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The large electron drift (relative to the ions) in the azimuthal direction of Hall-effect thrusters is well known to excite a strong instability. In a recent paper (Lafleur et al 2016 Phys. Plasmas23 053503) we demonstrated that this instability leads to an enhanced electron–ion friction force that increases the electron cross-field mobility to levels similar to those seen experimentally. Here we extend this work by considering in detail the onset criteria for the formation of this instability (both in xenon, and other propellants of interest), and identify a number of important characteristics that it displays within Hall-effect thrusters (HETs): including the appearance of an additional non-dimensionalized scaling parameter (the instability growth-to-convection ratio), which controls the instability evolution and amplitude. We also investigate the effect that the instability has on electron and ion heating in HETs, and show that it leads to an ion rotation in the azimuthal direction that is in agreement with that seen experimentally. [ABSTRACT FROM AUTHOR]