  During the last five years, serial femtosecond crystallography using x-ray
laser pulses has developed into a powerful technique for determining the atomic
structures of protein molecules from micrometer and sub-micrometer sized
crystals. One of the key reasons for this success is the "self-gating" pulse
effect, whereby the x-ray laser pulses do not need to outrun all radiation
damage processes. Instead, x-ray induced damage terminates the Bragg
diffraction prior to the pulse completing its passage through the sample, as if
the Bragg diffraction was generated by a shorter pulse of equal intensity. As a
result, serial femtosecond crystallography does not need to be performed with
pulses as short as 5--10 fs, as once thought, but can succeed for pulses
50--100 fs in duration. We show here that a similar gating effect applies to
single molecule diffraction with respect to spatially uncorrelated damage
processes like ionization and ion diffusion. The effect is clearly seen in
calculations of the diffraction contrast, by calculating the diffraction of
average structure separately to the diffraction from statistical fluctuations
of the structure due to damage ("damage noise"). Our results suggest that
sub-nanometer single molecule imaging with 30--50 fs pulses, like those
produced at currently operating facilities, should not yet be ruled out. The
theory we present opens up new experimental avenues to measure the impact of
damage on single particle diffraction, which is needed to test damage models
and to identify optimal imaging conditions.
