A water bag theory of autoresonant Bernstein-Greene-Kruskal modes

The adiabatic water bag theory describing formation and passage through phase-space of driven, continuously phase-locked (autoresonant) coherent structures in plasmas [L. Friedland et al., Phys. Rev. Lett. 96, 225001 (2006)] and of the associated Bernstein-Greene-Kruskal (BGK) modes is developed. The phase-locking is achieved by using a chirped frequency ponderomotive drive, passing through kinetic Čerenkov-type resonances. The theory uses the adiabatic invariants (conserved actions of limiting trajectories) in the problem and, for a flat-top initial distribution of the electrons, reduces the calculation of the self-field of the driven BGK mode to solution of a few algebraic equations. The adiabatic multiwater bag extension of the theory for applications to autoresonant BGK structures with more general initial distributions is suggested. The results of the theories are in very good agreement with numerical simulations.