In this work we study the electron drift instability in Hall-effect thrusters (HETs) using a 2D electrostatic particle-in-cell (PIC) simulation. The simulation is configured with a Cartesian coordinate system modeling the radial-azimuthal (r − θ) plane for large radius thrusters. A magnetic field, B 0 , is aligned along the Oy axis (r direction), a constant applied electric field, E 0 , along the Oz axis (perpendicular to the simulation plane), and the E 0 × B 0 direction is along the Ox axis (θ direction). Although electron transport can be well described by electron-neutral collisions for low plasma densities, at high densities (similar to those in typical HETs), a strong instability is observed that enhances the electron cross-field mobility; even in the absence of electron-neutral collisions. The instability generates high frequency (of the order of MHz) and short wavelength (of the order of mm) fluctuations in both the azimuthal electric field and charged particle densities, and propagates in the E 0 × B 0 direction with a velocity close to the ion sound speed. The correlation between the electric field and density fluctuations (which leads to an enhanced electron-ion friction force) is investigated and shown to be directly responsible for the increased electron transport. Results are compared with a recent kinetic theory, showing good agreement with the instability properties and electron transport.