Sinopsis
Excerpt from Electromagnetic Wave Propagation in Bounded Electron Beams
The propagation of sinusoidal electromagnetic waves in charge' free space, guided or unbounded, has been studied in great detail(l). The purpose of this report is to extend the study to the guided propagation of electromagnetic waves in regions containing charged particles, such as an electron beam. Although the equations for charge free space are linear, the equations for electron beams are nonlinear. A Similar study in the case of electron beams is possible only upon linearization of the equations. The linearization is accomplished by decomposing each field quantity into a sum of a time-independent term and of a relatively much smaller sinusoidal term. After substituting this into the original nonlinear equations, it is assumed that terms of higher order such as the product of two sinusoidal terms, may be neglected. The resulting linear equations govern the variation in space of the electric and magnetic fields, and, in addition, the variation of those field quantities which characterize the electron beam, namely, electron current density, velocity, and charge density.
We shall study the extensions of the two following problems in charge free Space. First is the uniqueness problem for charge-free Space.
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