We consider the nonlinear Vlasov-Poisson-Fokker-Planck system with an external confining potential. It is an important kinetic model in plasma physics and describes the evolution of a cloud of charged particles. In this model, the particles influence each other by means of Coulomb interactions. The collision effects of particles and their interaction with the environment are presented by a Fokker-Planck operator. We establish the existence, uniqueness of a global solution and a global equilibrium. We show that the solution converges the global equilibrium exponentially. Our results hold for a wide class of external potentials and the estimates on the rate of convergence are explicit and constructive. Our proof relies on the estimates on the semigroup of the linearized system around the equilibrium and fixed point arguments.

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