• DOI:10.1063/1.2186187
• Corpus ID: 45681322

Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problemsa)

@article{Ngb2006WeaklyCL,
  title={Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problemsa)},
  author={C. S. Ngb and Ashis Bhattacharjee},
  journal={Physics of Plasmas},
  year={2006},
  volume={13},
  pages={055903}
}

• C. S. Ngb, Ashis Bhattacharjee
• Published 8 May 2006
• Physics
• Physics of Plasmas

Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most fundamental concepts in plasma physics. While the former describes the surprising damping of linear plasma waves in a collisionless plasma, the latter describes exact undamped nonlinear solutions of the Vlasov equation. There does exist a relationship between the two: Landau damping can be described as the phase mixing of undamped eigenmodes, the so-called Case–Van Kampen modes, which can be viewed as BGK modes in the linear limit. While these concepts have been around for a long time, unexpected new results are still being discovered. For Landau damping, we show that the textbook picture of phase mixing is altered profoundly in the presence of collision. In particular, the continuous spectrum of Case–Van Kampen modes is eliminated and replaced by a discrete spectrum, even in the limit of zero collision. Furthermore, we show that these discrete eigenmodes form a complete set of solutions. Landau-damped solutions are then recovered ...