  When dilute charged particles are confined in a bounded domain, boundary
effects are crucial in the global dynamics. We construct a unique
global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex
domains with the diffuse boundary condition. The construction is based on an
$L^{2}$-$L^{\infty}$ framework with a novel \textit{nonlinear-normed energy
estimate} of a distribution function in weighted $W^{1,p}$-spaces and a
$C^{2,\delta}$-estimate of the self-consistent electric potential. Moreover we
prove an exponential convergence of the distribution function toward the global
Maxwellian.
