Radiation reaction force in a relativistic beam, also known as the CSR wakefield, is often computed using a 1D model of a line charge. While this model can serve as a useful tool for a quick calculation, in many cases its accuracy is not sufficient. In particular, this model misses the so-called compression effects associated with the change of the electromagnetic energy when the beam is compressed longitudinally or transversely. The existing 3D simulation codes that take this effect into account are often slow and are not easy to use. In this work, we propose a new approach to the calculations of radiation and space charge longitudinal forces in free space based on the use of the integrals for the retarded potentials. Our main result expresses the rate of change of particles’ energy through 2D (in a 2D model) or 3D integrals along the beam orbit.

中文翻译：

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相对论光束中辐射和空间电荷力引起的尾波的计算

相对论光束（也称为CSR尾场）中的辐射反作用力通常使用线电荷的一维模型来计算。尽管此模型可以用作快速计算的有用工具，但在许多情况下，其准确性还不够。特别地，当射束被纵向或横向压缩时，该模型错过了与电磁能的变化相关的所谓压缩效应。考虑到这种影响的现有3D模拟代码通常很慢并且不容易使用。在这项工作中，我们提出了一种新方法，该方法基于对延迟势的积分的使用来计算自由空间中的辐射和空间电荷纵向力。我们的主要结果表示粒子能量沿射束轨道通过2D（在2D模型中）或3D积分变化的速率。