In this paper, we discuss the physical mechanism of laser plasma wake wave and beat wave accelerators by means of theoretical analysis and particle simulation methods. The results show that: as long as laser plasma wave has Vph≈c and is strong enough, and with a proper transverse magnetic field applied, we may accelerate relativistic electrons to the order of magnitude of GeV within a distance of meters. We have also studied the problem of ES wave with low phase velocity generated by laser plasma Raman scattering to accelerate non-relativistic electrons by using particle simulation methods, and possibility of multistage, or multiwave, acceleration is explored as well. The results show that: taking the advantage of laser plasma wave accelerator, we will be able to get high energy electrons of the order of magnitude of Gev under ordinary laboratory conditions.
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