  We investigate a physical divergence of the third order polarization
susceptibility representing a photoinduced current in biased crystalline
insulators. This current grows quadratically with illumination time in the
absence of momentum relaxation and saturation; we refer to it as the
\textit{jerk current}. Two contributions to the current are identified. The
first is a hydrodynamic acceleration of optically injected carriers by the
static electric field, and the second is the change in the carrier injection
rate in the presence of the static electric field. The jerk current can have a
component perpendicular to the static field, a feature not captured by standard
hydrodynamic descriptions of carriers in electric fields. We suggest an
experiment to detect the jerk current and some of its interesting features.
