AWAKE: beam-plasma interactions and plasma wakefield acceleration

Plasma-based accelerators have demonstrated their ability to accelerate electrons at very high gradients (>100GeV/m). The AWAKE experiment, located at CERN, aims to produce high-energy electron bunches (50 to 200GeV) for application to particle physics. Large energy gain is in principle possible using a 400GeV proton bunch to drive wakefields in plasma. We will introduce AWAKE and summarize the main results obtained so far, including the observation of three beam-plasma instabilities. We control the self-modulation instability to accelerate externally-injected electrons from 19MeV to 2GeV. Based on results obtained with a self-modulated plasma wakefield, we have developed a plan to reach much higher energies by scaling up our plasma accelerator. After the success of these experiments, we will propose an application to particle physics.