Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling
Journal article, 2012

In this article, we derive equations approximating the Boltzmann equation for charged particle transport under the continuous slowing down assumption. The objective is to obtain analytical expressions that approximate the solution to the Boltzmann equation. The analytical expressions found are based on the Fermi-Eyges solution, but include correction factors to account for energy loss and spread. Numerical tests are also performed to investigate the validity of the approximations.


Fermi-Eyges equation

energy loss straggling

analytical solution


Tobias Gebäck

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

SuMo Biomaterials

Mohammad Asadzadeh

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Transport Theory and Statistical Physics

0041-1450 (ISSN) 1532-2424 (eISSN)

Vol. 41 5-6 325-336

Subject Categories


Physical Sciences



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