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Precision enhancement in boundary element methods with application to electron optics.

Jody S Loyd1, Don A Gregory2

  • 1Simulation Technologies, Huntsville, AL 35805, USA jloyd@simtechinc.com.

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Summary

This study introduces a hybrid method combining boundary element method (BEM) and Fourier series for precise electric potential calculations in electron optics. This approach enhances accuracy in modeling electron lenses and analyzing optical aberrations.

Keywords:
aberrationsboundary element methodelectron optics

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Area of Science:

  • Physics
  • Computational Science
  • Engineering

Background:

  • Accurate electric potential calculation is crucial for electron optics modeling.
  • Traditional methods may struggle with complex electrode geometries and precision requirements.
  • Boundary element method (BEM) offers flexibility, while analytic solutions provide precision.

Purpose of the Study:

  • To develop a hybrid approach for precise electric potential calculation in electron optics.
  • To combine the strengths of BEM and Fourier series for improved modeling.
  • To enhance the accuracy of electron ray tracing and aberration analysis.

Main Methods:

  • A hybrid method integrating Boundary Element Method (BEM) and Fourier series.
  • BEM is used for initial potential calculation and defining boundary conditions.
  • Fourier series solution is applied to cylindrical subdomains for high-precision results.

Main Results:

  • The hybrid approach yields higher precision in the resulting lens field.
  • Reduced errors in subsequent electron ray path calculations.
  • Improved ability to observe and analyze optical aberrations in non-paraxial rays.

Conclusions:

  • The hybrid BEM-Fourier series method offers a robust solution for electron optics modeling.
  • This approach enhances accuracy and facilitates detailed analysis of lens performance.
  • Validated through ray-tracing examples in a standard einzel lens.