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REVIEW 4 major objections 4 minor 20 references

Analysis of Measurements of the Magnetic Flux Density in Steel Blocks of the Compact Muon Solenoid Magnet Yoke with Solenoid Coil Fast Discharges

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Three accidental fast discharges of the CMS coil let the 2006 flux-loop data validate the magnet's steel-yoke model to within 3%.

desk verdict Eddy-current correction is plausible but the normalization to the full 18.164 kA swing looks wrong for the 2006 partial-swing discharges. read the letter →

arxiv 2501.01357 v1 pith:XCF2XNUM submitted 2025-01-02 physics.ins-det hep-ex

Vyacheslav Klyukhin , Benoit Curé , Andrea Gaddi , Antoine Kehrli , Maciej Ostrega , Xavier Pons This is my paper · ORCID
classification physics.ins-dethep-ex
keywords magneticfluxdensityloopseddycurrentssuperconductingmagnetflux-returnyokeCMSdetectorfastdischargefieldmeasurement
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that three accidental fast discharges of the CMS superconducting coil let the authors remove eddy-current contamination from magnetic flux measurements made in 2006, and that once this is done the measurements validate the three-dimensional computer model of the magnet's steel return yoke to within 3%. The 2006 measurements used 22 flux loops wound around 12 steel blocks of the 10,000-ton yoke; eddy currents induced in the steel by the fast discharge made the integrated voltages read too high. By comparing fluxes from fast discharges with fluxes from slow standard ramp-downs at three calibration currents, the paper obtains a current-dependent eddy-current correction, then interpolates it to the four 2006 discharge currents. A sympathetic reader would care because the steel yoke carries the magnetic flux that bends muon tracks in the detector's muon chambers, and the field-map accuracy in the yoke directly limits momentum measurement precision.

What carries the argument

The central object is the flux-loop system: 22 loops wound in grooves on 12 yoke steel blocks, each with area $A$ and $N$ turns, measuring the axial or vertical flux-density component $B_i$ orthogonal to the loop. The induced voltage is $v(t)=A N (dB_i/dI)(dI/dt)$, so integrating $v(t)$ over the discharge and dividing by $A N$ reconstructs the initial $B_i$. The load-bearing calibration is the eddy-current excess ratio $\varepsilon$ computed at three reference currents and extended to other currents by second-order polynomial interpolation; a continuously sampling readout, described as a waiting regime, is what allowed the 2023 accidental discharges to be captured as calibration data.

What would settle it

Trigger a fast discharge from an intermediate current not used in the calibration, for example 12.5 or 15 kA, with the modern 16-bit readout, and compare the directly measured eddy-current excess in each flux loop with the value predicted by the second-order polynomial; a disagreement larger than the quoted uncertainties would show the interpolation is unreliable. Reconnecting the two disconnected endcap loops during a fast discharge from 18.164 kA would test the assumption that their eddy-current contribution equals the 9.5 kA value.

Watch

Extended reading notes

Core claim

The central claim is that the 2006 flux-loop measurements can be made to agree with the CMS magnet model once the eddy-current contribution to each loop voltage is subtracted, and that this subtraction can be calibrated using fast discharges that occurred accidentally during routine operation. For each flux loop the paper defines the eddy-current contribution as the relative excess of the flux obtained when a standard ramp-down is followed by a fast discharge over the flux averaged over seven pure standard ramp-downs: $\varepsilon = (\Phi_{\mathrm{FD}}-\Phi_{\mathrm{SRD}})/\Phi_{\mathrm{SRD}} \times 100\%$. Using accidental fast discharges from 9.5 kA (2017), 15.221 kA (2023), and 18.164 kA (2023), the paper computes these excesses for 20 loops and interpolates them to the four 2006 currents (12.5, 15, 17.55, and 19.14 kA) with a second-order polynomial. For the two endcap loops that were disconnected during the 2023 discharges, the 9.5 kA value is used as an approximation. After correction, the measured and calculated magnetic flux densities in the yoke steel are compatible within 3%, and most of the remaining discrepancy after excluding three loops near the barrel-endcap gap is contained at roughly that level, while the model's agreement inside the tracking volume is 0.1%.

Load-bearing premise

The correction of the 2006 measurements assumes that the eddy-current contribution measured at only three discharge currents (9.5, 15.221, and 18.164 kA) can be interpolated by a second-order polynomial to the four older currents, and that the two endcap loops keep their 9.5 kA contribution at higher currents even though the observed trend decreases with current.

Editorial extensions

If this is right

  • The corrected 2006 dataset extends the steel-yoke model validation to four additional currents, with measured and calculated flux densities compatible within 3%.
  • The eddy-current excess decreases with increasing initial current, consistent with the steel magnetization curve, so any similar yoke measurement should treat the correction as current-dependent rather than constant.
  • Excluding the three flux loops on the negative edge of wheel YB-2 removes most of the remaining disagreement, indicating a localized model weakness near the barrel-endcap gap rather than a global field offset.
  • The waiting-regime readout means future accidental fast discharges can be used as free calibration data for the same flux-loop analysis.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the second-order interpolation is valid, the correction could be predicted for any discharge current from the local $dB/dI$ of the steel magnetization curve, avoiding the need for a dedicated calibration discharge.
  • The two endcap loops with borrowed 9.5 kA corrections are the weak link in the yoke-level claim; a future fast discharge with those loops connected would settle the 3% compatibility claim on direct measurement.
  • The localized mismatch at the YB-2 negative edge suggests the model's treatment of the gap between barrel and endcap yoke, or of steel properties near that boundary, should be revisited; a targeted array of Hall sensors at that edge could localize the modelling error.
  • For future iron-dominated detector magnets, the lesson implicit in the paper is that a readout that keeps sampling during standby converts rare operational transients into calibration measurements rather than lost data.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper analyzes flux-loop measurements of the magnetic flux density in the CMS magnet yoke during seven fast discharges of the solenoid coil. Using three accidental fast discharges (from 9.5, 15.221, and 18.164 kA) that occurred during standard ramp-downs, the authors estimate eddy-current contributions via Eq. (2) and interpolate/extrapolate them with a second-order polynomial to the four intentional 2006 fast discharges (from 12.5, 15, 17.55, and 19.14 kA). They then compare the eddy-corrected measured flux densities with TOSCA model predictions and report compatibility within 3% after excluding three discrepant barrel loops.

Significance. If the method is sound, it would allow fast-discharge flux-loop measurements to be used for a more precise validation of the CMS magnet model, with potential applicability to future detectors such as FCC-ee and CEPC. The paper provides a detailed description of the three generations of DAQ systems and the accidental-discharge data, which is a useful technical contribution. However, the significance is reduced by several methodological issues that affect the central 3% validation claim, so the result as presented is not yet established.

major comments (4)
  1. [Section 2.2, Eq. (2) and Section 3, Table 2] The eddy-current contribution E.c. contr is defined in Eq. (2) as (ΦFD − ΦSRD)/ΦSRD, i.e., normalized to the full flux swing from 18.164 kA to zero. The 2006 fast discharges, however, are partial swings from lower initial currents I to zero, so the measured flux is Φ(I→0) rather than Φ(18.164→0). The paper does not state how the E.c. contr percentage is applied to the 2006 measurements. If it is applied as a simple percentage of the measured partial-swing flux, the correction is too small by a factor of roughly Φ(I→0)/Φ(18.164) ≈ I/18.164, leaving a substantial residual eddy excess at low currents (e.g., about 30% of the excess remains at 12.5 kA). The authors must specify the correction formula and justify it physically; the current text is ambiguous on a point that is load-bearing for the 3% compatibility claim in Section 5.
  2. [Section 2.2, Eq. (2) and Section 3, Table 2] The three reference currents (9.5, 15.221, 18.164 kA) are used to define the eddy correction, and after correction they reproduce the standard ramp-down averages ΦSRD (at 18.164 exactly, and by construction at the other two after subtracting the known slow-ramp contribution). Therefore the agreement between measurement and model at these three currents is not a new validation; it is a restatement of the prior standard-ramp-down analysis. Only the four 2006 currents (12.5, 15, 17.55, 19.14 kA) provide genuinely new information. The paper should present the validation separately for these four points and acknowledge the circularity of using the reference points as evidence.
  3. [Section 2.2, paragraph 8 and Table 1] The eddy-current contributions for the four 2006 currents are obtained by second-order polynomial interpolation/extrapolation through only three measured points, with no uncertainty propagation. The polynomial form is ad hoc, and for 19.14 kA the result is an extrapolation beyond the highest reference point (18.164 kA). The reported (Meas−Calc)/Calc ratios in Table 2 do not include any uncertainty from this interpolation or from the shape choice of the fitting function. A sensitivity analysis or a physics-based model of the eddy-current scaling with current is needed to support the claimed precision.
  4. [Section 2.2, last paragraph and Table 2 footnote] For flux loops YE−2/2 and YE−2/3, the eddy-current contributions at 15.221 and 18.164 kA are taken to be equal to the value at 9.5 kA, because the loops were disconnected during the 2023 discharges. This contradicts the observed decreasing trend of E.c. contr with increasing initial current in all other loops (Figure 7). Since these two loops contribute to the endcap averages in Table 2, the assumption can bias the corrected endcap results. The authors should justify this choice or assess the sensitivity of the final ratios to it.
minor comments (4)
  1. [Figure 5a] The orange dashed line is said to cut the eddy contribution estimated at 4.6% [6]; it would be clearer to state that this is an earlier estimate from a previous publication, not from the present analysis.
  2. [Section 3, text above Table 2] The sentence 'The ratios described by Equation (1)' is imprecise: Eq. (1) is the voltage equation, while the ratio (Meas−Calc)/Calc is introduced later in the section. Please rephrase to refer to the correct equation or definition.
  3. [Table 2] The use of bold and italics to distinguish new, old, and reference rows is helpful, but the caption should explicitly state that italic rows are the standard-ramp-down comparison, as the text does only in the body.
  4. [Section 4, last paragraph] The phrase 'In contrast, the magnetic flux density distribution in the CMS tracking volume is perfectly homogeneous and is described...' could be softened, as the tracking volume field is not perfectly homogeneous but rather well modeled; consider rephrasing for accuracy.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the eddy-current corrections are derived from measured data, and the reference-current rows are explicitly labeled as reference measurements, not independent validations.

full rationale

The derivation chain is non-circular in the load-bearing sense. The eddy-current contributions are estimated from measured fast-discharge integrated fluxes ΦFD and prior standard ramp-down averages ΦSRD via Eq. (2), both of which are measurement inputs independent of the CMS magnet model; the model enters only on the comparison side in Table 2. The three reference discharges (9.5, 15.221, and 18.164 kA) are used to determine E.c. contr, and the 2006 fast-discharge data (12.5, 15, 17.55, and 19.14 kA) are corrected using the interpolated E.c. contr values before comparison with the model. The paper is transparent that the 18.164 kA row "exactly corresponds to the comparisons of the measured and calculated magnetic flux density values obtained by averaging the seven sets of measurements performed with the standard CMS magnet ramp-downs [6]", and it labels the new rows as "reference measurements for the eddy current contribution estimations". Thus the reference-current rows are calibration anchors, not disguised predictions, and the central validation claim rests on the four old 2006 discharges, whose corrected measured values are not built into E.c. contr by construction. A possible concern about applying full-swing eddy-current percentages to partial-swing 2006 discharges would be a normalization/correctness issue rather than a circularity of the kind defined here. The interpolation and extrapolation assumptions for the other currents are empirical approximations, not self-referential reductions.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central validation rests on the TOSCA model as an independent reference, the additive decomposition of eddy currents, and a quadratic interpolation of eddy contributions measured at only three currents. No new physical entities are introduced. The main free parameters are the interpolation curve and the constant eddy contribution assumed for two endcap loops.

free parameters (2)
  • Second-order polynomial coefficients for eddy current contribution vs initial current = not reported (interpolation through 3 measured points: 9.5, 15.221, 18.164 kA)
    Used in Section 2.2 to obtain E.c. contr for the 12.5, 15, 17.55, and 19.14 kA fast discharges of 2006 from three reference measurements.
  • Eddy current contribution for flux loops YE-2/2 and YE-2/3 at 15.221 and 18.164 kA = taken equal to the 9.5 kA value
    The loops were disconnected during the 2023 discharges; the paper assumes the 9.5 kA eddy contribution applies, despite the observed decrease of eddy contribution with increasing current.
assumptions (4)
  • domain assumption The TOSCA 3D model of the CMS magnet, including the steel magnetization curve, is accurate enough to serve as the reference for the measured-calculated comparison.
    The model is validated to 0.1% in the tracking volume but is known to deviate in the yoke; the paper uses the model as the reference and attributes discrepancies to model error.
  • standard math Flux loop voltage integrates linearly, so the eddy current contribution can be separated as the difference between a combined ramp-down plus fast discharge measurement and a standard ramp-down measurement.
    Equation (2) implicitly assumes the eddy current contribution is additive to the magnet flux signal and scales with the current rate.
  • ad hoc to paper The eddy current contribution varies smoothly and monotonically with initial current and is well described by a second-order polynomial over the range 9.5 to 19.14 kA.
    Only three reference points exist; the polynomial is an interpolation assumption with no error propagation.
  • domain assumption Magnetic flux density is uniform over the area enclosed by each flux loop, so dividing flux by area and turns yields the local flux density.
    Standard assumption in the flux loop technique; the cross-section areas vary from 0.3 to 1.59 m2 across blocks where the field is not perfectly uniform.

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Cite this review

Pith. "Pith review of Analysis of Measurements of the Magnetic Flux Density in Steel Blocks of the Compact Muon Solenoid Magnet Yoke with Solenoid Coil Fast Discharges." pith.science (2026). https://pith.science/paper/XCF2XNUM

@misc{pith2026250101357,
  author       = {Pith},
  title        = {Pith review of: Analysis of Measurements of the Magnetic Flux Density in Steel Blocks of the Compact Muon Solenoid Magnet Yoke with Solenoid Coil Fast Discharges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XCF2XNUM}},
  note         = {Machine review of arXiv:2501.01357}
}
read the original abstract

The Compact Muon Solenoid (CMS) detector at the Large Hadron Collider at CERN is used to study the production of new particles in proton-proton collisions at a center of mass energy of 13.6 TeV. The detector includes a magnet based on a 6 m diameter superconducting coil operating at a current of 18.164 kA. This current creates a central magnetic flux density of 3.8 T that allows for the high-precision measurement of the momenta of the produced charged particles using tracking and muon subdetectors. The CMS magnet contains a 10,000 ton flux-return yoke made from the construction steel blocks. These blocks are magnetized, with the coil returned magnetic flux and wrap the muons escaping the hadronic calorimeters. To describe the distribution of the magnetic flux in the magnet yoke layers, a three-dimensional computer model of the CMS magnet is used. To validate the calculations, special measurements are performed, with the flux loops wound in 22 cross-sections of the flux-return yoke blocks. The measured voltages induced in the flux loops during the CMS magnet current variations, are integrated over time to obtain the initial magnetic flux densities in the flux loop cross-sections. In the last time, three fast discharges occurred during the standard ramp-downs of the magnet. This allows us to single out the contributions of the eddy currents, induced in steel, to the flux loop voltages. Accounting for these contributions to the flux loop measurements during intentionally triggered fast discharges in 2006 allows us to perform the validation of the CMS magnet computer model with better precision. The technique for the flux loop measurements and the obtained results are presented and discussed. The method for measuring magnetic flux density in steel blocks described in this study is innovative.

Figures

Figures reproduced from arXiv: 2501.01357 by the authors.

Figure 1
Figure 1. Modeled distribution of the magnetic flux density B in Tesla in the vertical YZ-plane of the flux loop location area. Sixteen flux loops are installed in the 30° azimuthal sector at 270° of the CMS magnet barrel flux-return yoke on four layers (TC, L1, L2, L3) of the central barrel wheel YB0, and on three layers (L1, L2, L3) of the barrel wheels YB−1 and YB−2 at negative Z-coordinates, shown in meters on the Z-axis.… view at source ↗
Figure 2
Figure 2. Measured magnetic current variations during the fast discharges which occurred from the CMS magnet currents of 9.5, 12.5, 15, 15.221, 17.55, 18.164, and 19.14 kA. These currents create initial central magnetic flux densities of B0 of 2.02, 2.64, 3.16, 3.20, 3.68, 3.81, and 4.01 T, respectively, in the CMS superconducting coil. The voltages induced in the flux loops have been registered with three different DAQ syste… view at source ↗
Figure 3
Figure 3. DAQ block diagram of the flux loop signal processing. The measuring system contains six custom multiplexers assembled in the patch boxes to read out the voltages induced in the flux loops. Through the custom-made master PLC interface circuit, the multiplexers communicate to Siemens S7-1500 PLC drives to propagate the signals to the WinCC OA software that stores the voltage values in the database. This DAQ design inc… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: (a) One of six readout boxes with a custom multiplexer, a 24 V DC power supply, and a 19-pin Burndy connector (b) wiring from three to six flux loops to each multiplexer. The fast discharges induce voltages with rather complicated time dependence in the flux loops. Exa…
Figure 5
Figure 5. Figure 5: (a) Voltages measured in the flux loop P on the L2 layer of the external barrel wheel YB−2 during all seven fast discharges performed with different initial magnet currents. The orange short￾dashed line cuts the contribution of the eddy currents to the signal at the be…
Figure 6
Figure 6. Figure 6: Three fast discharges occasionally occurred from the currents of 9.5 (on 30 November 2017), 15.221 (on 8 August 2023), and 18.164 (on 22 March 2023) kA during the standard CMS magnet ramp-downs with a rate of 1–1.5 A/s from the operational magnet current of 18.164 kA. …
Figure 7
Figure 7. Figure 7: The eddy current contributions to 20 flux loops vs. initial currents of the fast discharges. The flux loops YE−2/2 and YE−2/3 were disconnected when the fast discharges from the currents of 15.221 (on 8 August 2023) and 18.164 (on 22 March 2023) occurred. In the furthe…
Figure 8
Figure 8. Figure 8: Initial axial Bz (negative) magnetic flux density or vertical By (positive) magnetic flux den￾sity components calculated in all 22 flux loop cross-sections at the seven CMS coil currents. In the barrel layers, the minimum absolute Bz value of 0.377 T is reached in the …
Figure 9
Figure 9. Figure 9: Initial axial magnetic flux density or vertical magnetic flux density components measured in all 22 flux loop cross-sections at the seven CMS coil currents. In [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: Comparison of measured and calculated axial magnetic flux density or vertical magnetic flux density components in all 22 flux loop cross-sections at the seven CMS coil currents [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: Averaged comparison of measured and calculated axial magnetic flux density, Bz (in the 16 barrel flux loops), or vertical magnetic flux density, By (in the 6 endcap flux loops), as well as of both components in all 22 flux loop cross-sections (yoke), versus the CMS co…
Figure 12
Figure 12. Figure 12: Comparison of measured and calculated axial magnetic flux density, Bz, or vertical mag￾netic flux density, By, in each of the 22 flux loop cross-sections performed in different sets of meas￾urements: new measurements at 9.5, 15.221, and 18.164 kA; old measurements at …

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Reviewed August 10, 2026 · model on record in the stance chip above.