FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

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

**Relativistic charge in plane wave**

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.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k022/k02211h.htm

Last modified: November 26, 2002