  We formulate a multi-physics model to describe the nonlinear propagation of a
femtosecond, near-infrared, tightly focused laser pulse in a transparent
dielectric. The application of our model to the case of bulk sapphire shows
that even under extreme excitation conditions, ionization is universally
clamped at about one tenth of the electron density in the upper valence band.
The earlier estimate of ~10 TPa pressure that could be attainable through the
internal excitation of transparent dielectrics by tightly focused ultrafast
laser beams is shown to be off by two orders of magnitude.
