  In this article, we study a collisionless kinetic model for plasmas in the
neighborhood of a cylindrical metallic Langmuir probe. This model consists in a
bi-species Vlasov-Poisson equation in a domain contained between two cylinders
with prescribed boundary conditions. The interior cylinder models the probe
while the exterior cylinder models the interaction with the plasma core. We
prove the existence of a weak-strong solution for this model in the sense that
we get a weak solution for the 2 Vlasov equations and a strong solution for the
Poisson equation. The first parts of the article are devoted to explain the
model and proceed to a detailed study of the Vlasov equations. This study leads
to a reformulation of the Poisson equation as a 1D non-linear and non-local
equation and we prove it admits a strong solution using an iterative
fixed-point procedure.
