  Using high resolution kinetic (VPPM-OMP 1.0) and fluid (BOUT++) solvers,
evolution of long-wavelength electron plasma wave (EPW) in the presence of
stationary periodic ion background non-uniformity is investigated. Mode
coupling dynamics between long-wavelength EPW mode of scale k and ion
inhomogeneity of scale $k_{0}$ is illustrated. Validity of well known Bessel
function $J_{n}(x)$ scaling in the cold plasma approximation (i.e., when phase
velocity $\omega /k >> v_{thermal}$) along-with the effect of ion inhomogeneity
amplitude (A) on temporal evolution of energy density in the long-wavelength
EPW mode is investigated. Effect of finite system sizes on the Bessel
$J_{n}(x)$ scaling is examined and scaling law for $\tau_{FM}$ i.e the time
required to attain first minimum of energy density of the corresponding
perturbed mode (also called phase mixing time for $k \sim 0$ modes) versus ion
inhomogeneity amplitude A obtained from both kinetic and fluid solutions for
each of the cases studied, along-with some major differences in $\tau_{FM}$
scaling for small system sizes is also reported.
