Ye, the jet engine analog is max apropos.
My take is that in addition to some relatively exotic particles, you might even radiate/produce miniature black holes, not dissimilar to what the LHC is believed to produce. Just like how the LHC works, it's a question of large energy densities, which an Alcub- ...which RAMA would bend spacetime with. It'd probably spawn vortices of space-time disturbances, too. Thing is that if lots of RAMAs are RAMAing around at variable distances, it just looks like noise in the LIGO data. At least for now. And that's a pretty nuts idea, looking for Alcubierre signatures in LIGO data, but someone is probably at least secretly doing it. Eventually, statistics could out the signals from background noise, it just might take another few decades or centuries, or it might take LISA. It's exciting to be alive in this new era of gravitational wave cosmology.
Also, remember, if you managed to go faster than light, you'd have to go back in time, at least relative to the frames of reference you started and/or stopped in. This presents some serious causality issues, and may be strictly forbidden, but exactly how is a curious thought experiment. Hollywood version: imagine warp driving to target solar system, but when you got there, it was only in the protoplaentary accretion disk stage. That'd kinda suck.