  The study of uncertainty propagation is of fundamental importance in plasma
physics simulations. To this end, in the present work we propose a novel
stochastic Galerkin (sG) particle {method} for collisional kinetic models of
plasmas under the effect of uncertainties. This class of methods is based on a
generalized polynomial chaos (gPC) expansion of the particles' position and
velocity. In details, we introduce a stochastic particle approximation for the
Vlasov-Poisson system with a BGK term describing plasma collisions. A careful
reformulation of such dynamics is needed to perform the sG projection and to
obtain the corresponding system for the gPC coefficients. We show that the sG
particle method preserves the main physical properties of the problem, such as
conservations and positivity of the solution, while achieving spectral accuracy
for smooth solutions in the random space. Furthermore, in the fluid limit the
sG particle solver is designed to possess the asymptotic-preserving property
necessary to obtain a sG particle scheme for the limiting Euler-Poisson system,
thus avoiding the loss of hyperbolicity typical of conventional sG methods
based on finite differences or finite volumes. We tested the schemes
considering the classical Landau damping problem in the presence of both small
and large initial uncertain perturbations, the two stream instability and the
Sod shock tube problems under uncertainties. The results show that the proposed
method is able to capture the correct behavior of the system in all test cases,
even when the relaxation time scale is very small.
