characterization of reactor fuel burn-up from antineutrino spectral distortions

Characterization of reactor fuel burn-up from antineutrino

spectral distortions E. Kemp, L.F. G. Gonzalez, T.J.C. Bezerra

and B. Miguezfor the ANGRA Collaboration

State University of Campinas - UNICAMPPhysics Institute- Cosmic Rays Department

ANGRA Neutrinos Project

So/Si

Neutrino Spectra Parametrization:• Precision spectroscopy with reactor anti-neutrinos.

Patrick Huber, Thomas Schwetz , hep-ph/0407026

Simulation Steps

Energy draw from selected spectrum

Isotope Selection

Weighting by cross-section

Fitting routine to extract the

isotope fraction

6,...,1

1,9,8,5

)exp(

j

i

Ebai

j

jji

1000 events

Fuel evolution

Static Fuel

Energy resolution dE = k.E

dE=0

Fitting convergence study:239Pu fraction

Events

239

Pu

Fis

sion

con

trib

utio

n

•Perfect energy resolution

•Static Fuel

•Assumed rate: 1000/day (Angra expectation)

High Statistics (exposure) Needs• Shape comparison: Kolmogorov-Smirnov test

– Neutrino spectrum: Composition from normalized Schreckemback’s spectra (235U, 239Pu and 241Pu)

Spectral Distortion:expectations from burn-up

• Taking the ratio between the spectra measured in the n-th month and the first one, we can observe the distortion induced by the burn-up

2 3 4 5 6 7 8 9 10 110.80

0.85

0.90

0.95

1.00

1.05

1.10

R(t) = Nith-bin

(t=n) / Nith-bin

(t=1)

R(t

)

Energy [MeV]

Month 1 2 3 4 5 6 7 8 9101112

Spectral Distortion:expectations from burn-up

Nucifer Simulations:we are in good agreement

Thanks to D. Lhuillier !

The Spectral Ratio Fit: an example

3 4 5 6 7 8 90.80

0.85

0.90

0.95

1.00

1.05

1.10S

(t=

6)/S

(t=

0) t

[mon

ths]

Energy (MeV)

Data Linear Fit of Spectral Ratio

6th Month after reactor starting

Spectral Ratio FitRed: linear fit

Green: 95% C.L. bands

The slope time dependence

0 2 4 6 8 10 12-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

red line: exponential modelA + B * exp(t-t

0/)

blue lines: 95% C.L. band

slo

pe

t [months]

Is the slope of R(t) a good indicator for deviations from the expected behavior ?

• Let’s assume a diversion of 1/3 of the reactor fuel during the 6th month

Burnup: impact on the spectrum shape with 1/3 of the fuel replaced at half-cycle

Day number

Fis

sion

fra

ctio

n

Day number

Fis

sion

fra

ctio

nBurnup:

impact on the spectrum shape with 1/3 of the fuel replaced at half-cycle

The slope time dependence

0 2 4 6 8 10 12-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

red line: exponential modelA + B * exp(t-t

0/)

blue lines: 95% C.L. band

slop

e

t [months]

Is it an outlier?

The slope time dependence

0 2 4 6 8 10 12-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

red line: exponential modelA + B * exp(t-t

0/)

blue lines: 95% C.L. band

slop

e

t [months]

Yes, with 75% C.L.

Simulation Steps

6,...,1

1,9,8,5

)exp(

j

i

Ebai

j

jji

Energy draw from selected spectrum

Isotope Selection

Weighting by cross-section

Χ2 – KS testsNull hypothesis:

No distortion

Repeat until

Fuel evolution:Poisson-like time interval

μ= f.Δt frequency f = f(D,M)

D,M: detector distance and mass

Static Fuel

Energy resolution dE = k.E

dE=0

Experimental Data

(Shreckemback’s Spectra)

T

Simulation Steps

6,...,1

1,9,8,5

)exp(

j

i

Ebai

j

jji

Energy draw from selected spectrum

Isotope Selection

Weighting by cross-section

Χ2 – KS testsNull hypothesis:

No distortion

Repeat until

Fuel evolution:Poisson-like time interval

μ= f.Δt frequency f = f(D,M)

D,M: detector distance and mass

Static Fuel

Energy resolution dE = k.E

dE=0

Experimental Data

(Shreckemback’s Spectra)

T

Simulation Steps

6,...,1

1,9,8,5

)exp(

j

i

Ebai

j

jji

Energy draw from selected spectrum

Isotope Selection

Weighting by cross-section

Χ2 – KS testsNull hypothesis:

No distortion

Repeat until

Fuel evolution:Poisson-like time interval

μ= f.Δt frequency f = f(D,M)

D,M: detector distance and mass

Static Fuel

Energy resolution dE = k.E

dE=0

Experimental Data

(Shreckemback’s Spectra)

T

Hypothesis Tests Results

Chi^2 vs. KS

• Chi^2 (is more optimistic…)– More Type II Errors

• KS test– More Type I Errors

• See T.J.C. Bezerra, B. Miguez and R.M.Almeida works (poster session) for detailed numbers and generalities on this (including oscillation studies)

Chi^2 vs. KS

• Is it possible to profit the better from both of the tests?– Fisher’s method:

• Combination of N different results (p-values) of independent statistical tests resulting in a Chi^2 like quantity with 2K degrees of freedom

Next step for this study…

Conclusions• Isotopic composition measurements by shape analysis

only requires a large number of events– Reduce the time integration:

• Large time intervals degrades information– High exposure:

source luminosity + detector mass+ time• Recognition of fuel diversion is possible by observing

UNEXPECTED spectral distortions (but, how much?)• Required Improvements:

– More sophisticated analysis methods to quote the sensitivity in mass of the recognition method

– Combining information: • Shape + Counting Rates• different statistical methods working together

– Fisher’s method• PCA, LDA: decomposition of a mixed signal (?)

• Thank you !