Instability and Seeded Self-Modulation of a Relativistic Proton Bunch in Plasma

In this work, I demonstrate the existence of two distinct self-modulation (SM) regimes for a relativistic proton bunch in plasma. I evaluate the variation in the phase of the modulation as a function of the initial transverse wakefield amplitude. I show experimentally for the first time that SM can evolve as an instability, i.e. growing from noise, or be seeded, i.e. controlled. With sufficient seed wakefield amplitude, the modulation phase is reproducible from event to event, all along the bunch. Further, I study the effect of linear plasma gradients on the self-modulation.