New theoretical approach to the self-coordinated problem in charged-particle optics

Mikhail A. Monastyrski; Victor A. Tarasov; Anatoly M. Filachev

doi:10.1117/12.255510

25 October 1996 New theoretical approach to the self-coordinated problem in charged-particle optics

Mikhail A. Monastyrski, Victor A. Tarasov, Anatoly M. Filachev

Author Affiliations +

Proceedings Volume 2858, Charged-Particle Optics II; (1996) https://doi.org/10.1117/12.255510
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

A new theoretical line of attack to solve the self- coordinated problem in charge particle optics is developed basing on the aberration theory and (tau) -variation technique. The self-coordinated problem is treated as initial-value problem for the evolution integro-differential equation which directly follows from the Lorentz equation with taking into account the space charge effects. The Coulomb potential of a beam is presented in the form of integral taken over the initial parameters domain, and the induced potential (the `mirror image' potential) is presented in the convolution form with a Green function satisfying the adjacent Fredholm integral equation of the first kind. Some considerations to numerical solution of the evolution equation obtained are applied.

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Mikhail A. Monastyrski, Victor A. Tarasov, and Anatoly M. Filachev "New theoretical approach to the self-coordinated problem in charged-particle optics", Proc. SPIE 2858, Charged-Particle Optics II, (25 October 1996); https://doi.org/10.1117/12.255510

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