Recent Cerenkov observations of the two BL Lac objects PKS 2155-304 and Mkn 501 revealed TeV flux variability by a factor ~2 in just 3-5 minutes. Even accounting for the effects of relativistic beaming, such short timescales are challenging simple and conventional emitting models, and call for alternative ideas. We explore the possibility that extremely fast variable emission might be produced by particles streaming at ultra-relativistic speeds along magnetic field lines and inverse Compton scattering any radiation field already present. This would produce extremely collimated beams of TeV photons. While the probability for the line of sight to be within such a narrow cone of emission would be negligibly small, one would expect that the process is not confined to a single site, but can take place in many very localised regions, along almost straight magnetic lines. A possible astrophysical setting realising these conditions is magneto-centrifugal acceleration of beams of particles. In this scenario, the variability timescale would not be related to the physical dimension of the emitting volume, but might be determined by either the typical duration of the process responsible for the production of these high energy particle beams or by the coherence length of the magnetic field. It is predicted that even faster TeV variability - with no X-ray counterpart - should be observed by the foreseen more sensitive Cerenkov telescopes.
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