Extreme driven ion acoustic waves

The excitation of large amplitude, strongly nonlinear ion acoustic waves from trivial equilibrium by a chirped frequency drive is discussed. Under certain conditions, after passage through the linear resonance in this system, the nonlinearity and the variation of parameters work in tandem to preserve the phase-locking with the driving wave via excursion of the excited ion acoustic wave in its parameter space, yielding controlled growth of the wave amplitude. We study these autoresonant waves via a fully nonlinear warm fluid model and predict the formation of sharply peaked (extreme) ion acoustic excitations with local ion density significantly exceeding the unperturbed plasma density. The driven wave amplitude is bound by the kinetic wave-breaking, as the local maximum fluid velocity of the wave approaches the phase velocity of the drive. The Vlasov-Poisson simulations are used to confirm the results of the fluid model, and Whitham's averaged variational principle is applied for analyzing the evolution of autoresonant ion acoustic waves.