The principle of plasma wakefield acceleration is shown in the schematic above. The incoming proton beam enters a plasma and attracts the free electrons to it; they accelerate towards it and overshoot. The electrons are then attracted back to the region of positive charge, the ions, and again accelerate in and overshoot.
These oscillating free electrons in the plasma create an accelerating electric field in the direction of travel of the proton beam. Another beam of electrons can then be injected in the right phase behind the protons so as to be maximally accelerated through the plasma.
The Advanced Wakefield (AWAKE) Experiment is a project at CERN which shall demonstrate that a proton beam can be used to drive a strong wakefield in a plasma. This in turn shall then be harnessed to accelerate a witness bunch of electrons.
The effect of high electric fields in a plasma has been observed before using either lasers or electron beams driving the initial disturbance. These fields can have gradients of up to 100 GV/m, or about 1,000 times higher than the fields that can be achieved in conventional RF accelerators.