the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Automated Static Magnetic Cleanliness Screening for the TRACERS SmallSatellite Mission
Cole J. Dorman
Chris Piker
Abstract. The Tandem Reconnection and Cusp Electrodynamics Reconnaissance Satellites (TRACERS) Small Explorers mission requires highfidelity magnetic field measurements for its magnetic reconnection science objectives and for its technology demonstration payload MAGnetometers for Innovation and Capability (MAGIC). TRACERS needs to minimize the local magnetic noise through a magnetic cleanliness program such that the stray fields from the spacecraft and its instruments do not distort the local geophysical magnetic field of interest. Here we present an automated magnetic screening apparatus and procedure to enable technicians to routinely and efficiently measure the magnetic dipole moments of potential flight parts to determine whether they are suitable for spaceflight. This procedure is simple, replicable, and accurate down to a dipole moment of 1.59 × 10^{3} N m T1. It will be used to screen parts for the MAGIC instrument and other subsystems of the TRACERS satellite mission to help ensure magnetically clean measurements onorbit.
Cole J. Dorman et al.
Status: open (extended)

RC1: 'Comment on egusphere2022480', Anonymous Referee #1, 04 Aug 2022
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See the attached PDF file.

CC1: 'Reply on RC1', Cole J Dorman, 19 Feb 2023
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Referee
Journal of European Geosciences Union
DOI: https://doi.org/10.5194/egusphere2022480
Title: Automated Static Magnetic Cleanliness Screening for the TRACERS SmallSatellite Mission
Authors: Cole J. Dorman^{1, 2}, Chris Piker^{1}, and David M. Miles^{1}^{1}Department Physics and Astronomy, University of Iowa, Iowa City, 52242, USA
^{2}Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, 48109, USA
Dear Referee,
We would like to thank you and for your careful consideration and time in handling our manuscript. We truly believe that the revised manuscript has been significantly improved by your suggestions.
The appendix below details our response to each of the comments. We hope that this revised and resubmitted manuscript addresses these comments appropriately. Please let us know if you have any questions regarding our resubmission. Thank you again for handling our manuscript.
Best Regards,

Cole J. Dorman
PhD PreCandidate
Department of Climate and Space Sciences and Engineering
University of Michigan, Ann Arbor
Email: cjdorman@umich.edu
Phone: (563) 2093148Appendix
Key:
Italics  Original Reviewer Comment
Bold – Author Response
(Text with Parenthesis) – Changed/Added Text
[[Text with Brackets]] – Large Changes to Manuscript, Not Detailed Here
No modifications – Original Text, Included for ContextLine 54, Figure 2, and line 97
It is better to specify the maximum size of an object to be tested. This point is related to an assumed farfield measurement.
RE: Thank you for the comment. We added further clarification in lines 103105 on the maximum sized objects to be tested:
“If the calculated dipole moment is less than its allocation then the measured object would be considered suitable to go on the spacecraft. (The farfield assumption of B relies heavily on the distance of the measuring sensors from the screening object. If the sensor is at least 5 times farther away from the centered screening objects characteristic radius, the farfield assumption holds (Bansal, 1999))”Figures 2 and 3
The subplots in Fig. 2 (times series measured by magnetometers at 11 cm and at 17 cm) are identical to the subplots in Fig. 3. This means that the authors can rearrange these figures to one figure.
RE: Thank you for your comment. While the subplots in Fig. 2 do reappear in Fig. 3, it is simply for continuity reasons for the reader. We believe Fig. 2’s schematic of collecting sinusoidal magnetic data using a spin modulated tray and Fig. 3’s demonstration of using discrete Fourier transform is distinct enough in meaning to be stay separated.
In the upperleft subplot of Fig. 3, the peaktopeak amplitude of Bz seems to be about or larger than 4000 nT, but the corresponding periodic amplitude in the upper right subplot is 3223.3 nT. Is this caused by a flattop window applied to time series? If it is the case, it is better to mention it. By the way, which is better, use of a flattop window or not?
RE: Thank you for the comment. An appeared change in periodic amplitude would be caused by the flattop window. We added clarification:
“(Due to the flattop window taking averages of magnetic intensity peaktopeak, it finds a periodic intensity of the sinusoidal peak divided by √2.)”
The flattop window lowers the frequency resolution of the Fourier transform in order to reduce amplitude noise. We believe we sufficiently explained the strength of using a flattop window over no window at all in lines 8185:
“Without a flattop window, slight changes in rotational frequency could disperse our target spinmodulated signal across multiple frequency bins in the DFT and degrade our estimate of the magnetic field component. A flattop window (D’Antona and Ferrero, 2005) is used to improve the accuracy of amplitude measurement at the expense of reduced frequency resolution (which is irrelevant in this application).”Equation (1)
The subscript m should be specified. Later, m is used as the magnetic dipole moment.
RE: Thank you for your comment. We decided to just remove the m subscript. It was not necessary and saves any confusion.Equations (2) and (3)
The subscript k should be specified.
RE: Thank you for your comment. We changed this subscript to be now a subscript “l”, as a k subscript appears unrelated later in the manuscript. The subscript l denotes the summation of variable x from l=0 to infinity and is common enough of mathematical notation that the reader will not need explanation. We also chose to remove the k subscript from ω.Equations (4) and (5)
Vectors r, ϑ, i, j, and k should be specified.
RE: We added additional information:
“Where B is the magnetic field, 𝜇0 is the vacuum permeability constant, m is the dipole moment, r is distance, θ is the dipole’s angle from the z axis, and 𝜑 is the dipole’s angle from the x axis. (Vectors r and ϑ denoted radial and azimuthal units in spherical coordinates, and vectors i, j, and k denote longitudinal, lateral and normal units in cartesian coordinates.)”
“ , ”between two equations for θ = ··· and φ = ··· is significant to separate these equations, so that add “comma” in Equation (5).
RE: We added a comma in between the two equations in Equation (5)
It is better to use different sign for the inner product of vectors, ·, and scalar multiplication.
RE: Thank you for your comment. We changed Equation (2) to use a “*” sign for scalar multiplication. Now every time a “·” sign is used, it is only for an inner product.Lines 106–110
“It is important that the object on the plate is centered.” I agree with it. However, a magnetic dipole in the object is not necessarily present at the center of the object. In the same sense, how about the height of magnetometers against the object? In other words, an offset dipole moment should be taken into account. This suggests that the present method may have any defect. To overcome this point, the authors can determine spherical harmonic coefficients up to degree 2…
RE: Thank you for the insightful comment and derivation. We have addressed concerns of a multipole expansion arising from a dipole moment not being geometrically centered below:
[[ We added an Appendix A after the conclusion to derive the multi expansion terms added to the magnetic scalar potential if the dipole moment is not geometrically centered in the object. The appendix serves to demonstrate if we express the magnetic field as a sum of multipole expansion terms and fit it to data, we can determine the offset and the dipole moment.
The length scale of the dipole, however, is much smaller than the measuring distance, so any higher order multipole terms fall off quickly enough to the point where they’re negligible. The negligibility of higher order terms preserves the integrity of the current screening method and is validated in Section 4, Validations. ]]
We now address a dipole offset in lines 113116:
“(If there is a dipole offset from the geometric center of the object, it will add multi expansion terms to the magnetic scalar potential as elaborated in Appendix A. However, the distances we are measuring the magnetic fields are much larger than that of the length of the dipole and hence multipole terms fall off quickly enough to be negligible for the scope of this project.)”Lines 125–126
“It ··· are centered ···” would be “It ··· is centered···.”
“··· a 40×40 cm cubic ···” would be “··· a 40×40×40 cm cubic···.”
RE: Thank you for the comment. We made the appropriate changes in the manuscript.
“It, along with 2+ Twinleaf VMR magnetometers for data collection, (is) centered in a 40 x 40 (x 40) cm cubic mumetal magnetic shield”Lines 144–147
The authors describe that there is a vertical alignment error as one of errors. This can be reduced if the position of a magnetic dipole moment is simultaneously determined as mentioned above.
RE: Thank you for the comment. We believe your response to comments on Lines 106110 is sufficient enough where this critique is no longer an issue.Figure 6
The red and black cables are likely to be used as power lines. Are they twisted? If it is not the case, such a configuration may cause additional magnetic field, so that they should be twisted. If it is the case, it is better to point out the configuration.
RE: The wires drawing power are twisted and we added an explanation in the Figure 6 caption to better reflect that:
“Figure 6: Independently characterized solenoid that was used to validate the automated magnetic screening apparatus and procedure. (The wires drawing current from the battery are twisted to minimize additional magnetic fields.)”Equation(6)
The subscript k should be clearly defined. If k stands for x, y or z, the lefthandside of Equation (6) should be mk, where m = (m^{2}_{x }+m^{2}_{y} +m^{2}_{z})^{1/2}.
RE: Thank you for the insight. The dipole, m, effectively only has a zcomponent. Since Line 97 now denotes “(vectors i, j, and k denote longitudinal, lateral and normal units in cartesian coordinates)” and we removed the k subscript from Equations (2) and (3), the reader is confidently informed the k subscript defines the z or normal coordinate unit. We changed Equation (6) to include a k subscript in the lefthand side of the equation, to address your comment and better reflect the system being measured.Citation: https://doi.org/10.5194/egusphere2022480CC1

CC1: 'Reply on RC1', Cole J Dorman, 19 Feb 2023
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Cole J. Dorman et al.
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