Calculation and use of first collision probabilities for one-dimensional heterogeneous media: the Alcoll and Cortina programmes

This report is devoted to the calculation of collision probabilities in the three one-dimensional geometries. We begin by obtaining simple analytical expressions and indicate the general principles of their programming. Three programs have been written to calculate these quantities in plane, spherical and cylindrical geometries (ALCOLL and ALCOLK). Two other programs solve the transport integral equation discretized by collision probabilities: CORTINA for source problems, CRITCOL for critical problems (determination of eigenfunctions and multiplication factors). Section I recalls the classical discretization of the Boltzmann integral equation through the introduction of first collision probabilities and defines the oriented probabilities required to calculate the diffusion coefficient. Sections II, III and IV give details of the analytical calculations used to simplify the numerical calculation of the probabilities in the three geometries. Section V describes the numerical formulation used and the broad lines of the programming; Section VI gives the specifications of the ALCOLL and ALCOLK sub-programmes; Section VII, those of the CORTINA and CRITCOL programmes