  In this article, we concentrate on the basic physics of relativistic plasma
wave accelerators. The generation of relativistic plasma waves by intense
lasers or electron beams in low-density plasmas is important in the quest for
producing ultra-high acceleration gradients for accelerators. A number of
methods are being pursued vigorously to achieve ultra-high acceleration
gradients using various plasma wave drivers; these include wakefield
accelerators driven by photon, electron, and ion beams. We describe the basic
equations and show how intense beams can generate a large-amplitude
relativistic plasma wave capable of accelerating particles to high energies. We
also demonstrate how these same relativistic electron waves can accelerate
photons in plasmas.
