Cross-field electron transport in partially magnetised plasmas arises from collective, nonlinear instability dynamics that remain only partially understood despite their importance to a wide range of E × B plasma devices. In systems such as Hall thrusters, azimuthal instabilities strongly affect electron confinement and spectral energy distribution, motivating efforts to examine how external modulation may influence these effects. Here, one-and two-dimensional particle-in-cell simulations are employed to investigate how an axially applied oscillatory electric field modifies the instability spectra and the associated cross-field electron transport. The simulations adopt local slab idealisations of an E × B discharge designed to isolate modulation–instability coupling mechanisms and the conclusions should be interpreted within this controlled modelling framework. The simulations show that the plasma response depends sensitively on modulation frequency and amplitude. Notably, modulation near 40 MHz diminishes the amplitude of the electron cyclotron drift instability and reduces axial electron transport by up to 30 %, while modulation near the electron cyclotron frequency leads to spectral broadening and enhanced transport. Bicoherence analysis of the azimuthal electric field fluctuations indicates nonlinear coupling among instability modes, suggesting that modulation reshapes energy pathways, thereby explaining the observed spectral variations. We further show that modulation modifies the phase alignment between azimuthal-electric-field and electron-density fluctuations, in turn directly affecting the observed suppression or amplification of electron transport across modulation regimes. The results provide quantitative evidence of how external modulation can alter instability characteristics in E × B plasmas and point to strategies for controlling electron transport in cross-field plasma technologies, such as Hall thrusters and magnetrons.
Reza et al. (2026) studied this question.