A tutorial description of plasma waves in a cold plasma, with emphasis on their application in plasma-based electron accelerators, is presented. The basic physics of linear plasma oscillations and waves and the principle of electron acceleration in a plasma wave are discussed without assuming any previous knowledge of plasma physics. It is shown that estimating key parameters for plasma acceleration such as the maximum or “wave breaking” amplitude and the corresponding energy gained by electrons “surfing” the wave requires a relativistic and nonlinear analysis. This can be done with little mathematical complexity by using a Lorentz transformation to a frame co-moving at the phase velocity of the wave. The transformation reduces the problem to a second-order ordinary differential equation as originally found by Chian [Plasma Phys. 21, 509 (1979)] so that the analysis can exploit the analogy with the mechanical motion of a particle in a potential well.

中文翻译：

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不同框架中的等离子体波

介绍了冷等离子体中的等离子体波的教程描述，重点介绍了它们在基于等离子体的电子加速器中的应用。讨论线性等离子体振荡和波的基本物理学以及等离子体波中电子加速的原理，而无需假设任何先前的等离子体物理学知识。结果表明，估计等离子体加速的关键参数，例如最大或“破波”振幅以及电子“冲浪”波所获得的相应能量，需要进行相对论和非线性分析。这可以通过使用洛伦兹变换到以波的相速度共同移动的坐标系来以很小的数学复杂度完成。转换将问题简化为二阶常微分方程，最初由 Chian [Plasma Phys. 21,