Density inhomogeneities are ubiquitous in space and astrophysical plasmas, in particular at contact boundaries between different media. They often correspond to regions that exhibits strong dynamics on a wide range of spatial and temporal scales. Indeed, density inhomogeneities are a source of free energy that can drive various instabilities such as, for instance, the lower-hybrid-drift instability which in turn transfers energy to the particles through wave-particle interactions and eventually heat the plasma. We aim at quantifying the efficiency of the lower-hybrid-drift instability to accelerate and/or heat electrons parallel to the ambient magnetic field. We combine two complementary methods: full-kinetic and quasilinear models. We report self-consistent evidence of electron acceleration driven by the development of the lower-hybrid-drift instability using 3D-3V full-kinetic numerical simulations. The efficiency of the observed acceleration cannot be explained by standard quasilinear theory. For this reason, we develop an extended quasilinear model able to quantitatively predict the interaction between lower-hybrid fluctuations and electrons on long time scales, now in agreement with full-kinetic simulations results. Finally, we apply this new, extended quasilinear model to a specific inhomogeneous space plasma boundary: the magnetopause of Mercury, and we discuss our quantitative predictions of electron acceleration in support to future BepiColombo observations.
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