  Due to ion-electron collisions, it is impossible to derive any two-fluid
model for plasma as a direct hydrodynamic limit of the Vlasov-Poisson-Landau
system for ions and electrons. At the same time, electrons are much lighter
than their ion counterparts.
  In this work, we derive the massless electron limit of the
Vlasov-Poisson-Landau system. This is done via a re-scaling of the electron
velocity, leading to multiple velocity scales. Importantly, we demonstrate that
ion-electron collisions vanish in this limit, due to special structure of the
Landau collisions. We also show that this is invalid for the classical
Boltzmann kernel with hard sphere interaction. This mechanism serves as the
first step for the derivation of the two-fluid model for ions from a
two-species kinetic equation.
