Autoresonant BGK modes

Resonant wave interactions play a major role in plasmas and other nonlinear media. The interacting waves may exhibit autoresonance, i.e. a continuous nonlinear phase-locking despite variation of system parameters [1]. We present a kinetic wave autoresonance paradigm, where a driven BGK mode is excited by slow variation of the driving wave frequency. We assume a flat- top initial electron distribution, drive the system by a slowly varying ponderomotive wave. Initially, the drive's phase velocity is outside the velocity distribution, so the electrons do not experience Cherenkov resonance. Later, as the driving frequency decreases, a stable phase-space hole is formed and, under certain conditions, remains phase-locked with the drive [2,3]. The electrostatic field associated with this structure comprises the autoresonant BGK mode. We study the problem analytically and numerically within the Vlasov-Poisson system and use the Whitham's averaged variational principle [4] to describe the adiabatic evolution of the BGK mode. [1] L. Friedland, Scholarpedia 4, 5473 (2009). [2] L. Friedland, P. Khain, and A.G. Shagalov, Phys. Rev. Lett. 96, 225001 (2006). [3] P. Khain and L. Friedland, Phys. Plasmas 14, 082110 (2007). [4] G.B. Whitham, Linear and Nonlinear Waves, Willey, New York, 1974.