AWAKE: one experiment, three beam-plasma instabilities

A relativistic particle bunch propagating in plasma is subject to a number of instabilities. These can occur separately or simultaneously, depending on the choice of parameters. In AWAKE, a bunch with rms duration of approximately 200ps, and 1 to 3e11, 400GeV protons travels in a 10m-long plasma with density adjustable in the 1e14 to 1e15/cc range. We will show that transverse self-modulation, hosing, and current filamentation instabilities can be observed in experiments. Self-modulation can be seeded to drive plasma wakefields for the purpose of accelerating an electron bunch to high energies (200GeV), in a single, high-gradient structure (1GeV/m), for application to particle physics. For quality acceleration, hosing must be avoided as an instability, but can be induced for physics studies. Current filamentation instability can be observed in its early stage over the 10m-long plasma, and must also be avoided in an accelerator. It is a possible source of magnetic fields in the cosmos. Understanding and controlling these instabilities is not only interesting, but also important in the context of basic and astro physics, as well as in that of the development of advanced accelerator concepts.