Energy spectra and LET spectra of protons behind shielding

With the advent of devices sensitive to SEU due to direct ionization by protons, it became important to know the flux and energies of protons behind aluminum shielding or within satellites. We present new analytically derived expressions for the energy distribution of incident protons, after passing the shielding, and of secondary protons emitted within the shielding. The results are compared with those of the MULASSIS code. In some cases, like a satellite in a GCR orbit, the contribution of the secondary protons to SEU might be the dominant one. Proton energy-distributions behind shielding are proportional, at low energy values, to inverse proton-LET in aluminum. Their calculated LET-spectra in silicon can be used for evaluating SEU-rate in space. The analytic expressions presented here can be useful in calculating the influence of shielding on other incident ions and secondary ions.