When transparent solids are irradiated with laser intensities above a certain threshold, strong absorption of laser
energy occurs. The increasing absorptivity is caused by the formation of a free electron gas in the conduction band
of the dielectric. The transient free electron density is a fundamental parameter for numerous theoretical and
experimental investigations and applications. We study the mechanisms of free-electron generation in the frame of
different approaches. A full kinetic treatment reveals a non-stationary behavior, which is neglected when applying
the standard rate equation. A new model, the multiple rate equation, keeps track of the non-stationarity of the
electron energy distribution while maintaining the conceptual and analytic simplicity of standard rate equation.
We present the analytical asymptotic solution of the multiple rate equation which yields an expression for the
avalanche coefficient and provides information about the validity of the standard rate equation. The numerical
calculation shows the transient distribution of free electrons and the effect of the non-stationarity of its shape on
the impact ionization probability. We study the role of different ionization processes and its dependence on laser
pulse duration. The fraction of impact-ionized electrons is found to depend only on the product of pulse duration
and intensity, i.e. on the fluence. A remarkable effect of the shape of the laserpulse on the total free electron
density and the conditions for dielectric breakdown is found.