EXPLICIT ANALYTICAL SOLUTION OF THE NONLINEAR VLASOV-POISSON SYSTEM

In order to describe the time evolution of an inhomogeneous collisionl ess plasma, the nonlinear Vlasov equation is solved perturbatively, us ing the subdynamics approach and the diagrammatic techniques. The solu tion is given in terms of a double perturbation series: one with respe ct to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be perfo rmed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to non linearities is computed. For a choice of initial perturbation the firs t-order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with ab initio numerical simulations. Analytical computation gives a b etter insight into the problem, and it has the advantage to be simpler , and also accessible, in some range of parameters where it is difficu lt to find numerical solutions.