Neutron flux variation in k0-INAA, experiences and solution in Kayzero for Windows R. van Sluijs, k0-ware, Heerlen, the Netherlands D. Bossus, J. Swagten, DSM Geleen, the Netherlands F. De Corte, A. De Wispelaere, RUG, Ghent, Belgium 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2005, Kona Hawai

Pre-requisite for the standard k0-formula: Constant neutron fluence rate during irradiation Fact: neutron fluence rate is never perfectly stable Un-expected and unwanted perturbation of the flux Typical variation well known for the irradiation facility: slow build-up of neutron flux when starting the reactor or shooting the sample to the irradiation position Increase in flux during irradiation Extra-ordinary irradiation over several reactors stops (maximum possible activation or neutron dose: fluence rate * irradiation time) Theoretically this problem was handled by DeCorte (1987) and later by Lin Xilei (2001) and Jaćimović (2003) 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

k0-formula - k0-Nuclear Data (published in open literature) - Result of the gamma spectrum measurement, dead-time, sample weight, counting time, coincidence correction etc. - Reactor parameters: f and α (HØgdahl-convention, well described) - Detection efficiency accounting for absortion in the sample - Neutron self absortion in the sample Saturation, Decay and Counting correction 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

k0-formula and epithermal flux With Comparator Factor Fc: Relation between Fc and neutron fluence rate 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Saturation correction factor (S in SDC-formula) S : Saturation correction for decay during irradiation Conditions: - neutron epi-thermal flux is constant during irradiation thermal to epi-thermal flux ratio (f) is constant during irradiation Normalized to 1 so Fc gives value of epi-thermal flux. 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Saturation correction factor (S in SDC-formula) SDC for the simplest form of activation: For more complex activation-decay, for example in case of mother-daughter relation, code 8 (one of the least complex), SDC has to be replaced by : 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Variability of the neutron fluence rate (DeCorte 1987) (Jaćimović 2003) F(t)=1+k.t : Jaćimović : k ranging from –0.4 to –0.6%/hr in Triga Mark II DSM : k approx +0.6%/hr in BR1 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Normalized Epi-Thermal Variability of the neutron fluence rate: summation of independent short irradiations tirr' 0.2 0.4 0.6 0.8 1 1.2 8:00 9:00 10:00 11:00 12:00 13:00 14:00 time Normalized Epi-Thermal Flux: F(t) td' As proposed by De Corte 1987 => 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Variability in epi-thermal flux and f (and ) Dividing an irradiation into short sub-irradiations allows: Handling variations in: epi-thermal neutron fluence rate thermal to epi-thermal neutron fluence rate ratio (f) even variations in  15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Sub dividing an irradiation in separate short irradiations Note: Epi-thermal and thermal neutron fluence rate (and ) have to be measured or The variation in time should be calculated For following trend of comparator factors the fluence rate measurement data need to be normalized to 1 Numerical integration using Jaćimović’s formulae It is an extra correction k t F 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Example 1: Measured flux Un-expected and unwanted perturbation of the flux For stable reactors (e.g. BR1) this can be noticed by a deviation of Fc from the typical value. Fc  e  reactor power Handled: recorded flux file, normalized using irradiation start-stop time Perturbation at begin Fc=+2.11% at end Fc +2.34% 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Example 2: Standardized flux variation Typical variation well known for the irradiation facility Slow build-up of neutron flux when starting the reactor or shooting the sample to the irradiation position, combined with constant de- or in-crease in flux Handled: - integration using fixed start-up/cool down flux profile - and using analytical formulae (Jaćimović, 2003) 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Example 3 (entering multiple irradiations): Extra-ordinary irradiation over several reactors stops Maximum possible activation or neutron dose: fluence rate * irradiation time 5x 7 hours Handled: by giving an irradiation flux profile or the measured flux Result : correct results even for the short living radionuclides! 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Conclusion The k0-method can also be used in case of variations in neutron flux on the condition that variations are known. Variations in thermal to epi-thermal neutron flux ratio and even  can be handled straight forward. Practical solutions are given and implemented in Kayzero for Windows for: slow transport to the irradiation position or starting the reactor with loaded samples and a constant increase or decrease in neutron flux. Activation during several reactor cycles can also be handled without problems. 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Example 2: Standardized flux variation Typical variation well known for the irradiation facility Slow build-up of neutron flux when starting the reactor or shooting the sample to the irradiation position, combined with constant de- or in-crease in flux Handled: - integration using fixed start-up/cool down flux profile - and using analytical formulae (Jaćimović, 2003) 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Example 1: Measured flux (implementation) Un-expected and unwanted perturbation of the flux Data to enter: Start irradiation date and time Stop irradiation date and time File name of a tabseparated file containing measured flux as a function of time, see figure (irradiation.flx in measurement directory) (09:00:00 1000000 09:01:00 1002123 09:02:00 1003453 09:03:00 1012345 etc.) AM/PM allowed! Start and stop time are used for calcu- lation the normalization average of the neutron flux gauge value. By doing this the Fc will be giving the neutron flux. Fc  e  reactor power. 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai

Example 2: Standardized flux variation (implementation) Typical variation well known for the irradiation facility Data to enter: Start irradiation date and time Stop irradiation date and time File name of a tabseparated file containing start-up and cool-down flux change as a function of time see figure (irr.flx in meas. directory) Slope= -0.6 %/hr -10 0 -5 0.5 -0 1 5 0.5 10 0 Slope: increase/decrease during given irradiation period. Start-up/Cool-down: Time in minutes Flux 0-1, see figure 15/11/2018 www.kayzero.com MARC VII, April 3th- 7th 2006, Kona Hawai