1. Reactor Flux at Daya Bay
Liang Zhan, Institute of High Energy Physics
1st Workshop on Reactor Neutrino Experiments, Seoul, Oct , 2016

2. Outline
Focus on oscillation-related flux prediction instead of absolute measurement.
Reactor flux prediction
Power
Fission fraction (core simulation)
Spent fuel/non-equilibrium
Energy per fission and IBD reaction per fission (correlated)
Error propagation and contribution in total uncertainty
Predicting expected flux/spectrum for each detector and comparison with data.
Correlated: completely canceled
Uncorrelated uncertainty ~0.9%,
reduced by a factor of 20 in the near and far relative measurement.

3. Neutrino Flux Calculation
J.Cao, Neutrino2010
E : Neutrino energy
fi : Fission rate of isotope i
Si(E) : Neutrino energy spectra/f
Neutrino Flux
(fi /F): Fission fraction
Wth : Reactor thermal power
ei : Energy release per fission
Heat balance test
Online calibration
Thermal Power
Wth
Core configuration
Thermal power
Operations
Temperature pressure
… …
Energy release/fission
Core Simulation fi/F
Flux
Spent fuel
Non-equilibrium
Spectra of Isotopes
Si(E)
Measurements
Calculations

4. Daya Bay Thermal Power
J.Cao, Neutrino2010
KME, thermal power, Secondary Heat Balance Method.
The most accurate measurement.
Offline measurement, weekly or monthly
Generally cited with ( )% uncertainties in literature.
KIT/KDO, thermal power. Good for analysis.
Primary Heat Balance
Online
Weekly calibrated to KME power.
RPN, nuclear power
Ex-core neutron flux monitoring
Safety and reactor operation control
Daily calibrated to KIT/KDO power

5. Power Uncertainties Chooz 0.6%, Palo Verde 0.7%.
J.Cao, Neutrino2010
Chooz 0.6%, Palo Verde 0.7%.
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. (RENO reactor?)
Orifice plate. French 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 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.)

6. An example
J.Cao, Neutrino2010
EPRI document prepared by EDF, Improving Pressurized Water Reactor Performance Through Instrumentation:…… (2006)
For EPR reactor (Chooz type) with 4 steam generators:
Empirical formula and uncertainty specified in ISO
Correlated or Uncorrelated for the 4 flow meters?
Orifice Plate

7. Daya Bay Power
Use lived time weighted power; however, the maximum daily difference from the simple average < 0.1%
All 6 reactor cores are the same type (M310) in the nuclear island.
Each core has 3 steam generators  3 orifice plate flow meters
To be conservative (valid for near-far relative analysis), we assume that the 3 flow meters in the same core are correlated, while flow meters in different cores are uncorrelated  yield the largest uncertainty in all possible assumptions.
We take 0.5% uncertainty for a single core (which is by chance similar to the power plant number 0.48%, where they take 95% CL but assume that the 3 flow meters are uncorrelated)

8. Core Simulation
Fission fractions, as a function of burn-up, is a by-product of the refueling calculation, provided by the power plant.
Daya Bay: SCIENCE/APOLLO code
Meanwhile, Daya Bay did standalone simulations with DRAGON
Two Daya Bay reactors replaces 1/3 fuel elements every 18 months
Four Ling Ao reactors replaces 1/4 fuel elements every 12 months.
One analysis of Apollo 2.5
Fission fraction uncertainty ~ 5%
Fission fraction vs. reactor burn-up in one cycle

9. Correlation among fuels
Standalone DRAGON simulation developed in Daya Bay yields similar fission fraction uncertainty as Apollo2 validation (arXiv: )
The 5% fission fraction uncertainty yield 0.6% uncorrelated uncertainty with the constraint of the total thermal power and the correlation among fuels.
The correlation is evaluated with DRAGON by adding perturbation to the normal core simulation.
Fission fraction uncertainty is conservatively assumed to be uncorrelated between reactors in the oscillation analysis via relative measurement.

10. Energy Release per Fission
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
Kopeikin et al, Physics of Atomic Nuclei, Vol. 67, No. 10, 1892 (2004)
M.F. James, J. Nucl. Energy 23, 517 (1969)
1. using updated nuclear databases
2. considering the production yields of fission fragments from both thermal and fast incident neutrons
3.updated calculation of the average energy taken away by antineutrinos.
DYB number: X. B. Ma et al., Phys.Rev. C88, (2013).

11. Non-equilibrium Isotopes and spent nuclear fuel
ILL spectra are derived after 1.5 days exposure time. Long-lived fission fragments have not reached equilibrium. Contribute only to low energy region.
These long-lived fission fragments will be accumulated in the reactors and produce additional antineutrinos.
Six chains have been identified, with half lives from 10h to 28y. (Kopeikin et al.)
Contributions to IBD events
SNF ~ 0.3%
Non-equilibrium ~ 0.6%
90Sr
90Y
Fission
89Sr neutron capture
89Y neutron capture
neutron capture
28.78y
0.546MeV
64.1h
2.284MeV

12. Error Cancellation with N/F detector
To cancel the reactor uncorrelated uncertainty, two strategies can be used.
Strategy 1: the near and far detector detect the identical fraction of flux from each reactor by ideal geometry placement (iso-flux)
Double Chooz uses this strategry
Strategy 2: use N+1 detectors for N reactors. For any geometry placement, a combination of N near detectors can yield identical fraction of flux from N reactors (PhysRevD  )
Daya Bay uses this strategy with two near halls and one far hall for two groups of reactors
2 reactors + 3 detectors scheme
No requirement on the symmetry of geometry placement by one additional detector
Iso-flux: Lf12/Lf22 = Ln12/Ln22 R1 R2 ND FD
Lf1
Lf2
Ln1
Ln2 R1 R2
ND1 FD
ND2

13. Error Cancellation for Daya Bay
Double Chooz near detector is not at the ideal location, and a residual of 10% uncorrelated uncertainty remains.
Daya Bay is also not a ideal 2-reactor + 3-detector experiments. A residual of 5% uncorrelated uncertainty remains.
A combination of EH1 and EH2 to predict the flux at far hall
Fraction of flux from DYB and Ling Ao
Weighting determined by
Considering 8 detectors + 6 reactors, we get the residual uncertainty vs. the weighting of EH2 to EH1
0.05

14. Predicting for each detector
Two methods
Detector Full Monte Carlo simulation (with power, spectrum, neutrino direction, etc.)
Analytical calculation of core flux, and convert to detector spectrum with detector response matrix
The energy model is covered in energy response talk.
Response matrix includes effects of energy leakage, non-linearity, and energy resolution

15. Comparison of predicted and measured reactor rate
Global fit of data/prediction
Measured IBD yield at 8 ADs

16. Comparison of antineutrino spectrum
Obvious bump in 4-6 MeV
Statistical evaluation of the significance of the whole spectrum yields 2.9 σ deviation
Significance in the energy window of 4-6 MeV is 4.4 σ

17. Investigation of the sources of bump
The rate of the excess events in the bump region is ~1.5%
Reject the detector response issue by studies of the beta decay spectra of natural radioactivities.
A beta decay branch of a mono-energetic peak can not reproduce the bump.
The events in the bump region have the same characteristic as the other region
MeV event rate is proportional to other region.
The neutron capture time
The delayed energy spectrum
The vertex distribution

18. Summary Reactor flux prediction and the uncertainties are reviewed
Rate and spectrum discrepancies between data and predicted was observed in Daya Bay