Plasma waves in a different frame

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.