Whitham's averaged variational principle is applied in describing the dynamics of the excitation process of BGK modes driven by a chirped frequency wave [1]. A flat-top electron velocity distribution is assumed as a model allowing Lagrangian formulation within the water bag theory [2]. The corresponding Lagrangian, averaged over the fast phase variable yields variational equations for the slow fields in the problem. Numerical solutions of the full nonlinear set of the variational equations are in a good agreement with Vlassov-Poisson simulations.

[1] L. Friedland, P. Khain, and A.G. Shagalov, Phys. Rev. Lett. 96, 225001 (2006).

[2] P. Khain and L. Friedland, Phys. Plasmas 14, 082110 (2007).