MODELING THE HEAVY-ION UPSET CROSS-SECTION

The standard Rectangular Parallelepiped (RPP) construct is used to derive a closed form expression for, ($) over bar sigma(theta, phi, L) the directional-spectral heavy ion upset cross section, This is an expected value model obtained by integrating the point-value cross section model, sigma(theta, phi, L, E), also developed here, with the Weibull density function, f(E), assumed to govern the stochastic behavior of the upset threshold energy, E. A comparison of ($) over bar sigma(theta, phi, L) with experimental data show good agreement, lending strong credibility to the hypothesis that E-randomness is responsible for the shape of the upset cross section curve, The expected value model is used as the basis for a new, rigorous mathematical formulation of the effective cross section concept, The generalized formulation unifies previous corrections to the inverse cosine scaling, collapsing to Petersen's correction, [cos theta - (h/l) sin theta](-1), near threshold and Sexton's, [cos theta + (h/l) sin theta](-1), near saturation, The expected value cross section model therefore has useful applications in both upset rate prediction and test data analysis.