  Ion-gyroradius-scale microinstabilities typically have a frequency comparable
to the ion transit frequency. Due to the small electron-to-ion mass ratio and
the large electron transit frequency, it is conventionally assumed that passing
electrons respond adiabatically in ion-gyroradius-scale modes. However, in
gyrokinetic simulations of ion-gyroradius-scale modes in axisymmetric toroidal
magnetic fields, the nonadiabatic response of passing electrons can drive the
mode, and generate fluctuations with narrow radial layers, which may have
consequences for turbulent transport in a variety of circumstances. In flux
tube simulations, in the ballooning representation, these instabilities reveal
themselves as modes with extended tails. The small electron-to-ion mass ratio
limit of linear gyrokinetics for electrostatic instabilities is presented, in
axisymmetric toroidal magnetic geometry, including the nonadiabatic response of
passing electrons and associated narrow radial layers. This theory reveals the
existence of ion-gyroradius-scale modes driven solely by the nonadiabatic
passing electron response, and recovers the usual ion-gyroradius-scale modes
driven by the response of ions and trapped electrons, where the nonadiabatic
response of passing electrons is small. The collisionless and collisional
limits of the theory are considered, demonstrating parallels in structure and
physical processes to neoclassical transport theory. By examining initial-value
simulations of fastest-growing eigenmodes, the predictions for mass-ratio
scaling are tested and verified numerically for a range of collision
frequencies. Insights from the small electron-to-ion mass ratio theory may lead
to a computationally efficient treatment of extended modes.
