Numerical Study of Turbulence in N-Body Hamiltonian Systems with Long Range Force: I. Relaxation

Abstract

We study the dynamics of a system of N identical classical particles on the circle of length 2π. The inter-particle force acts like a reduction of the Coulomb interaction to the first s Fourier components on the circle. Initial conditions generating turbulent structures are considered. The lifetime of those structures is shown to increase linearly with the number of particles N. Using a pulsating-separatrix argument we note that the evolution of the turbulent structures is controlled by the motion of the fraction of particles evolving in the (x, p)-space domain swept by the self-consistent potential’s separatrix. The relaxation time of the initial condition to Maxwellian distribution of velocities is investigated. It is not strongly sensitive to the presence of turbulent structures and it is independent of the small spatial scales.