Approximate solution of an adapted Bethe transport equation for electron scattering in foils
Abstract
A new semi-analytical model for electron scattering in foils is presented valid for thin foils and electron-beam kinetic energies up to roughly $100$ keV and from 20 keV at a dimensionless foil thickness of $20$, and higher energies for thinner foils. To perform calculations, an approximate solution is constructed by Hankel transforms of an adapted Bethe transport equation for electron scattering. The Wentzel differential cross section is used in the Bethe transport Eq. and resulting integrals are solved analytically or approximated. These approximate solutions of the transport Eq.'s were compared to the Goudsmit-Saunderson solutions in gold, for thin samples with dimensionless thicknesses λ=5,10,20. We also compare to the Kawrakow \cite{Kawr} model, which uses the small angle approximation. We show that in the regime of $20$ to $100$ keV beam energies, our model performs better than Kawrakow's model and this is opposite above about 100 keV. Exactly, some angularly distributed beams and the influence of energy loss of the beam can be simulated with our model.
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BibTeX
@misc{corstens2026approximate,
title = {{Approximate solution of an adapted Bethe transport equation for electron scattering in foils}},
author = {J. M. Corstens},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21634},
eprint = {2609.21634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21634},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Approximate solution of an adapted Bethe transport equation for electron scattering in foils
AU - J. M. Corstens
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21634
UR - https://arxiv.org/abs/2609.21634
AB - A new semi-analytical model for electron scattering in foils is presented valid for thin foils and electron-beam kinetic energies up to roughly $100$ keV and from 20 keV at a dimensionless foil thickness of $20$, and higher energies for thinner foils. To perform calculations, an approximate solution is constructed by Hankel transforms of an adapted Bethe transport equation for electron scattering. The Wentzel differential cross section is used in the Bethe transport Eq. and resulting integrals are solved analytically or approximated. These approximate solutions of the transport Eq.'s were compared to the Goudsmit-Saunderson solutions in gold, for thin samples with dimensionless thicknesses λ=5,10,20. We also compare to the Kawrakow \cite{Kawr} model, which uses the small angle approximation. We show that in the regime of $20$ to $100$ keV beam energies, our model performs better than Kawrakow's model and this is opposite above about 100 keV. Exactly, some angularly distributed beams and the influence of energy loss of the beam can be simulated with our model.
ER -