Energy loss of a charged particle during its interaction with a dielectric cylinder

Subject and Purpose. The creation of millimeter and submillimeter electromagnetic wave generators is a promising direction in radio physics. These generators are demanded in medicine, biology, spectroscopy, broadband wireless communications and other branches of science and technology. One of the ways of millimeter and submillimeter wave generation is interaction between charged-particle beams and super-dimensional electrodynamic structures in multimode operation. In this regard, elementary physical mechanisms underlying this interaction invite further investigation. In the paper, the problem of spatial-surface eigenmode excitation is considered for a solid-state cylinder when a nonrelativistic electron moves in a vacuum over the surface of this cylinder and parallel to its axis. Because of the nonrelativistic character of the electron motion, the electron field and the radiation field in a vacuum are treated in the electrostatic approximation, while the fields inside the cylinder are calculated with the delay effect taken into account.

Methods and Methodology. Maxwell’s equations in space-time field terms yield an analytical expression of the electron energy loss for the spatial-surface eigenmode excitation of a dielectric cylinder. This expression is numerically analyzed using the bisection method to find roots of the dispersion equation.

Results. The analysis of the electron energy loss suggests that the E-type modes are the most efficiently excited. The electron energy loss for the E-mode excitation is approximately two orders higher than the loss for the excitation of H-modes with the same azimuthal and radial mode indices. The largest electron energy loss corresponds to the HE₁₁ mode excitation.

Conclusion. The performed study gives a deeper insight into the physical mechanism underlying the eigenmode excitation of a dielectric cylinder under the action of charged particles. The obtained results can be generalized to the case of a multijet electron beam used to generate whispering-gallery electromagnetic modes.