A NON-GAUSSIAN TREATMENT OF RADIATION PENCIL BEAMS

The problem of describing steady-state transport of a perpendicularly incident particle beam through a thin slab of material is considered F or a scattering kernel sufficiently peaked in momentum transfer to all ow a Fokker-Planck description of the scattering process in both energ y and angle, an approximate closed form solution to this problem was o btained almost 50 yr ago and is referred to as the Fermi-Eyges formula . It is shown that a Fermi-Eyges-like formula can be derived for a bro ader class of scattering kernels. This class consists of scattering de scribed by the continuous slowing-down approximation (the Fokker-Planc k description in energy), but not sufficiently forward peaked in angle to allow an angular Fokker-Planck representation. This generalized fo rmula reduces to the classic Fermi-Eyges result for scattering operato rs,vith a valid Fokker-Planck limit and also describes problems that, while involving a forward-peaked scattering kernel, do not possess a F okker-Planck description. A classic example of such a kernel is the He nyey-Greenstein kernel, and the Fermi-Eyges-like solution in this case exhibits more beam spreading than that predicted by the classic Fermi -Eyges formula. In particular, the scalar flux is non-Gaussian in the radial coordinate, as contrasted with the Gaussian Fermi-Eyges result.