  Nonlinear dynamics of the electron-cyclotron instability driven by the
electron $\mathbf{E\times B}$ current in crossed electric and magnetic field is
studied. In nonlinear regime the instability proceeds by developing a large
amplitude coherent wave driven by the energy input from the fundamental
cyclotron resonance. Further evolution shows the formation of the long
wavelength envelope akin to the modulational instability. Simultaneously, the
ion density shows the development of high-k content responsible for wave
focusing and sharp peaks on the periodic cnoidal wave structure. It is shown
that the anomalous electron transport (along the direction of the applied
electric field) is dominated by the long wavelength part of the turbulent
spectrum.
