Bendel 1-parameter function

This functional form, which was first introduced by W.L. Bendel in 1983, provides a convenient and widely-used single-parameter description of proton-induced SEUs cross-section data.

The Bendel-1 parameter function is described by a single parameter, traditionally called "A". The functional form is somewhat complicated but may be written as follows:

F(E) = (24/A)¹⁴ [1.-exp(-0.18y^1/2 )]⁴

where

y(E) = (E-A) (18/A)^1/2 if E > A

= 0 otherwise.

For application to proton-induced SEUs, E is the proton energy in MeV and F(E) is the cross-section in units of 10^-12 cm²/bit.

For more information on the Bendel 1-parameter fit, see:

W.L. Bendel and E.L. Petersen, "Proton Upsets in Orbit", IEEE Transactions on Nuclear Science, NS-30, 4481 (1983).

For many devices, a modification, known as the Bendel 2-parameter fit, has been shown to give a better empirical description of the cross-section data. For more information on the Bendel 2-parameter fit, see:

W.J. Stapor, J.P. Meyers, J.B. Langworthy, and E.L. Petersen, "Two Parameter Model Calculations for Predicting Proton Induced Upsets", IEEE Transactions on Nuclear Science, NS-37, 1966 (1990).

Both Bendel functional forms, as well as the Weibull function, are available for characterizing proton-induced SEU cross-sections in the CREME96 PUP routine.