Determining Reactor Neutrino Flux
Jun Cao
caoj@ihep.ac.cn
Institute of High Energy Physics, CAS, Beijing
Neutrino 2010, Athens, Jun. 14-20, 2010
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Reactor Neutrino Experiments

The first neutrino observation
in 1956 by Reines and Cowan.

Determination of the upper
limit of mixing angle theta13 to
sin2213<0.17 (Chooz, Palo
Verde)

The first observation of reactor
anti-neutrino disappearance at
KamLAND in 2003.
• Precision Experiments on theta13 (Daya Bay, Double Chooz, RENO)
• -electron or -nucleus scattering (TEXONO, MUNU, GEMMA, CvNS)
• Non-proliferation monitoring (France, US, Russia, Japan, Brazil, Italy)
• Possible 60-km baseline experiment
Reactor Neutrino Flux at a Glance
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

Using PWR (Pressurized Water Reactor) as examples in the following.
(3-4)% U-235 enrichment. > 95% is U-238.
Neutrinos from subsequent -decays of fission fragments.
U-235 depletion
U-235, U-238
Pu-239, Pu-241
Isotope
evolvement,
Neutrino spectra,
ILL
Pu-239 breeding
X
More neutrinos from
a U-235 fission
than Pu-239
0.1%
Palo Verde
Peak at
4 MeV
Neutrino rate,
Palo Verde
Refueling outage
Power trips
Isotope evolvement
Visible spectrum,
multipled by
inverse -decay
(IBD) Xsec.
Neutrino Flux Calculation
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Neutrino Flux S ( E ) 
istopes

f i Si ( E )
i
Wth
S ( E ) 
 i ( fi F ) ei
istopes
 (f
Core configuration
Thermal power
Operations
Temperature
pressure
……
Measurements
Calculations
F )Si ( E )
i
Wth   i fi ei ,
Heat balance test
Online calibration
i
F   i fi
E : Neutrino energy
fi : Fission rate of isotope i
Si(E) : Neutrino energy spectra/f
(fi /F): Fission fraction
Wth : Reactor thermal power
ei : Energy release per fission
Thermal Power
Wth
Energy release/fission
Core Simulation
fi/F
Flux
Spent fuel
Non-equilibrium
Spectra of Isotopes
Si(E)
Thermal Power
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
KME, thermal power, Secondary Heat Balance Method.




The most accurate measurement.
Offline measurement, weekly or monthly
Generally cited with (0.6-0.7)% uncertainties in literature.
KIT/KDO, thermal power. Good for analysis.



Primary Heat Balance
Online
Weekly calibrated to KME power.
PKIT  PKME  0.1% FP

RPN, nuclear power




Ex-core neutron flux monitoring
Online
Safety and reactor operation control
Daily calibrated to KIT/KDO power
PRPN  PKME  1.5% FP
Core Simulation
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


Qualified core simulation code is normally licensed, not available for
scientific collaborations.
Need a lot of information from the power plant as inputs, such as
configurations, fuel composition, operations (control rods movement,
Boron dilution, etc), inlet temperature, pressure, flow rate, etc.
Fission fractions, as a function of burn-up, could be a by-product of the
refueling calculation, provided by the power plant.
Burn-up is the amount of
energy in Mega Watt Days
(MWD) released from unit initial
mass (ton) of Uranium (TU).
For small power variation,
fission fraction can be gotten
without redoing the simulation.
Provided by CNPRI
Spectra of Isotopes
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


Lack of data of the -decays of the complex fission fragments, theoretical
calculation on the neutrino spectra of isotopes carries large uncertainties.
ILL measured the  spectra of fissioning of U-235, Pu-239, and Pu-241 by
thermal neutrons, and converted them to neutrino spectra. Normalization
error 1.9%, shape error from 1.34% at 3 MeV to 9.2% at 8 MeV.
U-238 relies on theoretical calculation, 10% uncertainty (P. Vogel et al., PRC24,
1543 (1981)). Normally U-238 contributes (7-10)% fissions.
K. Schreckenbach et al. PLB118, 162 (1985)
A.A. Hahn et al. PLB160, 325 (1985)
Shape verified by Bugey-3 data
Normalization improved to 1.6%
Energy Release per Fission
8

Slightly varied for different cores due to neutron capture. Uncertainties in
(0.30-0.47)%.
Isotopes
Energy (MeV)
U-235
201.7±0.6
U-238
205.0±0.9
Pu-239
210.0±0.9
Pu-241
212.4±1.0
M.F. James, J. Nucl. Energy 23, 517 (1969)
Kopeikin et al, Physics of Atomic Nuclei, Vol. 67, No. 10, 1892 (2004)
U-238 (n,) Reaction
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
Besides fission products, U-238(n,)U-239 reaction contributes to neutrino
yield. It is below inverse- decay threshold (1.8 MeV) but it is important
to low energy neutrino-electron scattering experiments (TEXONO,
MUNU).
Non-equilibrium Isotopes
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


ILL spectra are derived after 1.5 days exposure time. Long-lived fission
fragments have not reached equilibrium. Contribute only to low energy
region.
In Chooz paper it is estimated to be ~0.3% and is ignored, comparing
to other errors.
Six chains have been identified, with half lives from 10h to 28y.
(Kopeikin et al.)
Fission
Weighted by inverse- decay Xsec.
Fission
Ratio to neutrinos
in 2-4 MeV
64.1h
28.78y
90Y
90Sr
0.546MeV
neutron
capture
89Sr
2.284MeV
neutron 89Y neutron neutron
capture
capture
capture
Ratio to all
neutrinos
X.C. Ruan et al. (CIAE)
Spent Fuel
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

Spent fuel stored temporarily adjacent to the core, could be up to 10 years.
Similar to non-equilibrium contributions, long-lived fragments in spent
fuel will emit neutrinos.
Weighted by IBD Xsec.
Ratio to neutrinos in 2-4 MeV
Ratio to all neutrinos
Contribution from one batch
spent fuel
It may accumulate to several
percent at 2-3 MeV.
top
Energy Spectra
X.C. Ruan et al.
Day
Day
Day
Day
Day
Day
Day
Day
Day
bottom
0
1
2
3
4
5
10
20
30
Uncertainties from Past Experiments
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CHOOZ, Eur. Phys. J. C27, 331 (2003)
R=1.012.8%(stat) 2.7%(syst)
Parameter
Relative error
Reaction cross section
1.9 %
Number of protons
0.8 %
Detection efficiency
1.5 %
Reactor power
0.7 %
Energy released per fission
0.6 %
Combined
2.7 %
Palo Verde, PRD62, 072002
Parameter
Relative error
Neutrinos/fission
1.4 %
Power, target, distance
1.5%
Combined
2.1 %
Power contributes ~0.7%
KamLAND,PRL94:081801, 2005.
•
Neutrino spectra (1.9%  1.6% with
Bugey data)
•
Inverse -decay cross section (0.2%)
•
Fission fraction fk (~5%)
•
Non-equilibrium fragments (0%)
Power Uncertainties
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


Chooz 0.6%, Palo Verde 0.7%.
Motivation of power uprates by the power plants  Study the power
uncertainties and improve the instrumentation.
Uncertainties of secondary heat balance is dominated by the flow rate.
 Venturi flow meter. Most US reactors. Uncertainty is often 1.4%. It
can be as low as 0.7% if properly calibrated and maintained, but
suffering from fouling effects, which could grow as high as 3% in a
few years.
 Orifice plate. France EDF reactors. Typically 0.72%. No fouling
effects. Could be improved to 0.4% with lab tests.
Note: Above flow meter uncertainties are at 95% C.L. as defined in
ISO 5167. Unless specified, the thermal power uncertainty given
by the power plant is also at 95% C.L.
 Ultrasonic. Start to use in some US and Japan reactors. Type I TT
0.45%, Type II TT 0.2% (Djurcic et al.)
An example
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

EPRI document prepared by EDF, Improving Pressurized Water Reactor
Performance Through Instrumentation:…… (2006)
For N4 reactor (Chooz type) with 4 steam generators:
Empirical formula and
uncertainty specified in
ISO 5167-1-2003.
Orifice Plate
Correlated or
Uncorrelated for the 4
flow meters?

If not assuming the discharge coefficients of the 4 orifice plates are
independent, the power uncertainty at 68.3% C.L. will be 0.37%.
Another Example
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

Daya Bay and Ling Ao reactors (EDF, 2.9GWth) are all calibrated with
SAPEC system, an EDF portable high precision secondary heat balance test
system with its own sensors, databases, and data processing, of uncertainty
0.45%. Ling Ao KME is predicted to have an uncertainty of 0.48% (95% C.L.)
4 tests on Ling Ao KME show differences from 0.031% to 0.065%. Why?
 Used the same orifice plates but different pressure transmitters.
 It proves that the uncertainty is dominated by discharge coefficient.
 Ling Ao KME is in very good agreement with SAPEC.
Test 1
(MW)
Thermal
power
Uncertainty
Analysis
(MW)
Difference (MW)
Difference
Test 2
Test 3
Test 4
Uncertainties of fission fraction
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

Depends on the simulation code. Only slightly on the inputs (has not been
checked on other simulation code.)
Compare measured and calculated concentration of fuel isotopes, sampled
at different burn-up. Part of the qualification of the code.
One analysis of Apollo 2.5
Lester Miller thesis, ROCS
Uncertainties of fission fraction
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
Djurcic et al. collected 159
analyses for various codes and
various reactors in US and
Japan. In average, the simulated
concentration of isotopes have
uncertainties
 U235:
~4%
 Pu-239: ~5%
 U-238: ~0.1%
 Pu-241: ~6%
Djurcic et al. J. Phys. G: Nucl.
Part. Phys. 36 (2009) 045002


Assuming the neutron flux in simulation isn’t affected by the small
variations, fission rate  concentration.
Due to the constraint of the total power, 5% error on simulated isotope
concentrations corresponds to ~0.5% uncertainty on the detected  rate via
IBD reaction.
IBD Event Rate Uncertainties
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

Greatly simplified calculation of IBD rate uncertainties.
Single reactor + single detector
 2  W2   2f   e2   s2   c2  (2.07%)2






W: thermal power ~ 0.4% (1 sigma),
f: average uncertainties due to 5% fission fraction uncertainty ~ 0.5%
e: average energy release per fission ~0.4%
s: spectra normalization 1.92%. Assuming U-238 contribute 8%.
c: IBD cross section = 0.2%
Single detector + two reactors (equal distance)
 2  W2 / 2   2f / 2   e2   s2   c2  (2.02%)2

Near-far detectors + multiple reactors. All correlated errors (common to all
reactors) will cancel out. Uncorrelated errors will reduce depending on the
configuration, e.g. to 0.05.
0.05   unc  0.05   W2   2f  0.05  0.64%  0.03%
Summary
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






Before 80’s, the reactor neutrino flux uncertainties ~10%.
With a lot of efforts, especially by ILL, Bugey, Chooz, Palo
Verde etc., it is improved to 2-3%.
More accurate thermal power, and more detailed study on errors.
A global picture of uncertainties of fission rate from core
simulation.
Small corrections from spent fuel and non-equilibrium
contributions.
No new data for neutrino spectra of fuel isotopes, which is
dominant for a single detector experiment. Thus for single
detector experiments, it is still ~2%.
Next theta13 experiments with near-far relative measurements
will suffer little from reactor flux uncertainties (~0.1%), while
complex correlation analysis should be done.
Thanks!
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Non-proliferation Monitoring
Bowden, LLNL, 2008