Collective modes in some Fokker-Planck Coulomb systems: One-dimensional case

The collective modes in two Fokker-Planck Coulomb systems are studied in one dimension and in the long wavelength limit. The Fokker-Planck “friction coefficient”, which can be related to the viscosity of the medium through the Stokes' law, is treated as a parameter. In a single component system it is shown under what circumstances the propagative plasma mode can become a diffusive mode. Depending on an inequality involving the friction coefficient and the plasmon frequency, the collective mode can illustrate certain properties of the so-called central peak. A two-component Vlasov-Fokker-Planck system exhibits three modes analogous to the Rayleigh scattering in a viscous fluid.