TEMGYM Advanced: Software for Electron Lens Aberrations and Parallelised Electron Ray Tracing

Characterisation of the electron beams trajectory in an electron microscope is possible in a few select commercial software packages, but these tools and their source code are not available in a free and accessible manner. This paper introduces the free and open-source software TEMGYM Advanced, which implements ray tracing methods that calculate the path of electrons through a magnetic or electrostatic lens and allow evaluation of the first-order properties and third-order geometric aberrations. Validation of the aberration coefficient calculations is performed by implementing two independent methods – the aberration integral and differential algebra (DA) methods and by comparing the results of each. This paper also demonstrates parallelised electron ray tracing through a series of magnetic components, which enables near real-time generation of a physically accurate beam-spot including aberrations and brings closer the realisation of a digital twin of an electron microscope. TEMGYM Advanced represents a valuable resource for the electron microscopy community, providing an accessible and open source means of characterising electron lenses. This software utilises the Python programming language to complement the growing ecosystem of free and open-source software within the electron microscopy community, and to facilitate the application of machine learning to an electron microscope digital twin for instrument automation. The software is available under GNU Public License number Three (GPL 3)

Uses Made of Computer Algebra in Physics

Computer algebra is a tool building activity. This paper is a review of acceptance of this tool by physicists and theoretical chemists during the period from the EUROSAM-79 survey to the Spring of 1988, as reflected by the literature which quotes computer algebra. After considering the traditional areas of application; celestial mechanics, relativity and quantum mechanics, we extend our examination to other areas of physics which would appear, from the literature, to be using computer algebra efficiently: fluid mechanics, plasma physics, optics, perturbation technology, continuum mechanics, numerical analysis for physics, mechanics, non-linear evolution equations, theoretical chemistry and other applications

An Introduction to Beam Physics

The field of beam physics touches many areas of physics, engineering, and the sciences. In general terms, beams describe ensembles of particles with initial conditions similar enough to be treated together as a group so that the motion is a weakly nonlinear perturbation of a chosen reference particle. Particle beams are used in a variety of areas

Progress in the Theory of Electron-Beam Deflection

Analysis, simulation, and design of electron-beam-deflection systems are reviewed in light of the current state of theoretical understanding. A brief review of the physical principles is followed by a detailed discussion of electrostatic, magnetostatic, mixed-field, traveling-wave, and scan-expansion systems. Each methodology is examined from a triple perspective: calculation of electromagnetic fields, calculation of electron trajectories, and calculation of the ensemble of trajectories forming the beam. Applications discussed include deflectors for television displays, lithography, scanning microscopes, and CRT oscillography. Developments of the last ten years are stressed, thereby supplementing and updating the author\u27s previous review on this subject. In field calculation, recent developments in the use of numerical methods on computers dominate. These methods include finite-difference, finite-element, and charge-density or integral-equation techniques. In trajectory calculations, increasing use of numerical integration as well as improvements and extensions of the aberration theory are found. In treatment of the beam bundle, the growing sophistication of numerical deflected-beam models has lead to increased use of aberration figures, current-density plots, and phase-space methods