Landau damping in one dimensional periodic inhomogeneous collisionless plasmas

Landau damping in a collisionless plasma is a well-known example of wave particle interaction. In the past, this phenomenon was addressed for homogeneous equilibria in the linear and non-linear limit of the perturbation amplitude. However, in reality, equilibria are almost always inhomogeneous or non-uniform in space. Considering a one dimensional, collisionless, unmagnetized, electrostatic plasma with stationary ions and kinetic electrons in a periodic inhomogeneous exact equilibrium of scale k0−1 as the starting point, the fate of a small amplitude (linear) perturbation of scale k−1 is investigated using a Vlasov–Poisson solver. Three different spatial regimes, namely, k0 > k, k0 ∼ k, and k0 < k, are addressed. In the k0 > k regime, long wavelength perturbation k is found to generate (k ± Nk0) modes (where N is an integer), which allows damping of long wavelength perturbation in an inhomogeneous plasma and formation of phase-space vortices at phase velocities vϕ = ω/(k ± Nk0). Perhaps for the first time, novel phenomena such as “inhomogeneity induced Landau damping arrest” and “inhomogeneity induced plasma echo” are observed in k0 ∼ k and k0 < k regimes, respectively. New scaling laws as a function of inhomogeneity amplitude are also reported.