The collisionless cross-field electron transport in an \(E\times B\) plasma configuration, representative of a Hall thruster, is studied using bispectral analysis on the data of a fully-kinetic simulation. The nonlinear, in-phase interaction of the oscillations of the azimuthal electric field and the electron density, both tied to the fundamental electron cyclotron drift instability (ECDI) mode, is found to be the main driver of electron transport. Higher-wavenumber ECDI modes do not drive anomalous transport directly; however, they are nonlinearly coupled with each other and with the fundamental ECDI mode. In addition, there is a smaller contribution from a lower-wavenumber mode, not predicted by linear ECDI theory. A reduced model obtained by sparse regression of the data suggests the existence of an inverse energy cascade from the higher ECDI modes to the fundamental one, which would mean that these modes do contribute to transport, albeit indirectly.
