Modeling of cascade and sub-cascade formation at high PKA energies in irradiated fusion structural materials

Abstract

A new theoretical model is developed for the investigations of cascade and sub-cascade formation in fusion structural materials under fast neutron irradiation at high primary knock-on atom energies. Light fusion structural materials: such as Be, C and SiC under 14 MeV neutron irradiation in fusion reactor will have the primary knock-on atoms with the energies up to 1 MeV. It is very difficult to use at such high energies the Monte-Carlo or molecular dynamic simulations [H.L. Heinisch, B.N. Singh, Philos. Mag. A67 (1993) 407; H.L. Heinisch, B.N. Singh, J. Nucl. Mater. 251 (1997) 77]. The developed model is based on the analytical consideration of elastic collisions between displaced moving atoms produced by primary knock-on atoms with some kinetic energies obtained from fast neutrons and crystal lattice atoms. The Thomas–Fermi interaction potential is used here for the description of these elastic atomic collisions. The suggested model takes into account also the electronic losses for moving atoms between elastic collisions. The self-consistent criterion for sub-cascade formation is suggested here which is based on the comparison of mean distance of primary knock-on atoms between consequent collisions of them with the target atoms and a size of sub-cascade produced by moving secondary knock-on atoms produced in such collisions. The analytical relations for the most important characteristics of cascades and sub-cascades are determined including the average number of sub-cascades per one primary knock-on atom in the dependence on its energy, the distance between sub-cascades and the average cascade and sub-cascade sizes. The developed model allows determining the total numbers, distribution functions of cascades and sub-cascades in dependence on their sizes and generation rate of cascades and sub-cascades for the different fusion neutron energy spectra. On the basis of this developed model the numerical calculations for main characteristics of cascades and sub-cascades in different fusion structural materials: Fe, V, C, Al, Be and W are performed here using the neutron fluxes and primary knock-on atom energy spectra for fusion reactors: ITER and DEMO.