Energy loss by relativistic electron ensembles due to coherent excitation and ionization of atoms

Coherent effects in the ionization loss of ultrarelativistic electron ensembles (bunches) are studied on the basis of perturbation theory of quantum mechanics. These effects originate from the interference of the electrons' proper electric fields with each other. General expressions for the ionization loss in this case, as well as their applicability conditions, are derived. It is shown that for ensembles of sufficiently small spatial size, achievable in modern accelerator facilities, the discussed effects lead to an increase of the ionization loss by several orders of magnitude compared to the result predicted by the Bethe-Bloch formula. In this case, the effective mean ionization potentials of the atomic shells depend not only on the structure of the atomic levels, but on the ensemble form factors as well. The numerical calculations are made for hydrogen atoms, taking into account the density effect in the ionization loss. The ionization loss due to resonant excitation and ionization of atoms by ensembles with periodical modulation of the particle density (realized at free-electron lasers) is investigated.