  We study existence and uniqueness of the solution to the Vlasov-Poisson
system describing a plasma constituted by different species evolving in
$\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species
can have both positive or negative charge. It is assumed that initially the
particles are distributed according to a spatial density with a power-law decay
in space, allowing for unbounded mass, and an exponential decay in velocities
given by a Maxwell-Boltzmann law, extending a result obtained by the same
authors, which was restricted to finite total mass.
