Controlled Growth of the Self-Modulation of a Relativistic Proton Bunch in Plasma

A long, narrow, relativistic charged particle bunch propagating in plasma is subject to the self -modulation (SM) instability. We show that SM of a proton bunch can be seeded by the wakefields driven by a preceding electron bunch. SM timing reproducibility and control are at the level of a small fraction of the modulation period. With this seeding method, we independently control the amplitude of the seed wakefields with the charge of the electron bunch and the growth rate of SM with the charge of the proton bunch. Seeding leads to larger growth of the wakefields than in the instability case.