[en] Recent observations on the growth of beam density fluctuations have demonstrated the existence of longitudinal instabilities of individual bunches at very high frequencies. It was suggested that a quantitative description could be obtained by treating the different sectors as if each was a distinct coasting beam and applying the usual coasting beam theory, while substituting local values of current and energy spread for the separate segments. This ad hoc procedure can be justified if the underlying source of the bunched induced instability was a combination of low Q, high frequency resonators. The underlying agreement is that these conditions imply such a fast wakefield that communication between bunch sectors is weakened, thereby allowing them to behave independently of each other. The fast growth rate implied by the high frequency to unstable oscillations allows the instability to evolve to significant proportions within a small part of a synchrotron cycle. From this it can be inferred that a single bunch could develop an unstable condition in spite of the damping character for unstable waves propagating along the top of a bunch. The dependence of the threshold impedance and growth rate on the local characteristics of a bunch was qualitatively confirmed by numerical simulation of a particle bunch interacting with high frequency resonators of low quality factor (i.e., low Q). However, when the quality factor of the resonant objects was changed, while keeping the frequency of the resonators fixed, a very strong impact on the results was observed, thus indicating that the simple picture of local bunch segments behaving independently is incomplete. The main results are presented of a theory for the fast bunch blow-up. The predictions of this theory are consistent with both computational and experimental observations