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X-ray free-electron lasers (XFELs) may allow to employ the single particleimaging (SPI) method to determine the structure of macromolecules that do notform stable crystals. Ultrashort pulses of 10 fs and less allow to outruncomplete disintegration by Coulomb explosion and minimize radiation damage dueto nuclear motion, but electronic damage is still present. The majorcontribution to the electronic damage comes from the plasma generated in thesample that is strongly dependent on the amount of Auger ionization. Since theAuger process has a characteristic time scale on the order of femtoseconds, onemay expect that its contribution will be significantly reduced for attosecondpulses. Here, we study the effect of electronic damage on the SPI at pulsedurations from 0.1 fs to 10 fs and in a large range of XFEL fluences todetermine optimal conditions for imaging of biological samples. We analyzed thecontribution of different electronic excitation processes and found that atfluences higher than $10^{13}$-$10^{15}$ photons/$\mu$m$^2$ (depending on thephoton energy and pulse duration) the diffracted signal saturates and does notincrease further. A significant gain in the signal is obtained by reducing thepulse duration from 10 fs to 1 fs. Pulses below 1 fs duration do not give asignificant gain in the scattering signal in comparison with 1 fs pulses. Wealso study the limits imposed on SPI by Compton scattering.

Theoretical study of electronic damage in single particle imaging experiments at XFELs for pulse durations 0.1 - 10 fs