One-dimensional time-dependent transport in thin slabs

This work is motivated by the recent observation that the third-order time moments of the transmitted current caused by a pulsed beam of photons normally incident on a one-dimensional, nonabsorbing slab tend to diverge with decreasing slab thickness. In stark contrast, a slab of zero thickness must have first and higher order time moments identically equal to zero, clearly demonstrating the existence of a nonuniform limit. This contradiction has been attributed to the one-dimensional slab geometry approximation and merits further investigation with a transport code. In this paper, we describe an accurate, high-order discretization scheme in time and space that is implemented in a transport code and that we use to address the divergent behavior of the time moments