Self-modulation instability of ultra-relativistic particle bunches with finite rise times

Abstract

We study the evolution of the self-modulation instability for bunches with finite rise times. Using particle-in-cell simulations we show that, unlike with long bunches with sharp rise times, there are large variations of the wake amplitude and phase velocity with finite rise time bunches. These results show that bunches with sharp rise times are important to seed the self-modulation instability and to ensure stable acceleration.