Electromagnetic Wave Propagation in Bounded Electron Beams

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Electromagnetic Wave Propagation in Bounded Electron Beams
Philip Parzen
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The linearization is accomplished by decomposing each field quantity into a sum of a tijne-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 tvio 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 characteriz...e 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, (2) It is well known that the fields within a multiply connected region are uniquely determined by either the component of the electric field or the component of the magnetic field which is tangent to the surface bounding the region, A similar uniqueness theorem is proven for the sinusoidal propagation of electromagnetic waves in electron beams.


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