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arxiv: 2606.10950 · v1 · pith:3TMJRGV3new · submitted 2026-06-09 · ⚛️ physics.ins-det · nucl-ex

Feasibility demonstration of continuous signal-based neutron noise measurements by experiments and simulations

M\'at\'e Istv\'an Boros , M\'at\'e Szieberth , Gergely Klujber , Imre P\'azsit , Istv\'an Barth , Yasunori Kitamura , Tsuyoshi Misawa This is my paper

Pith reviewed 2026-06-27 10:55 UTC · model grok-4.3

classification ⚛️ physics.ins-det nucl-ex
keywords neutron noise analysiscontinuous detector signalRossi alphaFeynman alphadead time effectssignal deconvolutionreactor diagnosticsprompt neutron decay constant
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The pith

Analyzing continuous detector current provides unbiased neutron noise parameters at high count rates.

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

The paper shows that neutron noise analysis can use the continuous current signal from detectors instead of counting individual pulses. This avoids problems like dead time and pile-up that distort results at high detection rates. By modeling the stochastic detector current and correcting for pulse shapes with deconvolution or paired detectors, the method derives standard Rossi and Feynman formulations that remain accurate. Simulations and reactor measurements confirm unbiased estimates of the prompt neutron decay constant even where traditional methods fail. This matters because it enables reliable kinetic parameter measurements in high-flux reactor conditions.

Core claim

The stochastic model of the detector current is applied to derive Rossi- and Feynman-type formulations for the prompt neutron decay constant. Pulse-shape distortions are mitigated using detector pairs or by deconvolving the average pulse-shape through inverse Fourier and Wiener filtering. Simulations demonstrate accurate alpha-parameter estimation at count rates where pulse-counting becomes unusable and enable evaluation of significantly higher alpha values. Measurements confirm that continuous and deconvolved signals provide unbiased results despite dead-time and electronic artifacts.

What carries the argument

Stochastic model of the detector current, from which Rossi- and Feynman-type alpha formulations are derived after pulse-shape mitigation.

If this is right

  • Accurate estimation of the alpha parameter at count rates where pulse counting fails.
  • Ability to evaluate higher values of the prompt neutron decay constant.
  • Establishment of continuous signal analysis as a practical alternative for high-rate reactor noise diagnostics.
  • Unbiased results from deconvolved signals in presence of dead-time artifacts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach may allow noise diagnostics in reactor regimes previously inaccessible due to high count rates.
  • If scalable, it could simplify instrumentation by tolerating standard electronics with post-processing corrections.
  • Similar continuous-signal techniques might apply to other stochastic processes in radiation detection.

Load-bearing premise

The stochastic model of the detector current accurately represents the physics and that pulse-shape distortions can be fully removed by detector pairs or deconvolution without introducing new bias.

What would settle it

Observation of systematic bias in the estimated prompt neutron decay constant from continuous signals after deconvolution at high rates would falsify the feasibility claim.

Figures

Figures reproduced from arXiv: 2606.10950 by Gergely Klujber, Imre P\'azsit, Istv\'an Barth, M\'at\'e Istv\'an Boros, M\'at\'e Szieberth, Tsuyoshi Misawa, Yasunori Kitamura.

Figure 2
Figure 2. Figure 2: Short section of a simulated detector signal before and after the deconvolution of the average pulse-shape. be mitigated when using pairs of detectors and computing the cross-covariance (CCF) and cross-covariance to mean ratio (CTM) functions of the two signals. Another possible way of mitigating the problem caused by the finite time constant of the detector pulse is by the deconvolution of the average pul… view at source ↗
Figure 1
Figure 1. Figure 1: The ACF and VTM functions of the continuous detector signal together with the additional terms caused by the finite decay speed of the detector pulses. ACF(𝜃) = 𝜙 ⋅ exp(−𝛼 ⋅ |𝜃|) + 𝜓1 ⋅ exp(−𝛼𝑒 ⋅ |𝜃|) + 𝜓2 ⋅ |𝜃| ⋅ exp(−𝛼𝑒 ⋅ |𝜃|) VTM(𝑇 ) = Φ ⋅ 𝑓1 (𝛼 ⋅ 𝑇 ) + Ψ1 ⋅ 𝑓1 (𝛼𝑒 ⋅ 𝑇 ) + Ψ2 ⋅ 𝑓2 (𝛼𝑒 ⋅ 𝑇 ) 𝑓1 (𝑥) = 1 − 1 − exp(−𝑥) 𝑥 𝑓2 (𝑥) = 1 + exp(−𝑥) − 2 ⋅ 1 − exp(−𝑥) 𝑥 (2) The full forms of the ACF and VTM function… view at source ↗
Figure 3
Figure 3. Figure 3: The process of simulating the different signal types. infinitely short pulse at the time of each neutron detection. The integral of this ideal continuous function would simply be the counting function of the neutron detection events. The effect of the deconvolution of the average pulse￾shape from the continuous signal in the ideal case is illus￾trated in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rossi-𝛼 and Feynman-𝛼 evaluations of the continuous and pulse-based detector signal, using a single detector and a pair of detectors. The theoretical 𝛼 value of the system is 10000 s−1, and the detection rate is 100000 neutrons/s/detector. time lags in the autocovariance function). Still, the contin￾uous signal provides more accurate results than the pulse￾based one, as some counts are still lost due to th… view at source ↗
Figure 6
Figure 6. Figure 6: Rossi-𝛼 (cross-covariance) and Feynman-𝛼 (cross-covariance-to-mean) results obtained from the Reference signal, the Pulse-based signal and the Continuous signal based on a simulation with 5 ⋅ 107 s −1 external source intensity. (a) Rossi-𝛼 results. (b) Feynman-𝛼 results [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Rossi-𝛼 (cross-covariance) and Feynman-𝛼 (cross-covariance-to-mean) results obtained from the Reference signal, the Pulse-based signal and the Continuous signal. 2 ⋅ 108 s −1 while keeping all other system parameters the same, resulting in a theoretical 𝛼 ≈ 107.2 s −1. Higher source intensities have not been tested because the computation time required for both the Monte Carlo simulation and the evaluation… view at source ↗
Figure 8
Figure 8. Figure 8: Simulated continuous signals and the result of the deconvolution, of the same simulation, but with different levels of additive Gaussian white noise (0.1% and 2.5% NSR). With the noisier signal, the deconvolution was also performed using a frequency-dependent Wiener-filter, significantly improving the stability of the deconvolution in exchange for some sharpness. At this level of source intensity, the trad… view at source ↗
Figure 9
Figure 9. Figure 9: Rossi- and Feynman-𝛼 values estimated using signals obtained by performing a pulse-shape deconvolution from raw voltage signals having NSR ranging from 0 to 62.5% First, the sensitivity of the proposed inverse Fourier deconvolution technique with regard to additive white noise was investigated. Short sections of the simulated continuous signal and its deconvolved form are shown in [PITH_FULL_IMAGE:figures… view at source ↗
Figure 11
Figure 11. Figure 11: Rossi-𝛼 and Feynman-𝛼 evaluations of different sig￾nal types with different theoretical 𝛼 values. For the continuous and (traditional) pulse-based signals, the charts contain the results obtained from using a single detector (ACF, VTM) and detector pairs (CCF, CTM). traditional pulse-based signal, but especially the continu￾ous signal in terms of evaluability and/or uncertainty of the estimation. The cont… view at source ↗
Figure 12
Figure 12. Figure 12: Illustration of the compressed recording of the continuous signal [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: KUCA A-core configuration. Red = fuel; yellow = polyethylene moderator; orange = polyethylene reflector; gray = graphite. C1, C2 and C3 denote the control rods; S3, S4, and S5 refer to safety rods. A, B, C and D in green cells show the detector positions. rate so that the pulse pile-up and the induced dead time was expected to be insignificant. This condition is fulfilled in sufficiently subcritical, give… view at source ↗
Figure 14
Figure 14. Figure 14: The squared magnitude of the Fourier transform (proportional to the power spectral density), its relevant section fitted with the appropriate functions defined in eq. 6 and the autocovariance function of the continuous signal of detector ’A’ in the CR-3 configuration (compressed recording) and the CR-2 configuration (continuous recording). quickly decaying (decay constant of ∼ 104 s −1) negative correlati… view at source ↗
Figure 15
Figure 15. Figure 15: Rossi-𝛼 evaluation of the continuous- and pulse￾based signals of detector ’A’ in the SCR-2 configuration. where 𝜔 is the angular frequency. Three terms were used for the CR-3 configuration and two terms for the CR-2 configu￾ration, where the prompt decay constant of the reactor could not be found by fitting. The results of the fits are shown on [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: Relation between the estimated 𝛼-parameters and the reactivity of the system for different detectors and evalua￾tion techniques. of delayed neutrons are missing in eq. 2. Examples of the Feynman-evaluation of measurement CR-3 are presented on [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Short section of the continuous signal of detector ’A’ recorded in the CR-2 measurement, the result of the inverse Fourier deconvolution, and the result of the deconvolution using a Wiener filter assuming additive white noise. which also limits the conclusions from the measurements. According to [PITH_FULL_IMAGE:figures/full_fig_p013_18.png] view at source ↗
Figure 20
Figure 20. Figure 20: The autocovariance function and the ITD of the deconvolved pulse-based signal of detector ’A’ in the CR-2 configuration. the pulses in the deconvolved signal too much [PITH_FULL_IMAGE:figures/full_fig_p014_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Squared magnitude of the Fourier transform of signals recorded in the CR1 (compressed recording) and the CR3 (continuous recording) configurations [PITH_FULL_IMAGE:figures/full_fig_p015_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: A short section of the continuous signal recorded in configuration CR3, before and after the deconvolution of the average pulse-shape [PITH_FULL_IMAGE:figures/full_fig_p016_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: OpenMC model of the vicinity of the detector position, and the time distribution of detection events after starting a pulse of neutrons from the detector position. signals in the CR1 configuration. In some cases, especially at higher power, the correlations in the signals were dominated by a decay constant of ∼ 1500 s −1, and not the expected fundamental prompt decay factor of ∼ 100 s −1. In one instance,… view at source ↗
read the original abstract

Neutron noise methods are used to determine kinetic parameters such as the prompt neutron decay constant, but traditional pulse-counting suffers from dead-time and pile-up at high detection rates. Recent theory shows that analysing the continuous detector current can avoid these limitations if pulse-shape effects are properly treated. This work presents a feasibility study of continuous-signal neutron noise analysis based on simulations and experiments performed at two research reactors. The stochastic model of the detector current is applied to derive Rossi- and Feynman-type formulations, and pulse-shape distortions are mitigated using detector pairs or by deconvolving the average pulse-shape through inverse Fourier and Wiener filtering. Simulations demonstrate accurate $\alpha$-parameter estimation at count rates where pulse-counting becomes unusable, and enable evaluation of significantly higher $\alpha$ values. Measurements at KUCA and BME TR confirm that continuous and deconvolved signals provide unbiased results despite dead-time and electronic artifacts, establishing the method as a practical alternative for high-rate reactor noise diagnostics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that continuous detector current signals, analyzed via stochastic-model-derived Rossi- and Feynman-type formulations with pulse-shape mitigation by detector-pair subtraction or inverse-Fourier/Wiener deconvolution of the average pulse shape, yield accurate and unbiased estimates of the prompt neutron decay constant alpha at high count rates where traditional pulse counting fails due to dead time and pile-up. This is supported by simulations showing accurate alpha recovery and by reactor measurements at KUCA and BME TR that confirm unbiased results despite artifacts.

Significance. If the unbiasedness claim holds after proper validation of the deconvolution step, the method would provide a practical alternative for high-rate neutron noise diagnostics, enabling measurements at higher alpha values and count rates than pulse-based techniques allow, which is relevant for reactor kinetics and safety analysis.

major comments (2)
  1. [Abstract / mitigation steps] Abstract and methods section on mitigation: the claim that continuous and deconvolved signals provide unbiased alpha estimates requires explicit demonstration that the average pulse shape used in the Wiener filter was not extracted from the identical high-rate traces (which contain dead-time and pile-up). If the shape is data-derived rather than from separate low-rate calibration, residual correlated artifacts can propagate into the autocorrelation or variance, violating the unbiasedness asserted in the derivation of the Rossi/Feynman expressions from the stochastic current model.
  2. [Results] Results section (simulations and reactor measurements): the abstract states 'accurate alpha-parameter estimation' and 'unbiased results' but the provided text contains no quantitative values, error bars, comparison metrics, or exclusion criteria for the reported alpha; without these, the central claim that the method works 'at count rates where pulse-counting becomes unusable' cannot be verified.
minor comments (2)
  1. [Theory/derivation] Clarify notation for the stochastic current model and the exact form of the derived Rossi- and Feynman-type expressions; ensure they are written out with all assumptions stated.
  2. [Results] Add quantitative tables or plots comparing alpha from continuous vs. pulse methods, including uncertainties, for both simulations and the two reactor experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and will revise the paper to improve clarity and verifiability.

read point-by-point responses

  1. Referee: [Abstract / mitigation steps] Abstract and methods section on mitigation: the claim that continuous and deconvolved signals provide unbiased alpha estimates requires explicit demonstration that the average pulse shape used in the Wiener filter was not extracted from the identical high-rate traces (which contain dead-time and pile-up). If the shape is data-derived rather than from separate low-rate calibration, residual correlated artifacts can propagate into the autocorrelation or variance, violating the unbiasedness asserted in the derivation of the Rossi/Feynman expressions from the stochastic current model.

    Authors: We agree this requires explicit clarification. The average pulse shape for the Wiener filter was derived from separate low-rate calibration measurements acquired under conditions without pile-up or dead-time, not from the high-rate analysis traces. We will revise the methods section to state this explicitly and confirm the separation of calibration and analysis datasets, thereby preserving the unbiasedness of the derived Rossi/Feynman expressions. revision: yes

  2. Referee: [Results] Results section (simulations and reactor measurements): the abstract states 'accurate alpha-parameter estimation' and 'unbiased results' but the provided text contains no quantitative values, error bars, comparison metrics, or exclusion criteria for the reported alpha; without these, the central claim that the method works 'at count rates where pulse-counting becomes unusable' cannot be verified.

    Authors: The full results section reports quantitative alpha values with uncertainties from simulations and KUCA/BME TR experiments, including direct comparisons to pulse-counting limits. To enhance verifiability as requested, we will add an explicit summary table listing alpha estimates, error bars, count rates, and comparison metrics in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations are self-contained from stochastic model

full rationale

The paper derives Rossi- and Feynman-type formulations directly from the stochastic model of the detector current, then applies standard mitigation techniques (detector-pair subtraction or Wiener deconvolution) to handle pulse-shape effects. No quoted equations or steps reduce the target quantities (such as alpha) to fitted parameters by construction, nor do any load-bearing premises collapse to self-citations whose content is unverified. The central claim that continuous signals yield unbiased results after mitigation rests on the external validity of the stochastic model and the deconvolution method, not on internal redefinition. This is the normal case of a derivation that remains independent of its fitted outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the central claim rests on the accuracy of the stochastic detector-current model and the effectiveness of the chosen pulse-shape corrections, both of which are domain assumptions rather than derived results.

axioms (2)
  • domain assumption The stochastic model of the detector current accurately represents neutron detection events and their timing statistics
    Invoked to derive the adapted Rossi- and Feynman-type formulations from the continuous signal.
  • domain assumption Pulse-shape distortions can be removed without residual bias by either detector pairing or Fourier/Wiener deconvolution
    Required for the claim that the method remains unbiased at high count rates.

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discussion (0)

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Reference graph

Works this paper leans on

16 extracted references · 14 canonical work pages

  1. [1]

    BME, NTI,

    doi:http://dx.doi.org/10.1016/j.anucene.2010.11.009. BME, NTI, . Training reactor description. URL:http://www.reak.bme.hu/ en/training-reactor.html. Endo, T., Yamamoto, A.,

    work page doi:10.1016/j.anucene.2010.11.009 2010

  2. [2]

    Annals of Nuclear Energy 124, 606–615

    Comparison of theoretical formulae and bootstrap method for statistical error estimation of feynman-𝛼 method. Annals of Nuclear Energy 124, 606–615. URL:https: //www.sciencedirect.com/science/article/pii/S0306454918305589, doi:https://doi.org/10.1016/j.anucene.2018.10.032. Feynman, R.P., De Hoffmann, F., Serber, R.,

    work page doi:10.1016/j.anucene.2018.10.032 2018

  3. [3]

    Journal of Nuclear Energy (1954) 3, 64–IN10

    Dispersion of the neutron emission in u-235 fission. Journal of Nuclear Energy (1954) 3, 64–IN10. Gunawan, F.E.,

    1954

  4. [4]

    Inverse Problems in Science and Engineering 24, 1107–1132

    Impact force reconstruction using the regularized wiener filter method. Inverse Problems in Science and Engineering 24, 1107–1132. doi:10.1080/17415977.2015.1101760. Hazama, T.,

    work page doi:10.1080/17415977.2015.1101760 2015

  5. [5]

    de Izarra, G., Jammes, C., Geslot, B., Di Salvo, J., Destouches, C.,

    doi:http://dx.doi.org/10.1016/S0306-4549(02)00091-9. de Izarra, G., Jammes, C., Geslot, B., Di Salvo, J., Destouches, C.,

    work page doi:10.1016/s0306-4549(02)00091-9

  6. [6]

    Review of Scientific Instruments 86, 115111

    Spectron, a neutron noise measurement system in frequency domain. Review of Scientific Instruments 86, 115111. URL:https://doi.org/ 10.1063/1.4935250, doi:10.1063/1.4935250. Kitamura, Y., Misawa, T.,

    work page doi:10.1063/1.4935250

  7. [7]

    Annals of Nuclear Energy 123, 119–134

    Delayed neutron effect in time-domain fluctuation analyses of neutron detector current signals. Annals of Nuclear Energy 123, 119–134. URL:https: //www.sciencedirect.com/science/article/pii/S0306454918304778, doi:https://doi.org/10.1016/j.anucene.2018.09.004. Kitamura, Y., Pázsit, I., Misawa, T.,

    work page doi:10.1016/j.anucene.2018.09.004 2018

  8. [8]

    Annals of Nuclear Energy 120, 691–706

    Determination of prompt neutron decay constant by time-domain fluctuation analyses of detector current signals. Annals of Nuclear Energy 120, 691–706. URL:https: //www.sciencedirect.com/science/article/pii/S0306454918303232, doi:https://doi.org/10.1016/j.anucene.2018.06.021. Lux, I., Baranyai, A.,

    work page doi:10.1016/j.anucene.2018.06.021 2018

  9. [9]

    second edition ed

    Chapter 10 - power spectral density, in: Probability and Random Processes. second edition ed.. Academic Press, Boston, pp. 429–471. URL:https: //www.sciencedirect.com/science/article/pii/B9780123869814500138, doi:https://doi.org/10.1016/B978-0-12-386981-4.50013-8. Nagy,L.,Pázsit,I.,Pál,L.,Klujber,G.,Szieberth,M.,2020. Measurements and simulations to inves...

    work page doi:10.1016/b978-0-12-386981-4.50013-8 2020

  10. [10]

    Pál, L., Pázsit, I.,

    doi:10.1109/TNS.2018.2831180. Pál, L., Pázsit, I.,

    work page doi:10.1109/tns.2018.2831180 2018

  11. [11]

    Nuclear InstrumentsandMethodsinPhysicsResearch794,90–101.URL:https: //www.sciencedirect.com/science/article/pii/S0168900215006166, doi:https://doi.org/10.1016/j.nima.2015.05.006

    Campbelling-type theory of fission chamber signals generated by neutron chains in a multiplying medium. Nuclear InstrumentsandMethodsinPhysicsResearch794,90–101.URL:https: //www.sciencedirect.com/science/article/pii/S0168900215006166, doi:https://doi.org/10.1016/j.nima.2015.05.006. Pál, L., Pázsit, I., Elter, Zs.,

    work page doi:10.1016/j.nima.2015.05.006 2015

  12. [12]

    Nuclear Instruments and Methods in Physics Research 763, 44–52

    Comments on the stochastic characteristics of fission chamber signals. Nuclear Instruments and Methods in Physics Research 763, 44–52. URL:https: //www.sciencedirect.com/science/article/pii/S0168900214007220, doi:https://doi.org/10.1016/j.nima.2014.06.018. Pázsit, I., Pál, L., 2008.Neutron Fluctuations: a Treatise on the Physics of Branching Processes. El...

    work page doi:10.1016/j.nima.2014.06.018 2014

  13. [13]

    Annals of Nuclear Energy 82, 90–97

    Openmc: A state-of-the-art monte carlo code for research and development. Annals of Nuclear Energy 82, 90–97. URL:https://www.sciencedirect.com/science/article/pii/ S030645491400379X, doi:https://doi.org/10.1016/j.anucene.2014.07

    work page doi:10.1016/j.anucene.2014.07 2014

  14. [14]

    Measure- mentofmultiple𝛼-modesattheDelphisubcriticalassemblybyneutron noise techniques

    Szieberth,M.,Klujber,G.,Kloosterman,J.L.,deHaas,D.,2014. Measure- mentofmultiple𝛼-modesattheDelphisubcriticalassemblybyneutron noise techniques. Annals of Nuclear Energy (accepted). Szieberth, M., Nagy, L., Klujber, G., Misawa, T., Barth, I., Pázsit, I.,

    2014

  15. [15]

    ANS - American Nuclear Society doi:10.13182/M& C21-33878

    Experimentaldemonstrationofneutronfluctuationanalysisbasedonthe continuous signal of fission chambers: neutron multiplicity and reactor noise measurements. ANS - American Nuclear Society doi:10.13182/M& C21-33878. Werner, C.J., et al.,

    work page doi:10.13182/m

  16. [16]

    The MIT Press

    Extrapolation, Interpolation, and Smoothing of Sta- tionary Time Series: With Engineering Applications. The MIT Press. URL:https://doi.org/10.7551/mitpress/2946.001.0001, doi:10. 7551/mitpress/2946.001.0001. Williams, M.M.R.,

    work page doi:10.7551/mitpress/2946.001.0001