Formation of multiple BGK-like structures in the time-asymptotic state of collisionless Vlasov-Poisson plasmas

The time-asymptotic state of a finite-amplitude perturbation in a collisionless and Maxwellian plasma is typically represented as a steady state of two nonlinearly superposed, counterpropagating Bernstein-GreeneKruskal (BGK) modes. Using high-resolution Vlasov-Poisson simulations, we show that the plasma evolves self-consistently into a time-asymptotic state of multiple vortexlike structures that gradually fill the phase space and reduce filamentation. This occurs without the need for external forcing or the presence of an energetic plasma population. This finding suggests that the time-asymptotic regime of the plasma is rather akin to a nonlinear superposition of multiple BGK-like modes associated with nearly constant phase-speed waves. The electric field and the space-averaged particle distribution function exhibit a power-law broad spectrum, which is consistent with an energy cascade towards smaller scales in both position and velocity spaces.