  Experimental and theoretical studies of laser-induced breakdown in
dielectrics provide conflicting conclusions about the possibility to trigger
ionization avalanche on the sub-picosecond time scale and the relative
importance of carrier-impact ionization over field ionization. On the one hand,
current models based on single ionization-rate equations do not account for the
gradual heating of the charge carriers which, for short laser pulses, might not
be sufficient to start an avalanche. On the other hand, models based on
multiple rate equations that track the carriers kinetics rely on several free
parameters, which limits the physical insight that we can gain from them. In
this paper, we develop a model that overcomes these issues by tracking both the
plasma density and carriers' mean kinetic energy as a function of time, forming
a set of delayed rate equations that we use to match the laser-induced damage
threshold of several dielectric materials. In particular, we show that this
simplified model reproduces the predictions from the multiple rate equations,
with a limited number of free parameters determined unambiguously by fitting
experimental data. A side benefit of the delayed rate equations model is its
computational efficiency, opening the possibility for large-scale,
three-dimensional modelling of laser-induced breakdown of transparent media.
