Electron-Mediated Transport in Space, Astrophysical, and Laboratory Plasmas

Electron-mediated transport is fundamental to the thermal and dynamical evolution of plasmas across a vast range of physical environments, from the solar wind and solar atmosphere to astrophysical systems such as galaxy clusters and accretion flows, to laboratory and fusion plasmas. This article reviews the current state of understanding of electron transport, drawing together observations, simulations, and theory to contextualise key challenges and open questions. We characterise plasma environments using the Knudsen number and electron beta, and highlight that some systems fall in an intermediate regime between the collisional and collisionless limits. In the collisional limit, transport is well described by the Chapman-Enskog-Braginskii framework, yielding anisotropic heat fluxes and momentum transfer rates governed by the ratio of the electron mean free path to the electron gyroradius. In the collisionless limit, Landau-fluid closures and quasilinear wave-particle interaction theory describe heat flux regulation through resonant instabilities, particularly whistler-mode waves, which suppress parallel electron heat flux below Spitzer-Härm predictions in high-beta plasmas. We review approaches to bridging collisional and collisionless regimes, including velocity-space-dependent collision operators, moment-based interpolating closures, and data-driven methods trained on fully kinetic simulations. Comparison with solar wind observations from the Parker Solar Probe and Wind missions reveals that the current attempts at bridging collisional and collisionless closures account for only limited regions of parameter space, underscoring the need for improved models. Four central challenges are identified for future transport theory: capturing the velocity-space dependence of collisional and collisionless scattering, describing spatial transitions between transport regimes, incorporating turbulence, and developing computationally tractable effective collision operators for large-scale simulations.