1. “Influence of atomic displacement rate on radiation-induced ageing of power reactor components” Ulyanovsk, 3 -7 October 2005 Displacement rates and primary knocked atom spectra in WWER vessel steels Pechenkin V.A., Konobeev Yu.V., Pyshin I.V. Petrov E.E., Khoromsky V.A ( Institute of Physics and Power Engineering, Obninsk ), Kryuchkov V.P. ( Concern “ROSENERGOATOM”, Moscow ), Voloschenko A.M., ( Keldysh Institute of Applied Mathematics, Moscow ), Tsofin V.I., Rozanov K.G. ( OKB “Gidropress”, Podolsk )

2. INTRODUCTION For the present, fast neutron fluence (E> 0.5 MeV in Russia and E>1 MeV in USA and France) is used in Regulatory guides for forecasting the irradiation embrittlement of WWER, PWR and BWR reactor pressurized vessels Number of displacements per atom (dpa) should be considered as an improved correlation parameter, that allows to take into account neutrons of all energies  This parameter allows to compare results of irradiation in various neutron spectra as well as by various particles: neutrons, ions and fast electrons  The calculation of dpa and PKA spectra is important for development of irradiation embrittlement models and physically based regulatory guides

3. DOSE RATE At an arbitrary location in the reactor the dose rate K (dpa/s) is given by the following expression : (1) where  (E) is the neutron energy spectrum, and  d (E) is the displacement neutron cross section (2)

4. PKA - SPECTRUM where the integral over E is the spectrum of primary knocked atoms (PKA-spectrum). Inserting eqn. (2) in eqn. (1) and changing the order of integration, one can find

5. CASCADE MODELS If to neglect energy loss mechanisms such as electronic excitation and ionization, the NRT displacement model NRT (T) is given by the following simple expression: NRT (T) =10T, where T is the PKA kinetic energy in units of keV. By molecular dynamics (MD) simulations of cascades in alpha-Fe, Doan (2000) has found (T)  8.25 T 0.967. This result can be obtained from NRT (T)=10T, if to take the effective threshold displacement energy for Fe equal to 48.5 eV instead of 40 eV in the NRT-model. Using another interatomic potential for the MD-simulation of cascades in Fe, Stoller found that (T)/ NRT (T) <1 at the effective threshold displacement energy of 40 eV.

6. «EFFECTIVE DPA» Below the number of displacements per atom calculated with account of defects surviving in-cascade recombination is called as «effective dpa» Energy dependence of total point defect survival fraction (per NRT) obtained by R. Stoller in MD cascade simulations. The ratio  = (T)/ NRT (T) was approximated as follows:  =0.5608T -0.3029 +3.227  10 -3 T

7. DETAILS OF CALCULATIONS For calculation of dose rates at different locations in WWER - 440 neutron and gamma spectra were obtained using the 3D transport code KATRIN developed by A.M. Voloschenko et al. In WWER-1000 the approximate 3D distributions have been received using the 3D synthesis of 2D (r, ϑ ) and (r,z) and 1D cylindrical (r ) solutions PKA-spectra were calculated using the SPECTER code developed by L. Greenwood

8. NEUTRON SPECTRA AT DIFFERENT LOCATIONS IN WWER - 440 Neutron energy, MeV Nomlised neutron group fluxes

9. CALCULATED NEUTRON FLUXES, DOSE RATES AND MEAN PKA ENERGIES Neutron flux, point defect generation rate and mean PKA energy at different locations in WWER-440 and WWER-1000 Type of reactor Cylindrical coordinates Neutron flux, 10 9 n/cm 2 s Dose rate, 10 -12 dpa NRT /s Dose rate calculated using  D, eq.(1) 10 -12 dpa NRT /s Dose rate, 10 -12 dpa eff /s Mean energy of PKA (keV) Heig ht Z, cm Angle , radian Radius R, cm >0.5 MeV >1 MeV WWER – 440 surveillance specimens 1450.5191604450254041304080133010.9 WWER – 440 inner surface 1450.519178 245 15424324275.714.5 WWER – 440 outer surface 1450.519192 66.5 25.5 57.755.618.810.6 WWER – 1000 inner vessel surface35.422.335.034.911.016.6 WWER – 1000 outer vessel surface5.231.674.774.551.578.82

10. EFFECT OF NEUTRON SPECTRA ON DPA AND FLUENCES in WWER-440 Damage rates and neutron fluxes R (cm) 160178192 10 -11 for neutrons with E> 0.5 MeV (contribution to the total rate) 324 (78%)19.7 (81%)3.94 (68%) 10 11 for neutrons with E> 0.5 MeV (contribution to the total flux) 44.5 (16.9%) 2.45 (12.4%) 0.665 (28.3%) 10 -22 ratio of the total rate to the flux of neutrons with E> 0.5 MeV (with all energies) 9.28 (1.7)9.92 (1.25)8.88 (2.36)

11. EFFECTS OF GAMMA-QUANTA AND RPVS COMPOSITION ON THE DOSE RATE The contributions of gamma-quanta to dose rates dpa eff /s were calculated for surveillance specimens (R = 160 cm), inner (R = 178 cm) and outer (R = 192 cm) vessel surfaces in WWER-440. For the calculation displacement cross sections for Fe have been taken from the paper by K. Fukuya and I. Kimura (2003). The ratios of gamma to neutron dpa eff /s equal 0.007, 0.035 and 0.004 respectively. Although the total content of alloying elements (Cr, Ni, Mn, Mo,V) in RPVS does not exceed several percents, additional calculations of dose rates were performed with account of main alloying elements. There are only small differences in the dose rates at the internal vessel surface calculated for pure Fe and for base metal in WWER- 440 (2.43  10 -10 dpa/s и 2.44  10 -10 dpa/s) and in WWER-1000 (3.50  10 -11 dpa/s and 3.51  10 -11 dpa/s).

12. CONCLUSIONS  In WWER-440 displacement rates (dpa/s) at surveillance specimen locations exceed ones at the internal vessel surface by more than one order of value  The evaluated ratios of the displacement rate to the neutron flux depend on the neutron spectra at specified locations in WWER  PKA-spectra at different locations of WWERs differ significantly. In WWER- 440 these spectra are harder at the internal vessel surface as compared with the outer vessel surface and surveillance specimen locations