  The electrons and phonons in metal films after ultra-short pulse laser
heating are in highly non-equilibrium states not only between the electron
sub-system and the phonon sub-system but also within the electron sub-system.
An electrohydrodynamics model consisting of the balance equations of electron
density, energy density of electrons, and energy density of phonons is derived
from the coupled non-equilibrium electron and phonon Boltzmann transport
equations to study the nonlinear transport phenomena, such as the electron
density fluctuation and the transient electrical current in metal films, after
ultra-short pulse laser heating. The time-dependent temperature distributions
is calculated by the coupled electron and phonon Boltzmann transport equations,
the electrohydrodynamics model derived in this work, and the two-temperature
model for different laser pulse durations, film thicknesses, and laser
fluences. We find that the two-temperature model overestimates the electron
temperature at the frontsurface of the film and underestimates the damage
threshold when the nonlinear thermal transport of electrons is important. The
electrohydrodynamics model proposedin this work could be a more accurate
prediction tool to study the non-equilibrium electron phonon transport process
than the two-temperature model and it is much easier to be solved than the
coupled electron and phonon Boltzmann transport equations.
