Intense colinear laser beams ω0, k0 and ω1, k1, shone on a plasma with a frequency separation equal to the electron plasma frequency ωpe are capable of creating a large coherent longitudinal electric field EL = mcωpe/e of the order of 1 GeV/cm for a plasma density of 1018 cm-3 by the laser beat excitation of plasma oscillations. Accompanying favourable and deleterious physical effects using this process for a high energy beatwave accelerator are discussed: longitudinal dephasing, pump depletion, transverse laser diffraction, plasma turbulence effects, self-steepening, self-focusing, etc. The basic equation, the driven nonlinear Schrödinger equation, is derived to describe this system. Advanced accelerator concepts to overcome some of these problems are proposed, including various forms of the plasma fiber accelerator. An advanced laser architecture suitable for the beat-wave accelerator is suggested. Accelerator physics issues such as the luminosity are discussed. Applications of the present process to the current drive in a plasma and to the excitation of collective oscillations within nuclei are also discussed.