Interplay between Macro- and Microscales in Ion-Acoustic Phase-Space Turbulence

Many plasmas are characterized by an interplay of physics occurring on both macro- and microscales. In weakly collisional plasmas, this interplay manifests not only in real space but also in velocity space. For example, macroscale motions can cause deformations in velocity space, which then drive unstable fluctuations at microscales, which in turn interact with the plasma particles to feed back on the macroscales. Here we study this multi-scale phase-space coupling in a relatively simple system: a one-dimensional, electrostatic, quasi-neutral plasma in which ion-acoustic fluctuations are driven at large scales. The electrons exhibit a Boltzmann response while the perturbed ion distribution function is phase-mixed, developing bumps and beams in velocity space that ultimately go unstable at small scales. We develop a theory explaining the observed electric-field power spectrum, and study how irreversibility is achieved by considering the conservation and cascade of various Casimir invariants.