ELOS 2022

Valentin Ivanov

Valentin Ivanov, Speaker at Optics conferences
Budker Institute of Nuclear Physics, Russian Federation
Title : Comparative analysis mathematical models for the problems of electron optics


The comparative analysis of modern mathematical models for 3D problems in electron optics is presented. These methods include both stationary and non-stationary self-consistent problems in the optics of intense beams of relativistic charged particles, as well as problems in the optics of imaging systems. Models of "current tubes" for stationary problems, "particles- in-cell" for non-stationary problems, as well as various versions of aberration theory methods for two-dimensional and three-dimensional problems of imaging optics are considered. Comparative characteristics of the effectiveness of the models under consideration are given in relation to the accuracy of the solutions obtained and the required resources of computing systems.
The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the boundary element method (BEM) for the field evaluation, and 3-rd order aberration expansion for the trajectory analysis. The described  approaches are illustrated  by solving complex problems for physical electronics devices.

Audience Take Away:

  • When solving complex problems of electron optics, on the basis of the presented report, the audience will be able to choose the most appropriate and effective method that meets the goal.
  • The report presents in sufficient detail the features of mathematical models.
  • The persuasiveness of the presented material is illustrated by examples of solving complex problems of electron optics.


Ivanov studied Physics and Applied Mathematics at the Novosibirsk State University, Russia and graduated as MS in 1973. He reseived Ph.D degree in 1975 at the Computing Center in Novisibirsk, Prof. degree in 1991 at the. St.-Petersburg Institute of Analytical Instrumentation of Russian Academy of Sciences. Then he worked at the Institute of Nuclear Physics, Russia; Stanford Linear Accelerator Center, US; FNAL, US; ANL, US as physicist. He published more than 250 research articles and 6 monographs.