Paper detail

Transition to chaos in magnetized, weakly coupled plasmas

We report the results of numerical simulations for a model of a one component plasma (a system of N point electrons with mutual Coulomb interactions) in a uniform stationary magnetic field. We take N up to 512, with periodic boundary conditions, and macroscopic parameters corresponding to the weak coupling regime, with a coupling parameter Γ=1/64. We find that a transition from order to chaos takes place when the density is increased or the field decreased so that the ratio ω_p/ω_c between plasma and cyclotron frequencies becomes of order 1 (or equivalently the ratio r_L/λ_D between Larmor radius and Debye length becomes of order 1). The result is in agreement with the theoretical prediction obtained in [1], on the basis of an old estimate of Iglesias, Lebowitz and MacGowan [2] for the intensity of the electric field acting on one electron and due to all the other ones. A comparison can be made with the threshold obtained from kinetic theory arguments, which corresponds to the condition ν_{ee}/ω_c=1, where ν_{ee} is the electron collision frequency. The latter threshold has a completely different dependence on the physical parameters and, for Γ=1/64, gives a critical value of ω_p about 80 times larger.