Electrostatic trapping as a key to the dynamics of plasmas, fluids and other collective systems

This review article focusses on the phenomenon of collective particle trapping in dilute plasmas and related fluid-like systems. A coherent electrostatic wave or fluctuation, being excited by some mechanism in a plasma, is able to trap collectively charged particles in its potential trough(s) with the ultimate feedback of stabilizing and manipulating the original cause of growth. This phenomenon is well-known from particle simulations of a current-driven two-stream instability and its subsequent quenching by particle trapping. But also the nonlinear Landau damping process resulting in a BGK-like (Bernstein, Green, Kruskal) trapped particle mode sets an example. However, as shown in this report, already a slightly driven plasma has many possibilities of generating trapped particle modes-the mentioned cases representing only two examples-through which it generally becomes nonlinearly unstable. A direct consequence of this feedback of particle trapping is that the macroscopic (dielectric) properties of such a structured plasma may have changed fundamentally such that the relationship to what is known from linear wave theory is lost. We, hence, have to deal with a nonlinear kinetic description which, in case of a collisionless, electrostatic plasma, is the Vlasov-Poisson description. The present report is devoted to a large extent to a ID Vlasov-Poisson system but also consequences for other physical systems will be derived and mentioned.