Inward microjets are commonly observed in collapsing cavities, but her
e we show that jets with exceptionally high velocities and acceleratio
ns occur in certain critical flows dividing jet formation from bubble
pinch-off. An example of the phenomenon occurs in the family of hows w
hich evolve from a certain class of initial conditions: the initial fl
ow field is that due to a moving point sink within the cavity. A numer
ical study of the critical flow shows that in the neighbourhood of mic
rojet formation the flow is self-similar. The local accelerations, vel
ocities and distances scale as t(beta-2), t(beta-1) and t(beta) respec
tively, where beta = 0.575. The velocity potential is approximately a
spherical harmonic of degree 1/4.