Analytical formulae for estimating damage rate in the final mirrors of laser inertial fusion energy reactors based on the uncollided neutron flux

Analytical expressions were derived to calculate the average damage rate in grazing incidence mirrors (last mirrors) in an inertial fusion energy (IFE) reactor subjected to the uncollided neutrons streaming from the cavity center through the beam ducts. These expressions account for the dependence of the damage in the mirror on parameters such as the distance between the cavity center and the mirror, D, the angle of incidence, θ, the length of the mirror, X, and the mirror thickness T. The expressions lend themselves to a simple but effective means to study the impact of variations in mirror parameters and location on the damage in the mirror (quantified in terms of dpa/FPY) without the need to carry out expensive 2D or 3D calculations. Applying these expressions gives results that are in a good agreement with those based on Monte Carlo calculations. The derived formulae were used in a parametric study on the impact of variations in D, X, θ and T on the damage rate in aluminium, silicon and copper, the candidate materials in the Prometheus-L IFE reactor.