On the solutions of the coupled system of oscillators and electromagnetic fields excited by an external charge

Abstract

A systematic study of the longitudinal, transverse and total solutions of a coupled system of oscillators and electromagnetic fields in the presence of an external point charge is carried out. The space-time dependence of the solutions as well as their values in specific cases and asymptotic behavior are analyzed. It is shown that, in general, the longitudinal fields show two well-defined contributions: (a) a symmetric field surrounding the particle and carried convectively which is interpreted as a screening field. (b) an excitation defined in principle in a whole semispace and identified with an oscillator plasma wave which corresponds to the excitation predicted in A. Bohr's microscopic theory of energy losses, although showing somewhat different properties. The transverse solutions appear as differences between the fields given in Fermi's macroscopic theory of energy losses and the longitudinal solutions. Using methods of complex variable theory it is shown how we can separate the total perturbations created by the particle in a medium represented by oscillators into three intimately related contributions: screening, oscillator-plasma excitation and Cherenkov radiation. The space-time configuration of these fields as well as their relation to the longitudinal solutions and their evolution for different ranges of the velocity of the particle is given. The problem of the energy loss associated to the creation of the plasma wave is treated.