A Quasi-Monte Carlo Method for an Elastic Electron Back-Scattering Problem
The elastic electron back-scattering is a problem that is important for many theoretical and experimental techniques, especially in the determination of the inelastic mean free paths. This effect arises when a monoenergetic electron beam bombards a solid target and some of the electrons are scattered without energy loss.The description of the flow can be written as an integral equation and may be solved by Monte Carlo methods.
In this paper we investigate the possibility of improving the convergence of the Monte Carlo algorithm by using scrambled low-discrepancy sequences. We demonstrate how by taking advantage of the smoothness of the differential elastic-scattering cross-section a significant decrease of the error is achieved. We show how the contribution of the first few collisions to the result can be evaluated by an appropriate integration method instead of direct simulation, which further increases the accuracy of our computations without increase of the computational time. In order to facilitate these techniques, we use spline approximation of the elastic cross-section, which is more accurate than the widely used tables of Jablonski.
KeywordsMonte Carlo Algorithm Spline Approximation Halton Sequence Sobol Sequence Monoenergetic Electron Beam
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