The dynamic adjoint as a Green’s function

Highlight•The relationship between the direct Green’s function and the dynamic adjoint function is discussed in two-group theory.•It is shown that the elements of the direct Greens’ function matrix are identical to those of the transpose of the adjoint Green’s function matrix, with an interchange of arguments.•It is also remarked how the dynamic adjoint function of van Dam can be given in terms of the direct Green’s function matrix.

The concept of the dynamic adjoint was introduced by Hugo van Dam for calculating the in-core neutron noise in boiling water reactors in the mid-70’s. This successful approach found numerous applications for calculating the neutron noise in both PWRs and BWRs since then. Although the advantages and disadvantages of using the direct (forward) or the adjoint (backward) approach for the calculation of the neutron noise were analysed in a number of publications, the direct relationship between the forward Green’s function and the dynamic adjoint has not been discussed. On the other hand, in particle transport theory the relationship between the direct and adjoint Green’s function has been discussed in detail, in which Mike Williams has had many seminal contributions. In this note we analyse the relationship between the direct Green’s function and the dynamic adjoint in the spirit of Mike’s work in neutron transport and radiation damage theory. The paper is closed with some personal remarks and reminiscences.