The role of passing electrons in long-wavelength electrostatic instabilities in the small electron-to-ion mass ratio limit

Microinstabilities with binormal wavenumbers at scales of the ion gyroradius evolve with frequencies comparable to the ion transit frequency. Passing electrons are often assumed to play a negligible role in long-wavelength modes: it is argued that the rapid free streaming of electrons along magnetic field lines leads to an adiabatic passing electron response in the limit of small electron-to-ion mass ratio. However, gyrokinetic simulations of electrostatic^1,2  and electromagnetic³ (micro-tearing) modes reveal that the passing electron response can drive instability. The small electron-to-ion mass ratio limit of electrostatic gyrokinetics is obtained, revealing a novel branch of electrostatic modes driven purely by the passing electron response in narrow layers near rational flux surfaces. The width of the layer is set by electron free streaming, finite Larmor radius and finite orbit width physics in the collisionless regime, and by a balance of perpendicular and parallel diffusion in the collisional regime. Scaling predictions are compared to numerical simulations with favourable results for the theory. Finally, the extension of the theory to the electromagnetic case is considered, with possible relevance for the description of micro-tearing modes.

¹K Hallatschek and W Dorland, Phys. Rev. Lett 95:055002, 2005

²J Dominski et al., Phys. Plasmas 22:062303, 2015

³D J Applegate et al., Plasma Phys. Control. Fusion 49:1113--1128, 2007