Phase space holes in non-periodic plasmas

We study the dynamics of phase space holes in a non-collisional plasma by numerical integration of the one-dimensional Vlasov equation. The plasma is bounded and connected to vacuum by two interfaces, which gives rise to non-periodic boundary conditions. By choosing different initial conditions, we consider four different situations: development of a sinusoidal wave, two-stream instability, development of an ab initio Bernstein Greene Kruskal state and the expansion of a plasma into vacuum. For the latter situation ions move with a realistic mass of 1837 electron masses. The most prominent results of our investigation are: (a) a clockwise revolution of holes in phase space; (b) the appearance of stable oscillations of the total electron momentum, which, despite their striking linearity, cannot be related to electrostatic plasma oscillations. To the best of our knowledge none of these phenomena have been reported in kinetic simulations before: indeed we prove that the non-periodicity of the boundary conditions is an essential requirement for the sustainment of both hole revolution and momentum oscillations.