  The standard model of femtosecond filamentation is based on phenomenological
assumptions which suggest that the ionization-induced carriers can be treated
as free according to the Drude model, while the nonlinear response of the bound
carriers follows the all-optical Kerr effect. Here, we demonstrate that the
additional plasma generated at a multiphoton resonance dominates the saturation
of the nonlinear refractive index. Since resonances are not captured by the
standard model, we propose a modification of the latter in which ionization
enhancements can be accounted for by an ionization rate obtained from
non-Hermitian Floquet theory. In the adiabatic regime of long pulse envelopes,
this augmented standard model is in excellent agreement with direct quantum
mechanical simulations. Since our proposal maintains the structure of the
standard model, it can be easily incorporated into existing codes of filament
simulation.
