  Recently resonant inelastic x-ray scattering experiments reported fine
details of the charge excitations around the in-plane momentum ${\bf
q}_{\parallel}=(0,0)$ for various doping rates in electron-doped cuprates ${\rm
La_{2-x}Ce_xCuO_4}$. We find that those new experimental data are well captured
by acoustic-like plasmon excitations in a microscopic study of the layered
$t$-$J$ model with the long-range Coulomb interaction. The acoustic-like
plasmon is not a usual plasmon typical to the two-dimensional system, but has a
small gap proportional to the interlayer hopping $t_z$.
