  The multi-wavelength anomalous diffraction (MAD) method is used to determine
phase information in x-ray crystallography by employing dispersion corrections
from heavy atoms on coherent x-ray scattering. X-ray free-electron lasers
(FELs) show promise for revealing the structure of single molecules or
nanocrystals within femtoseconds, but the phase problem remains largely
unsolved. Due to the ultrabrightness of x-ray FEL, samples experience severe
electronic radiation damage, especially to heavy atoms, which hinders direct
implementation of the MAD method with x-ray FELs. We propose a generalized
version of the MAD phasing method at high x-ray intensity. We demonstrate the
existence of a Karle--Hendrickson-type equation for the MAD method in the
high-intensity regime and calculate relevant coefficients with detailed
electronic damage dynamics of heavy atoms. Our results show that the bleaching
effect on the scattering strength of the heavy atoms can be advantageous to the
phasing method. The present method offers a potential for \textit{ab initio}
structural determination in femtosecond x-ray nanocrystallography.
