  This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$
for the Vlasov-Poisson system with massless electrons (VPME). We consider
solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a
homogeneous equilibrium satisfying a Penrose stability condition. We show that
for such solutions, the corresponding density and force field decay
exponentially fast as time goes to infinity. This work extends the results for
Vlasov-Poisson on the torus to the case of ions and, more generally, to
arbitrary analytic nonlinear couplings.
