Multi-channel energy conversions and heat flux transport associated with pressure-anisotropy driven instabilities for electrons in magnetosheath turbulence

Turbulence in the terrestrial magnetosheath drives rapid energy exchanges between electromagnetic fields and flows through strong intermittent compressions, shear layers, and velocity gradient structures. These concurrent and competing processes can generate temperature anisotropies and drive plasma instabilities. Yet the dynamical pathways linking velocity-gradient processes to anisotropy evolution in compressible collisionless plasmas remain poorly understood. We combine high cadence multi-point MMS measurements to quantify the pressure–strain interaction Π: ∇u (decomposed into compressible and incompressible parts), the non-ideal work J·E′, and the electron heat flux q (and ∇·q, where the signal-to-noise ratio is sufficiently large) for selected turbulent magnetosheath intervals. Physically motivated thresholds (percentile-based and background relative) identify episodes of enhanced Π: ∇u, J·E′, and heat flux activity. Then, the electron temperature anisotropy Te_⊥/Te, versus parallel electron plasma β_e(“Brazil”) plots are obtained from the time series under investigation, with added theoretical thresholds corresponding to whistler and firehose instabilities. In this parameter space, the trajectories of the plasma, associated with the various enhanced energy conversion and transport terms, are visualized. Case studies and ensemble statistics reveal that a dominance of different channels occurs in overlapping but non-identical regions: Π: ∇u peaks are associated with rapid anisotropy excursions and compressive structures, J·E′, with localized current and electromagnetic activity, and heat flux events with directed heat-transport toward whistler and firehose thresholds. This approach offers a practical pathway to quantify how turbulence and localized structures push plasma toward or beyond linear instability thresholds, with implications for modeling dissipation and wave generation in collisionless plasmas.