Plasma-based accelerators of particles are of great interest because,unlike traditional acceleration structures, plasmas can sustain very strong electric fields without electric breakdown, since they are already fully ionized. In a plasma accelerator, charged particles can be continuously accelerated by a relativistic plasma wave with a phase velocity close to the speed of light; this wave can be driven by a relativistic electron bunch or a high-power laser beam. A plasma has a natural frequency of oscillation which is fixed by the plasma density, and such an oscillation will be excited by the fields of a charged-particle bunch or a laser pulse propagating through the medium. The oscillation will travel at the velocity of the driver, meaning that a relativistic electron bunch or a laser pulse will create a speed-of-light wave that can be used for acceleration. [ref] However, efficient wave excitation can only occur if the exciting disturbance has a time duration less than one oscillation period, which in practice means that only laser or electron pulses of less than about 100 fs in length are useful for acceleration. Until recently, lasers could not approach these short pulse lengths, and in 1979 Tajima and Dawson pointed out that the electric field generated by the beating of two laser pulses of slightly differing frequency is in effect a train of very short pulses that can be tuned until the separation between pulses matches the wavelength of the plasma. This effect, known as the plasma beatwave acceleration (PBWA), was first demonstrated at UCLA in 1984-5. Because of the need for specialized laser sources, the UCLA Neptune Lab is one of the only PBWA-capable labs in the world. On the other hand, it is straightforward to create electron beams, especially using modern electron sources -- rf photoinjectors and compressors -- that have short enough pulses to efficiently excite plasma waves. This effect, known plasma wake-field acceleration (PWFA), was proposed by Pisin Chen and colleagues at UCLA in 1985. It was first experimentally observed in experiment run by Rosenzweig in 1988; activities in PWFA experimentation continue at UCLA and collaborating labs to this day.