advanced neutron monitoring with fission chambers · self-intro phd work neutron ux monitoring i...

Advanced neutron monitoring with fissionchambers

Zsolt Elter

SNEC meeting, 2016. June

IntroductionHigher Order Campbelling

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Self-introPhD work

Short intro of myself

I From Hungary, 28 years old

I BSc in physics: Budapest University ofTechnology (MCNP simulations ofgeophysics density measurement probe)

I MSc in physics: Budapest University ofTechnology (MCNP simulations ofAllegro gas cooled fast reactor)

I Researcher at the Atomic EnergyResearch Institute + CEA internship(Eranos calculations; participate indiffusion code development)

I PhD: at Chalmers (2.5 years spent atCEA Cadarache) supervised byImre Pazsit (2012-)

Zs. Elter Advanced neutron monitoring 2/10


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Self-introPhD work

Neutron flux monitoring

I Online flux measurement inASTRID: fission chamber

I Stochastic electric signal on theelectrodes

I 3 different processing modes (anddifferent electronics)

I Pulse mode (low flux)I Campbelling (medium flux)I Current mode (high flux)

I High order Campbelling (HOC) forunifying Pulse and Campbellmodes? + Simple measurementsystem with self-monitoringcapability?



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Self-introPhD work

Fission chamber signal - Numerical Matlab calculationsI The signal is considered as sum of pulses with exponentially

distributed arrival times (Poisson Pulse Train, shotnoise)

I Interest: unfold the count rate from the signal. Processingmethods?



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Numerical studiesExperimental studiesSmart detector

Higher order Campbell mode, HOC

I Linearity gap between Pulse and Campbell mode (Zs. Elter et al. NIMA

Vol. 774 p60-67 (2015))

I Generalization of Campbell mode(L. Pal et al. NIMA Vol. 768. p44-52 (2014))

I Relationship between the cumulants of the signal with and thecount rate s0 (for pulses with random amplitude)

κn = s0〈xn〉+∞∫−∞

f (t)ndt (1)

I Normal distribution κn = 0 n > 2

I The cumulants are estimated from a finite sample

I Calibration coefficient: known in a simulation, but otherwise?



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Main numerical results - HOC mode

I n = 3 order is satisfactory (above not plausible)

I Convergence in short measurement times (1− 10ms)

I Most common noises are suppressedI Transient events can be monitored (when s(t))

Zs. Elter et al. NIMA Vol. 813 p10-12 (2016) & Zs. Elter et al. NIMA Vol. 821 p66-72 (2016)



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Experimental work - HOC Calibration I.

Goal: Cn = 〈xn〉+∞∫−∞

f (t)ndt



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Experimental work - HOC Calibration II. Zs. Elter et al. been submitted to NIMA

C2 (A2Hz−1) (2.00 ± 0.04) · 10−19

C3 (A3Hz−1) (5.32 ± 0.32) · 10−25

C3,empir (A3Hz−1) (5.19 ± 0.53) · 10−25



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Self diagnosing detector

I A measurement system which could identify malfunction (theleakage of filling gas)

I pyFC simulations: the pulse shape change due to leakage

I Calibration term changes: underestimation of count rate

I FWHM of the PSD of the signal changes due to the pulseshape change (and not due to the count rate change)

Cn ↓ = 〈xn〉 ↓+∞∫−∞

f (t)ndt ↓

Zs. Elter et al. Physor 2016



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Summary and ongoing work

I Lack of overlap between pulse and Campbell mode

I Higher Order Campbell: wider count rate range

I Numerical and experimental verification

I Implementing HOC on FPGA board (G. de Izarra et al. to be submitted (2016))

I PSD FWHM measurement implementation on FPGA

I Uncertainty study of the calibration coefficient (with theFANISP algorithm developed by Z. Perko, TU Delft)


Thank you for the attention!

Appendix


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Simulation of the pulse creation - pyFC

Trajectory of heavyions, and electron-ionpair creation

Zs. Elter CTH-NT-318 report (2015)

Current induced bythe electrons



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The toolbox/Model discretization

I Discretization works like in a real detector system

I Time resolution set by user (usually 109 1/s)

I The pulse shape is stored on finite memory

I If more pulses occur during one time step the code sums upthem

I Note: the simulations have a statistical error as well (numberof pulses in a given measurement time is Poisson distributed),which has nothing to do with the toolbox



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Count rate measurement goals

I What are we looking for? Count rate

I Best methods to estimate the intensity (count rate) of thesignal (which is related to the neutron flux!)

I Linear relation between the Input and the Estimation possiblyon a wide intensity range



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Pulse mode vs Campbell mode

Pulse mode

I Counting the pulses (with logicalcircuits)

I Robust, simple method

I Cannot distinguish overlappingpulses (deadtime)

Campbell mode

I Relationship between the varianceof the signal and the intensity (forpulses with random amplitude x)

D2(η) = s0〈x2〉+∞∫−∞

f (t)2dt (2)



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Calculations - Pulse width sensitivity5% noise applied

Linearity defect(depending on noise)PM: Pulse modeCM: Campbell mode

Zs. Elter et al. NIMA Vol.774 p60-67 (2015)

I Shorter pulse: better performance (but dedicated filling gas isneeded)



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Statistical uncertainty

I The statistical uncertainty originated from the finitemeasurement time



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Pulse shape used

I Exponential pulse shape (quick damped pulse)

I Pulse width: when the pulse reaches the 90% of the amplitude

I All defined to have the same charge

I (At this moment deterministic amplitudes)



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Theoretical workI The signal is considered as sum of pulses with exponentially

distributed arrival timesI Derivations are based on solving the backwards Master

equation (Pal et al.)



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Theoretical work

I The signal is considered as sum of pulses with exponentiallydistributed arrival times

I Derivations are based on solving the backwards Masterequation (Pal et al.)

I The work treated various pulse shapes, and amplitudedistributions

I My contributionI Creating a Mathematica simulation (continuous model, easy to

build)I Checking the results of the derivations



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Conclusion of theoretical work (Limitation of Mathematica)

I Reaching an analytical solution is not always possibleI Realistic pulse shapesI Realistic pulse amplitude distributions

I Including any noise is problematic

I Investigating the ”reality” needs computer simulation

I Due to the noise this has to be numerical simulation

I It is possible to include this in Mathematica (down sampling)

I But Mathematica was not created for this: slow

I The following simulations were made in Matlab



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Master equation

W (x) =

∫ x

−∞w(x ′) dx ′ = P {ξ ≤ x} (3)

H(y , t) =

∫ +∞

−∞∆[y − ϕ(x , t)]w(x) dx (4)

h(y , t) =

∫ +∞

−∞δ [y − ϕ(x , t)] w(x) dx . (5)

T (t0, t) = exp

{−∫ t

t0

s(t ′) dt ′}. (6)



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Master equation

P {η(t) ≤ y |η(t0) = 0} = P(y ,t|0, t0) =

∫ y

−∞p(y ′, t|0, t0) dy ′

(7)

p(y , t|0, t0) = T (t0, t) δ(y) +

∫ t

t0

T (t0, t′)s(t ′)∫ y

−∞h(y ′, t − t ′) p(y − y ′, t|0, t ′) dy ′ dt ′



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Theoretical limitations

I Reaching an analytical solution is not always possibleI Realistic pulse shapesI Realistic pulse amplitude distributions

I Including any noise is problematic

I Even simple cases can cause problems (rectangular pulses withdeterministic amplitudes

I The process has onlydiscrete values



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Experimental verificationI Experimental verification of the Poisson characteristicI Experiment performed in Minerve reactorI FC + pre-amplifier + oscilloscope



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Theoretical verification

I The validity of the implementation was checkedI For this the level crossing intensity was calculated (proposed

by L. Pal et al.)I Intensity of arrival of particles which induce a jump above a

certain level (arbitrary units on the plot)

s0: intensity; T0: pulse widthµ: parameter of the amplitudedistribution

nst(A) = s0

A∫0

pst(y)[1−W (A− y)]dy

(8)pst : Probability distribution function ofthe signalW (A− y): Distribution function of thepulse amplitude (optional)



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Theoretical verification 2.

I Exponential pulse shape: f (t) = e−t/p

I Exponentially distributed amplitude with parameter µ

nst(A) = s0(µA)s0p

Γ(s0p + 1)e−µA (9)

s0 = 10−8 s−1

p = 20 nsµ = 0.5 µA−1



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Representation of related electronic system

I The toolbox creates the signal such as it appears after thepre-amplifier

I Band-pass filter has no impact on the studied count rate range

I Difference in simulation: post processing is solved with thecomputer as well



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Calculations - white noise sensitivity of current methods

PM: Pulse ModeCM: Campbelling Mode

I Pulse mode is relatively insensitive

I Second order Campbelling method is biased by noise at lowintensity levels



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Calculations - Amplitude distribution sensitivity of methods


I Truncated Gaussian amplitude distribution(Var(x) = c2 · 〈x〉2)

I Pulse mode would need additional calibration



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Calculations - Pulse width sensitivity

I 5% noise applied


I Shorter pulse: better performance



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Calculations - Pulse vs Campbell conclusionsI Linearity defect depending on noiseI Campbell: high sensitivity to noiseI Pulse: problems with amplitude distributionI Need for some method solving these issues



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Overview of the calculations - What is a cumulant?

The κn cumulants of an rv. X are defined via thecumulant-generating function:

g(t) = logE(etX )

g(t) =∞∑n=1

κntn

n!

κ1 is the mean

κ2 is the variance

If X is normally distributed κn = 0 for n ≥ 3



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Overview of the calculations - Campbell mode

κn = s0〈xn〉+∞∫−∞

f (t)ndt (10)

I Higher order methods can suppress the impact of noise

I They could suppress the effect of smaller pulses (like gammabackground)

I In measurement calibration is needed (in simulation the inputsare ”known”)



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Calculations - HOC methods

I Without noise (Tmeasurement = 10−2 s)



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Calculations - HOC methods - inaccuracy?

Unbiased estimator:〈kn〉 = κnvar(kn) ∝ κn2 ⇒ Large n requires longermeasurement

At higher count ratesthe variance (and othercumulants) are higher,thus the estimation ofthe cumulants is lessaccurate



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Convergence of the cumulants (theory)



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Biased and unbiased estimators

κn = µn −n−1∑i=1

(n−1i

)κn−1µi

Where µn can be estimated as µn = SnN =

N∑jX nj

N

This leads to a so called biased estimator.X is the random variable, N samples.



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Biased and unbiased estimators 2.

Unbiased estimators can be found for examplehttp://mathworld.wolfram.com/k-Statistic.html

k3 =2S3

1−3NS1S2+N2S3

N(N−1)(N−2)

This is the unbiased estimator of the third cumulant.I showed that in our studies the unbiased and the biased estimatorslead to the same result (N is really high).



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Calculation time for biased and unbiased estimators



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Reliability of calculation time

I We have to be sure that calculating the cumulant is notlonger than the measurement time

I We compared C++ with Matlab (same pulse train was used)

Used language Calculation Time

Matlab (unbiased k3, Tmeas = 10−2 s) 0.78 sC++ (unbiased k3, Tmeas = 10−2 s) 5 ms



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Variance of the cumulant estimator



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Calculations - HOC methods: noise sensitivity

I The higher order methods can suppress noise



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Calculations - HOC methods shot noise sensitivity 1.

I Background radiation can trigger pulses

I For example: gamma radiation

I Also creates a Poisson Pulse train

I Possibly smaller amplitudes

I Simple model: same pulse shape, proportional parametersIntensity: sγ = αsnAmplitude: aγ = βan

I What is the caused error of Campbelling?Which background can be suppressed?



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Calculations - HOC methods shot noise sensitivity 2.

sγ = αsn & aγ = βan (α, β ∈ [0,1])

2nd order 3rd order 4th order



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Calculations - HOC: inhomogeneous process (transient) 1.

The intensity is a time dependent parameter: s0(t)

Homogeneous Inhomogeneous



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Preliminary calculations - HOC: transient 2. (count rate)



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Calculations - HOC: transient 3. (moving cumulant)



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Calculations - HOC: transient 4. (result)



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Conclusion of HOCI Due to convergence only up to 4th orderI Filters noise regardless the frequencyI Suppress small pulses (but it is already solved with 2nd order)I Article draft is ready for ”iteration”, to be submitted ASAP



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Gamma sensitivity of HOC in Astrid-like reactorI Astrid-like neutron and gamma flux, reaction rate from

TRIPOLI (V. Verma)I Gamma pulses in CFHT from Chester (P. Filliatre)I Gamma sensitivity of HOC mode from the toolbox (Zs. Elter)I Note to be written and to be submitted ASAP



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Experimental work conclusions (+Chester simulation)

I The applicability and linearity of HOC methods are verified X

I The measurements provide an opportunity to validate Chester(CFUL01 has 4 fissile layers)

I Article is under progress


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