped flux reach equilibrium eventually? Or the intensity of the signal at each location change with time?
   
   Answer:
   A trapped flux is constant after switching off the  magnetic field cooling  and the AC field.
   Therefore,  the intensity of the measured signal does not change  with time
   
   
4. Figure 7 and 8. It seems the experimental data is quite different from the simulation data. What is the reason for this? Is this due to the selection of the experimental data, which changes with time? Or the selection of the magnetic field in simulation? Or the error in the experiment, such as the angle of the field and sample, the design of the equipment, or the environmental noise?
   
   Answers:
   In Fig.7, the measured and calculated images agree indeed worse with each other than in Fig.8, where they agree better, however, they still agree well although this does not appear to be the case:
   In the calculations, one can assume a constant trapped field throughout the sample, when it is in the superconducting phase.  In the measurement the neutron spin is additionally influenced by superposition of smallest inhomogeneities of the Helmholtz field and by smallest stray fields of the analyzer, which manifests itself in a false color representation. However, this is a constant contribution to all measurements. It is extremely difficult to take these contributions into account, so we compared the corresponding line plots with each other.
   
   
5. So the summary of this manuscript is that no magnetic flux trap can be suppressed with small alternating magnetic field. So how about stronger magnetic field or higher/lower frequency? The size/shape of the superconductor? Temperature? Uniformity of the magnetic field? More study is needed to get a more convincing conclusion.
   
   Answer:
   Indeed, more study is needed, but keeping in mind the very  experimental time consuming  and  evaluations and the coming shut down of the BER II did not allow for further investigations on this subject. But they will be continued at the high flux reactor in Grenoble where an instrument is going to be set up. 
   
   

We would like to thank the reviewer for all the errors found, precise comments and suggestions that really helped to improve our work. We have addressed all points in the text and captions and hope to have answered all questions satisfactorily.

Many thanks

1. Treimer

Author Response File: Author Response.docx

Reviewer 2 Report

The authors report on a study of magnetic field trapping in niobium, and about how trapping may be affected by small AC magnetic fields. The polarized neutron study on Nb single crystals produced quantitative and spatially resolved magnetic flux values which were compared to calculated values. The hypothesis of alternating fields affecting the trapping behaviour remained inconclusive but could not be ruled out for an untreated Nb sample. Overall, the data are sound and the conclusions are reasonable. The study is an excellent example of how polarised neutron imaging is unique for visualizing flux trapping.

The authors were careful not to over-interpret their results: slight frequency dependencies visible in the recorded images (Fig. 3 - Fig. 6) and in the analysed images (Fig. 10) were not considered significant; a trapped field decreases with frequencies for the treated sample.

The manuscript needs minor corrections and adjustments. I recommend that the following points are addressed:

Page 2 Line 33:  The text mentions spin analysers before the experiment is described. Also, the stray field was mentioned (0.19mT) at a sample-analyser distance of 18cm etc. Such details seem to be misplaced in the theory section. I wonder if such details can be moved to the experimental section.

Page 3 Fig 1:  The label says: Pb sample. This needs to be: Nb sample

Page 5 Line 3:  The central pixel areas were selected to determine the trapped field etc. It would be good if the authors gave some more detail about which region of interest was selected. Was it one row, or several rows? Is this related to the yellow box in Fig. 4?

Page 6 Line 53:  There is some inconsistency with regard to the sample crystallinity: … polycrystalline sample …  On page 3 line 1 the samples are introduced as single crystalline.

The manuscript is well written overall. There are a number of formatting and language issues to be addressed:

• several references appear non-sequentially on pages 1+2: #18-#23; #23; #26; #28
• The authors appended enlarged figures 3-8 at the end of the manuscript. This helped reading the paper a lot. One should think about enlarging those same figures in the manuscript.
• Leave a blank between values and units (multiple occasions in the manuscript).

Language:

• Page 1 Line 40: what is RRR?
• Page 1 Line 41: which methods?
• Page 1 Line 87: led (instead of lead
• Page 2 line 80 ( and at several other places): flux trap; amount of trapping; etc :  maybe better: flux trapping; level of trapping; etc
• At several places: should it be: buffered chemical polished, instead of: buffered chemically polished?
• Page 2 line 3: complementary (instead of: complimentary
• Page 2 line 45 only (remove preceding comma); appears more than once in the paper;
• Page 2 line 60 … alpha is constant in this calculation …
• Page 2 line 82 what is being quantified?
• Page 3 line 13 … were …
• Page 3 line 55/56 images? items?
• Page 4 line 22 fourth row in Fig. 4 is referred to but there are only three rows in the figure
• Page 4 line 29 … for the sample orientation (instead of: in the sample orientation); occurs more than once in the paper;
• Page 5 Fig 7 caption: (… first row in Fig. 3)
• Page 5 line 30: weaker (instead of smaller
• Page 6 line 32: remove ‘themselves’
• Page 6 line 4: there is no fourth row in Fig. 6
• Page 7 line 30 small angle scattering (instead of: angled)
• Page 7 line 62 … assess … (instead of: access)

Author Response

ANSWER TO REVIEWER II

The authors report on a study of magnetic field trapping in niobium, and about how trapping may be affected by small AC magnetic fields. The polarized neutron study on Nb single crystals produced quantitative and spatially resolved magnetic flux values which were compared to calculated values. The hypothesis of alternating fields affecting the trapping behaviour remained inconclusive but could not be ruled out for an untreated Nb sample. Overall, the data are sound and the conclusions are reasonable. The study is an excellent example of how polarised neutron imaging is unique for visualizing flux trapping.

The authors were careful not to over-interpret their results: slight frequency dependencies visible in the recorded images (Fig. 3 - Fig. 6) and in the analysed images (Fig. 10) were not considered significant; a trapped field decreases with frequencies for the treated sample.

The manuscript needs minor corrections and adjustments. I recommend that the following points are addressed:

Page 2 Line 33:  The text mentions spin analysers before the experiment is described. Also, the stray field was mentioned (0.19mT) at a sample-analyser distance of 18cm etc. Such details seem to be misplaced in the theory section. I wonder if such details can be moved to the experimental section.

Answer:

We agree and moved this part at the end of section III. A, where it fits much better.

Page 3 Fig 1:  The label says: Pb sample. This needs to be: Nb sample

Yes, we have changed the label in Fig.1

Page 5 Line 3:  The central pixel areas were selected to determine the trapped field etc. It would be good if the authors gave some more detail about which region of interest was selected. Was it one row, or several rows? Is this related to the yellow box in Fig. 4?

Answer:
Yes, we clarify and add (please see also text):
The size of each image was  500 x 600 pixel   (21.5mm x 25.8mm), the area of integration was  1024 pixel  =  32 pixel x 32 pixel (1.37 mm x 1.376mm = 1.893mm²), the yellow boxes in Fig.4  show the projected volumes of yellow circles  in Fig.6.   

Page 6 Line 53:  There is some inconsistency with regard to the sample crystallinity: … polycrystalline sample …  On page 3 line 1 the samples are introduced as single crystalline.

Answer:
The used Nb sample was polycrystalline,

The manuscript is well written overall. There are a number of formatting and language issues to be addressed:

• several references appear non-sequentially on pages 1+2: #18-#23; #23; #26; #28
  The authors appended enlarged figures 3-8 at the end of the manuscript. This helped reading the paper a lot. One should think about enlarging those same figures in the manuscript.
      OK that must be done be the journal
  
  
• Leave a blank between values and units (multiple occasions in the manuscript).
      OK, done

Answer:
 Concerning non-sequentially: The references  are given corresponding to the text, and  authors are cited belonging to different subjects, however we agree with Reviewer

Language:

• Page 1 Line 40: what is RRR?
      Is added to text: residual resistivity ratio
• Page 1 Line 41: which methods?
      Methods cited in [1] –[11]
• Page 1 Line 87: led (instead of lead) :  
      Corrected
• Page 2 line 80 ( and at several other places): flux trap; amount of trapping; etc :  maybe better: flux trapping; level of trapping; etc
      Throughout  the  paper flux trapping is used,
• At several places: should it be: buffered chemical polished, instead of: buffered chemically polished?
      buffered chemically polished is correct
• Page 2 line 3: complementary (instead of: complimentary
  Corrected
• Page 2 line 45 only (remove preceding comma); appears more than once in the paper;
      Corrected
• Page 2 line 60 … alpha is constant in this calculation …
•     Corrected
• Page 2 line 82 what is being quantified?
     Amount/level of flux trapping
• Page 3 line 13 … were …
     OK
• Page 3 line 55/56 images? items?
      corrected: images  
• Page 4 line 22 fourth row in Fig. 4 is referred to but there are only three rows in the figure
       there are only three rows …. is  corrected
• Page 4 line 29 … for the sample orientation (instead of: in the sample orientation); occurs more than once in the paper;
       Through the paper corrected (in / for)
• Page 5 Fig 7 caption: (… first row in Fig. 3)
      corrected
• Page 5 line 30: weaker (instead of smaller)
     corrected
• Page 6 line 32: remove ‘themselves’
  removed
• Page 6 line 4: there is no fourth row in Fig. 6
     corrected
• Page 7 line 30 small angle scattering (instead of: angled)
    corrected
• Page 7 line 62 … assess … (instead of: access)
      corrected

 We would like to thank the reviewer for all the errors found, precise comments and suggestions that really helped to improve our work. We have addressed all points in the text and captions and hope to have answered all questions satisfactorily.

Many thanks

1. Treimer

Reviewer 3 Report

Polarised-neutron imaging offers the unique possibility to image magnetic fields directly with a typical resolution of 0.1 – 0.2 mm which is well suited to investigating the magnetic fields within components of interest in current technological and instrumental application. This article applies polarised-neutron imaging to the study of the effect of the application of small-amplitude oscillatory variation of a magnetic field on the trapped magnetic flux while cooling a sample of niobium into its superconducting phase, with the hope that it might indicate that field oscillation reduces the magnetic flux trapping. This study is a logical consequence in a series of experiments by some the authors. Although polarised-neutron imaging is barely 13 years old, the technique is now quite well established, albeit at just a handful of facilities, and there have been numerous detailed descriptions of the theory in previous publications. Nevertheless, section II in this article (Short theory of polarized neutron imaging) will be useful for readers who are not so familiar with the technique. The description of the experiments (section III a) is reasonably clear and concise. The study showed directly that AC variation of the field while cooling through the superconducting phase transition does not suppress the degree of flux trapping but does improve the homogeneity. This result should be of interest to other researchers in the field. I therefore recommend publication, if the authors consider the following:

• While the article has been written quite lucidly, it does contain some typographical errors. I attach an annotated copy of the submission, which indicates recommended (most) typographical and grammatical changes, as well as highlighting most of the following points.
• Some abbreviations which may not be obvious to many readers are not defined. These include CW, RRR, and L/D.
• State why niobium was chosen for this experiment.
• The indicated B-field direction at the polariser in Figure 1 is next to the magnetic guide field. Does it indicate the field direction in both the polariser and the guide field?
• Replace ‘lead sample’ by ‘sample’ in Figure 1.
• I suggest rephrasing the description of the detector to something like ‘the 2D detector (2048 x 2048 pixels, pixel size = 13.5 <mu>m)’. (<mu> is the Greek symbol mu)
• The sentence starting at line 33 on page 3 is not very clear to me. Is the sample-to-screen distance 60 mm in the non-polarised configuration of the instrument and increased to 200 mm with polarised neutrons due to the analyser?
• Add a colour intensity scale to Figure 2, even if the absolute values are arbitrary.
• Give the values of blue and red in the captions to Figs. 4, 5, and 6, as is done in Fig. 3.
• The sample is rotated to the 90 degree orientation only after field cooling in the 0 degree orientation. Thus the sequence for a particular AC-field frequency is: field cooling to 5 K in the 0 degree orientation, external field turned off, imaging at 5K in the 0 degree orientation, rotation to the 90 degree orientation, imaging at 5K in the 90 degree orientation, warming to 15 K. Make it clear in the text (Line 16, page 3) that the sample was warmed up to 15 K before tackling the next parameter set.
• Although it is clear after a little thought that the line plots correspond to projections onto the vertical axis of the 2D plots within the central areas, state this in the captions of Figs 7 and 8.
• The terms ‘trapped field’, ‘flux trap’, ‘flux trapped’, and ‘trapped flux’ appear to be used interchangeably. Please choose one term and use it consistently. If there is a difference between ‘trapped field’ and ‘trapped flux’ in their uses here, please define the difference clearly.

Comments for author File: Comments.pdf

Author Response

ANSWER TO REVIEWER III

Polarised-neutron imaging offers the unique possibility to image magnetic fields directly with a typical resolution of 0.1 – 0.2 mm which is well suited to investigating the magnetic fields within components of interest in current technological and instrumental application. This article applies polarised-neutron imaging to the study of the effect of the application of small-amplitude oscillatory variation of a magnetic field on the trapped magnetic flux while cooling a sample of niobium into its superconducting phase, with the hope that it might indicate that field oscillation reduces the magnetic flux trapping. This study is a logical consequence in a series of experiments by some the authors. Although polarised-neutron imaging is barely 13 years old, the technique is now quite well established, albeit at just a handful of facilities, and there have been numerous detailed descriptions of the theory in previous publications. Nevertheless, section II in this article (Short theory of polarized neutron imaging) will be useful for readers who are not so familiar with the technique. The description of the experiments (section III a) is reasonably clear and concise. The study showed directly that AC variation of the field while cooling through the superconducting phase transition does not suppress the degree of flux trapping but does improve the homogeneity. This result should be of interest to other researchers in the field. I therefore recommend publication, if the authors consider the following: 

• While the article has been written quite lucidly, it does contain some typographical errors. I attach an annotated copy of the submission, which indicates recommended (most) typographical and grammatical changes, as well as highlighting most of the following points.
• Some abbreviations which may not be obvious to many readers are not defined. These include CW, RRR, and L/D.
      CW = continuous wave, RRR = residual resistivity ratio, L/D = distance source-
      sample / source size = inverse divergence 
       We have added this  to text
  
  
• State why niobium was chosen for this experiment.
      Niobium is an important material in all superconducting cavities;
       added in text
  
  
• The indicated B-field direction at the polariser in Figure 1 is next to the magnetic guide field. Does it indicate the field direction in both the polariser and the guide field?
       Thank you, an important comment: Guide field direction is parallel to polarizer and
        analyzer field direction. We have added this to text.
• Replace ‘lead sample’ by ‘sample’ in Figure 1.
        Corrected
  
  
• I suggest rephrasing the description of the detector to something like ‘the 2D detector (2048 x 2048 pixels, pixel size = 13.5 <mu>m)’. (<mu> is the Greek symbol mu)
      Yes, corrected in text
  
  
• The sentence starting at line 33 on page 3 is not very clear to me. Is the sample-to-screen distance 60 mm in the non-polarised configuration of the instrument and increased to 200 mm with polarised neutrons due to the analyser?
     Yes, we have  added clarifying text
• Add a colour intensity scale to Figure 2, even if the absolute values are arbitrary.
    We have added numbers in figure caption
  
  
• Give the values of blue and red in the captions to Figs. 4, 5, and 6, as is done in Fig. 3.
     We have added explanation in all figures captions,  please see text.
  
  
• The sample is rotated to the 90 degree orientation only after field cooling in the 0 degree orientation. Thus the sequence for a particular AC-field frequency is: field cooling to 5 K in the 0 degree orientation, external field turned off, imaging at 5K in the 0 degree orientation, rotation to the 90 degree orientation, imaging at 5K in the 90 degree orientation, warming to 15 K. Make it clear in the text (Line 16, page 3) that the sample was warmed up to 15 K before tackling the next parameter set.
       Yes ….  we have completed the text in this regard
      
• Although it is clear after a little thought that the line plots correspond to projections onto the vertical axis of the 2D plots within the central areas, state this in the captions of Figs 7 and 8.
     Yes, good idea! Done, see text.
  
  
• The terms ‘trapped field’, ‘flux trap’, ‘flux trapped’, and ‘trapped flux’ appear to be used interchangeably. Please choose one term and use it consistently. If there is a difference between ‘trapped field’ and ‘trapped flux’ in their uses here, please define the difference clearly.
     Corrected: Throughout the MS we use “trapped field”

We would like to thank the reviewer for all the errors found, precise comments and suggestions that really helped to improve our work. We have addressed all points in the text and captions and hope to have answered all questions satisfactorily.

Many thanks

1. Treimer

Round 2

Reviewer 1 Report

Dear Authors,

Thank you for your updated manuscript. The experimental methods and results analysis are more clear and understandable now for readers.

Yours Sincerely.

Author Response

Dear Reviewer,

Again, we would like to thank the reviewer for accepting our revision.

W. Treimer