Coherent Spontaneous Emission from Short Electron Bunches: Competition between Different Transverse Waveguide Modes

Abstract

In this paper, we study spontaneous coherent undulator emission from a short dense electron bunch. A special “negative-mass” undulator ensuring stabilization of the axial size of the bunch is considered. We focus on the situation where the competition between two different transverse waveguide modes takes place, so that the undulator resonance is provided simultaneously for three waves placed on the dispersion diagram symmetrically with respect to electrons (namely, the group velocity of the higher waveguide mode coincides with the electron velocity, whereas two resonance frequencies of the lower transverse mode correspond to wave group velocities, one of which slightly exceeds the translational velocity of electrons, with the other being less than the electron velocity). We show that the higher waveguide mode can win this competition due to its proximity to group synchronization with the electron bunch.

Correction of the Mathematical Method for Studying a Cathode Lens with Two Planes of Symmetry

“…Currently, charged particle beams are widely used in many high-tech analytical devices and scientific and technological systems [13][14][15][16]; therefore, solving theoretical problems that have not yet been considered for the study of properties and design of various modified cathode lens circuits with improved focusing characteristics is an important task.…”