ExB guiding-centre motion in three electrostatic waves: statistics of separatrix crossings

E x B guiding-centre (GC) motion in a special configuration of three low-frequency electrostatic waves can be considered as a paradigmatic Hamiltonian system for studying adiabatic motion and separatrix crossings. A peculiarity of this system is that a single initial condition gives rise to two stroboscopic phase-space trajectories. According to the classical Hamiltonian theory, the proportion of points on the stroboscopic trajectories is a function of the time evolution of the surfaces enclosed by the separatrices in the phase space. This behaviour is qualitatively observed in test-particle numerical experiments. The ability of numerical integration methods like the 'classical' fourth-order Runge-Kutta integration scheme or a third-order symplectic integrator to reproduce the statistics is analysed.