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A system of N particles eN=(x1,v1,...,xN,vN) interacting self-consistentlywith M waves Zn=An*exp(iTn) is considered. Hamiltonian dynamics transportsinitial data (eN(0),Zn(0)) to (eN(t),Zn(t)). In the limit of an infinite numberof particles, a Vlasov-like kinetic equation is generated for the distributionfunction f(x,v,t), coupled to envelope equations for the M waves. Any initialdata (f(0),Z(0)) with finite energy is transported to a unique (f(t),Z(t)).Moreover, for any time T>0, given a sequence of initial data with N particlesdistributed so that the particle distribution fN(0)-->f(O) weakly and withZn(0)-->Z(O) as N tends to infinity, the states generated by the Hamiltoniandynamics at all time 0<t<T are such that (eN(t),Zn(t)) converges weakly to(f(t),Z(t)). Comments: Kinetic theory, Plasma physics.Comment: 18 pages, LaTe

Kinetic Limit of N-Body Description of Wave–Particle Self-Consistent Interaction