FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 2, PAGES 547-557

V. V. Ternovskii

A. M. Khapaev

Abstract

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It is proved that the system of Maxwell--Lorentz equations in
```$z$ -presentation has many solutions. Determination
of the energetic condition of the charge is reduced to analysis
of the parametric system as a Kepler problem. The extreme conditions
and configuration of the electromagnetic wave field determine the value
of the reflection parameter, which changes the efficiency of
electron-wave interaction and dynamics of the charge's motion.
A visual geometric interpretation of possible energetic state
of the electron is given.
We present expressions that determine the change of the
charge's energy and coordinates as functions
of the length of interaction space and laboratory time.
Four possible regimes of the electron energy change are found.
We obtain a functional connection of the initial impulses
with the electromagnetic wave amplitude.

The exact theoretical solution of electron motion relativistic
equations is constructed in the form of a uniformly converging
Fourier series.

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Last modified: November 26, 2002