Representation of the Electromagnetic Field of an Arbitrarily Moving Charged Particle by Electric Field Lines

IF 1 Q4 OPTICS Optical Memory and Neural Networks Pub Date : 2024-01-30 DOI:10.3103/s1060992x23070032

S. G. Arutunian, M. A. Aginian, E. G. Lazareva, M. Chung

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Abstract

The paper discusses the representation of the electromagnetic field of an arbitrarily moving charged particle by means of electric field lines. Expressions for the field line equations are derived on the basis of exact Lienar-Wichert field formulas. Parameterization of field lines by means of light signals (dots) emitted at delayed moments of time allows us to avoid the problem of solving the retardation equation. The resulting nonlinear equations are linearized using the Lorentz transformation applied to the emission rate of these light dots in the particle’s rest frame. These linear equations coincide with the Thomas precession equation, which allows us to state that field lines can be thought of as comprised of light dots that were emitted isotropically in the particle’s rest frame at speed \(c\). The exact solution of the equations is found in the case when the ratio of the trajectory torsion to the product of the trajectory curvature by the Lorentz factor of the particle is a constant value for the trajectory. The class of such fields in particular includes all flat trajectories. Illustrations of field lines are given for two applications of practical interest – the motion of a charged particle in the field of a plane monochromatic linearly polarized wave and for a helical undulator. In addition, it is shown that the developed mathematical apparatus admits consideration of the superluminal motion of the charge. Exact solutions and illustrations of lines for the superluminal motion of a particle along a circle (superluminal synchrotron radiation) are given.

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用电场线表示任意运动的带电粒子的电磁场

摘要本文讨论了用电场线表示任意运动的带电粒子的电磁场。场线方程的表达式是在精确的利纳尔-维切特场公式基础上推导出来的。通过在延迟时刻发射的光信号（点）对场线进行参数化，可以避免求解延迟方程的问题。利用洛伦兹变换对这些光点在粒子静止帧中的发射率进行线性化，就可以得到非线性方程。这些线性方程与托马斯前冲方程相吻合，因此我们可以认为场线是由光点组成的，这些光点在粒子的静止帧中以 \（c\）的速度等距发射。当轨迹扭转与轨迹曲率与粒子洛伦兹系数的乘积之比为轨迹的恒定值时，方程的精确解就会出现。此类场尤其包括所有平面轨迹。我们给出了两个具有实际意义的场线示例--带电粒子在平面单色线性偏振波场中的运动和螺旋起伏器。此外，还证明了所开发的数学装置可以考虑电荷的超光速运动。给出了粒子沿圆周超光速运动（超光速同步辐射）的精确解和线条图示。

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来源期刊

Optical Memory and Neural Networks OPTICS-

CiteScore

1.50

自引率

11.10%

发文量

期刊介绍： The journal covers a wide range of issues in information optics such as optical memory, mechanisms for optical data recording and processing, photosensitive materials, optical, optoelectronic and holographic nanostructures, and many other related topics. Papers on memory systems using holographic and biological structures and concepts of brain operation are also included. The journal pays particular attention to research in the field of neural net systems that may lead to a new generation of computional technologies by endowing them with intelligence.