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Nonlinear dynamics of the electron-cyclotron instability driven by theelectron $\mathbf{E\times B}$ current in crossed electric and magnetic field isstudied. In nonlinear regime the instability proceeds by developing a largeamplitude coherent wave driven by the energy input from the fundamentalcyclotron resonance. Further evolution shows the formation of the longwavelength envelope akin to the modulational instability. Simultaneously, theion density shows the development of high-k content responsible for wavefocusing and sharp peaks on the periodic cnoidal wave structure. It is shownthat the anomalous electron transport (along the direction of the appliedelectric field) is dominated by the long wavelength part of the turbulentspectrum.

Nonlinear structures and anomalous transport in partially magnetized $\mathbf{E\times B}$ plasmas