  In this paper, we study the quasineutral limit (in other words the limit when
the Debye length tends to zero) of Vlasov-Poisson like equations describing the
behaviour of ions in a plasma. We consider massless electrons, with a charge
density following a Maxwell-Boltzmann law. For cold ions, using the relative
entropy method, we derive the classical Isothermal Euler or the (inviscid)
Shallow Water systems from fluid mechanics. In a second time, we study the
combined quasineutral and strong magnetic field regime for such plasmas.
