WEAK TURBULENCE AND STRUCTURE EVOLUTION IN N-BODY HAMILTONIAN-SYSTEMSWITH LONG-RANGE FORCE

The dynamics of a family of one-dimensional spatially periodic systems of N classical particles interacting by a repulsive pair force is inv estigated. This force is the long-range part of the one-dimensional Co ulomb interaction; the family includes the mean-field Hamiltonian rota tor model. Initial conditions generating turbulent structures are cons idered. These structures are density holes in (x,nu) space that produc e a non-Gaussian probability distribution of fluctuations of the parti cle distribution function f(x,nu,t). These density holes appear in a v elocity domain where f(x,nu) has large derivative partial derivative(n u)f as predicted by the kinetic theory of clumps in plasmas. Their evo lution is shown to be controlled by the motion of the particles in the (x,nu) space domain swept by the separatrix associated with the longe st-range coupling field components, which implies that their lifetime is proportional to the number N of particles. The relaxation time of t he velocity distribution function of tagged particles in the system (f or various initial conditions) is also shown to be quite insensitive t o the presence of turbulent structures and to spatial scales smaller t han the Debye length.