Critical Phenomena Associated with the Formation of Multiple Electron-Acoustic BGK-Like Waves

The nonlinear evolution of electrostatic plasmas composed of two electron populations is studied in a regime where electron-acoustic waves (EAWs) are supported. High-resolution Vlasov-Poisson simulations show that the plasma can evolve toward a time-asymptotic state characterized by the formation of multiple BGK-type vortices in phase-space. These structures emerge through nonlinear wave-wave interactions and cascade processes that fill phase-space with coherent structures. Additionally, a critical phenomenon is identified that marks the transition between cases where multiple BGK-like vortices can or cannot be formed. This transition is described by a power-law scaling involving the characteristic time tBGK, which signals the onset of BGK-like vortex formation in the asymptotic phase-space dynamics. From this scaling, a critical value is determined corresponding to a critical density nc^ of the colder electron population, which separates plasma asymptotic states where the phase-space is filled by small vortices, from states that do not form them.