A naive collective coordinate analysis leads to no damping of the acoustic modes of a classical fluid. A similar analysis of the linearized Vlasov equation leads to the well-known phenomenon of Landau damping. The qualitative form of Landau damping is, however, inaccurate for nonsingular forces and probably for low-k propagation in plasmas. Comparison of the two approaches shows that retention of the velocity variable in the Vlasov equation allows for an accurate description of positional fluctuations due to velocity dispersion by itself, but a poor assessment of collective forces. If, instead, the phase mixing of collective modes due to velocity dispersion is taken into account, a damping mechanism is introduced with the anticipated hydrodynamic form in fluids at low k, and with a k4 dependence for plasmas.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics