The dynamic response of a Bell-and-Bloom magnetometer to a parallel
(to the bias field) time-dependent field is modelled beyond the
commonly assumed quasi-static regime. The results unveil features
that are related to the parametric nature of the considered system.
It is shown that a for low-amplitude time-dependent field different
operating conditions are possible and that, beside the
commonly reported low-pass-filter behaviour, a band-pass response
emerges. Moreover, we numerically show that for larger field
amplitude the system, due to its parametric nature, has a kind of
``non-linear'' response.