  We introduce a simplified model of the electron-beam/plasma system to model
the electrical breakdown caused by the inductive electric field created by a
rapidly rising electron beam current. The rigid-beam model is a reduction to
the problem geometry to cylindrical coordinated and simplifications to
Maxwell's equations that are driven by a prescribed electron beam current
density. The model is very convenient for comparing various reductions of the
plasma dynamics and air chemistry equation while maintaining a good
approximation to the overall magnitude of the beam-created electric field. The
usefulness of this model is demonstrated by comparing results for two different
fluid reductions of the plasma dynamics: one where the collision rates are
computed from the local reduced electric field (E/p) and another where the
collision rates are determined from the mean energy per particle. We find that
the two methods give similar results at higher pressures where the energy
relation rate is large but differs significantly at lower pressures where the
characteristic inelastic energy loss time scale is comparable to or greater
than the rise time of the electron beam current.
