Discoveries in plasmas while teaching simulation

Once PC's became ubiquitous, we have been using them for teaching plasma simulation, hands-on by instructors and by students. The transfer of skills from instructor to class has been very rapid (most desirable). However, occasionally some unanticipated results are observed with plausible explanations expected from the instructor (scary). Our examples are all one-dimensional. First, we show the famous two-stream instability in a periodic model, starting either cold or warm, which does not (quite) Maxwellianize; why not? Second, we show Landau damping also in a periodic model, with what appears to be small (hence linear) excitation, but observe trapping in the wave frame; going to very small excitation the trapping diminishes and the damping rate approaches that from Landau linear theory. Lastly, we show a warm plasma bounded by two grounded metal planar walls, uniform in density at t=0, bounded, one-dimensional. For t>0 we observe spontaneous plasma frequency oscillations in the midplane, sheath formation at ion sound speed at both walls, trapping of electrons, and acceleration of the ions to the walls; however, we also observe an oscillatory axial current, and ‘staircasing’ of the number of electrons in time. Both can come only from some degree of asymmetry in the system. The frequency of the current is the series resonance between the sheath capacitance (almost no electrons, so vacuum) and the bulk plasma ‘inductance’ (as ωseries⪡ωp).