The effect of Coulomb repulsion on the space-time resolution limits for ultrafast electron diffraction

The development of electron sources capable of temporal resolution on the order of 1 ps or less raises a number of questions associated with the estimation of the physical meaning and accuracy of the dynamic parameters based on the analysis of time-dependent scattering intensity. The use of low brightness ultrashort pulses with few electrons leads to the necessity for increasing the total exposure time and lengthening the time of data acquisition, with attendant problems with the limited sample. The sample restrictions can be mitigated by increasing the charge per pulse, i.e., by going to high brightness sources. Increasing in the number of electrons, however, is limited by the Coulomb repulsion between them, which leads on one hand to distortion of the diffraction pattern and on the other hand to an increase in the duration of the pulse. An analytical technique for estimating the deformation of the diffraction pattern caused by the Coulomb repulsion of the electrons in electron bunches with duration of less than 10 ps and the influence of this effect on the accuracy of determination of the interatomic distances is developed for the non-relativistic and relativistic regimes for electron energies.