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

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.

Citation Download Citation

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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