Piero Ravetto

An Approximate method to study the one-velocity neutron Integral transport equation

Abstract An approximate method to study the monokinetic linear transport equation is outlined, starting from its integral form, rather than the integro-differential one. The approximate solution may be deduced either analytically, in simple cases, or numerically by means of typical space discretization techniques, through a system of second-order differential equations, associated to proper boundary conditions. Both the system and the boundary conditions may be matched with the standard neutron diffusion multigroup ones, by means of a proper correspondence of the coefficients and of the unknowns. The slab and the radially-symmetric sphere are then analysed in detail. It is shown how, in the plane case, the present approximation is perfectly equivalent to the well-known discrete ordinate one. For curved geometries no such equivalence exists, and it is in these cases that the application of the method at hand looks promising, in order to avoid complications and numerical problems in practical applications.