Parametric Landau damping of space charge modes
  Landau damping is the mechanism of plasma and beam stabilization; it arises through energy transfer from collective modes to the incoherent motion of resonant particles. Normally this resonance requires the resonant particle's frequency to match the collective mode frequency. We have identified an important new damping mechanism, {\it parametric Landau damping}, which is driven by the modulation of the mode-particle interaction. This reveals new possibilities for stability control through manipulation of both particle and mode-particle coupling spectra. We demonstrate the existence of parametric Landau damping in a simulation of transverse coherent modes of bunched accelerator beams with space charge. 
Alexandru Macridin, Alexey Burov, Eric Stern, James Amundson,   Panagiotis Spentzouris
physics.acc-ph