An exact, closed‐form expression of the integral chord‐length distribution for the calculation of single‐event upsets induced by cosmic rays Available to Purchase

In a previous paper [J. Appl. Phys. 50, 3799 (1979)] Bradford derived a distribution function for the chord lengths through a rectangular parallelepiped (a×b×c, a≤b≤c). This chord‐length distribution describes the path‐length distribution of cosmic‐ray particles in an object exposed to the isotropic cosmic‐ray flux outside the earth’s magnetosphere. It is an essential quantity needed for computing the rate of single‐event upsets (SEUs) induced in space‐borne random‐access memory cells by cosmic rays. While Bradford’s distribution is exact for chord length x within the range 0<x≤b, it is only approximate for b<x≤w, where w=(a²+b²+c²)^1/2. In this paper we present an exact distribution which is valid for all values of chord length (0<x≤w). The extent to which the two distributions differ is explored. It is found that the two distributions agree exactly for 0<x≤b, but are very different for b<x≤w, and that this difference can lead to serious errors when Bradford’s distribution is used for computing the SEU rate. We also present an integral for computing the SEU rate in which the actual shape of the SEU cross‐section curve is explicitly taken into consideration. Our formulation is much easier to evaluate numerically than the one proposed recently by Shoga et al. [IEEE Trans. Nucl. Sci. NS‐34, 1256 (1987)].