Particle beam self-modulation instability in tapered and inhomogeneous plasma

The particle beam self-modulation instability in tapered and inhomogeneous plasmas is analyzed via an evolution equation for the beam radius. For a sufficiently fast taper, the instability is suppressed, and the condition for growth suppression is derived. The form of the taper to phase lock a trailing witness bunch in the plasma wave driven by a self-modulated beam is determined, which can increase the energy gain by several orders of magnitude. Growth of the instability places stringent constraints on the initial background plasma density fluctuations. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677358]