  Femtosecond x-ray nanocrystallography exploiting XFEL radiation is an
emerging method for protein structure determination using crystals with sizes
ranging from a few tens to a few hundreds nanometers. Crystals are randomly hit
by XFEL pulses, producing diffraction patterns at unknown orientations. One can
determine these orientations by studying the diffraction patterns themselves,
i.e. by indexing the Bragg peaks. The number of indexed individual images and
the SASE bandwidth are inherently linked, because increasing the number of
Bragg peaks per individual image requires increasing the bandwidth of the
spectrum. This calls for a few percent SASE bandwidth, resulting in an increase
in the number of indexed images at the same number of hits. Based on
start-to-end simulations for the baseline of the European XFEL, we demonstrate
here that it is possible to achieve up to a tenfold increase in SASE bandwidth,
compared with the nominal mode of operation. This provides a route for further
increasing the efficiency of protein structure determination at the European
XFEL. We illustrate this concept with simulations of lysozyme nanocrystals.
