Higher-order multiple scattering theories for charged particle transport.

The Fermi pencil beam formula and the higher-order multiple scattering theory due to Jette are shown to result from a perturbative treatment of the linear Boltzmann equation with Fokker-Planck scattering. Using asymptotic one-dimensional solutions for the transverse integrated (spherical) fluence as well as its variance, approximate higher-order pencil beam theories are constructed. These simple and explicit formulae are shown, by comparison with benchmark Monte Carlo results, to be significantly more accurate than the Fermi and Jette equations, particularly at large distances from the beam axis.