  While electron kinetic effects are well known to be of fundamental importance
in several situations, the electron mean-flow inertia is often neglected when
lengthscales below the electron skin depth become irrelevant. This has led to
the formulation of different reduced models, where electron inertia terms are
discarded while retaining some or all kinetic effects. Upon considering general
full-orbit particle trajectories, this paper compares the dispersion relations
emerging from such models in the case of the Weibel instability. As a result,
the question of how lengthscales below the electron skin depth can be neglected
in a kinetic treatment emerges as an unsolved problem, since all current
theories suffer from drawbacks of different nature. Alternatively, we discuss
fully kinetic theories that remove all these drawbacks by restricting to
frequencies well below the plasma frequency of both ions and electrons. By
giving up on the lengthscale restrictions appearing in previous works, these
models are obtained by assuming quasi-neutrality in the full Maxwell-Vlasov
system.
