Self-modulation instability of a long proton bunch in plasmas.

@article{Kumar2010SelfmodulationIO,
  title={Self-modulation instability of a long proton bunch in plasmas.},
  author={Naveen Kumar and A. Pukhov and K. V. Lotov},
  journal={Physical review letters},
  year={2010},
  volume={104 25},
  pages={
          255003
        }
}
An analytical model for the self-modulation instability of a long relativistic proton bunch propagating in uniform plasmas is developed. The self-modulated proton bunch resonantly excites a large amplitude plasma wave (wakefield), which can be used for acceleration of plasma electrons. Analytical expressions for the linear growth rates and the number of exponentiations are given. We use full three-dimensional particle-in-cell (PIC) simulations to study the beam self-modulation and transition to… 

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