Kinetic Theory and Large-N Limit for Wave-ParticleSelf-Consistent Interaction

Abstract

A system of N particles ξN = (x1, v1, ..., xN, vN) interacting self-consistently with M waves Z = (Aj e-iθj) is considered in d-dimensional space. Given initial data [Z(0), ξN(0)], it evolves according to Hamiltonian dynamics to [ZN(t), ξN(t)]. Assuming that the particles interact only with the waves and conversely, in a mean-field way, we obtain an upper bound for the largest Liapunov exponent which depends on the total energy per particle but not on N.