ASYMPTOTIC DERIVATION OF THE FERMI PENCIL-BEAM APPROXIMATION

The Fermi pencil-beam approximation describes the broadening of a mono energetic, nearly monodirectional particle beam in an optically thick system in which the mean scattering angle tr;small and large-angle sca ttering is negligible. This physical problem has applications in such diverse fields as astrophysics, materials science, electron microscopy , and radiation cancer therapy. The Fermi equation is derived two diff erent ways: as an asymptotic limit of the Fokker-Planck equation for s igma(tr) --> 0 and as an asymptotic limit of the linear Boltzmann equa tion for sigma(tr) --> 0 and sigma(t) --> infinity. Some numerical res ults illustrating the Fermi approximation are also given.