Ultimate-gradient accelerators: physics and prospects

As introduction, the needs and ways for ultimate acceleration gradients are discussed briefly. The Plasma Wake Field Acceleration is analized in the most important details. The structure of specific plasma oscillations and "high energy driver beam SP-plasma" interaction is presented, including computer simulation of the process. Some pratical ways to introduce the necessary mm-scale bunching in driver beam and to arrange sequential energy multiplication are dicussed. The influence of accelerating beam particle - plasma binary collisions is considered, also. As applications of PWFA, the use of proton super-colliders beams (LHC and Future SC) to drive the "multi particle types" accelerator, and the arrangements for the electron-positron TeV range collider are discussed.