By Joseph E. Rowe

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Extra resources for Nonlinear Electron-Wave Interaction Phenomena

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T h e field p r o b l e m for a surface-mode propagation on an ideal plasma c o l u m n provides a basis for developing t h e a p p r o p r i a t e t e l e g r a p h i s t s equations ( P a i k ) . Collision effects are ignored a n d a cold stationary plasma is considered. O n e proceeds in a m a n n e r similar to t h a t for t h e electron b e a m treated in t h e previous section. It is necessary to identify voltage a n d c u r r e n t in t h e stationary plasma as in t h e drifting electron b e a m .

F l o q u e t ' s t h e o r e m for one-dimensional structures states t h a t t h e fields at any particular cross section of a periodic s t r u c t u r e can differ from those o n e period away in either direction b y at most a complex constant. Consider a t w o - d i m e n s i o n a l lattice in w h i c h t h e wave function or wave potential m a y b e expressed as follows, according t o F l o q u e t ' s theorem: V(x z) = &(x, z)e-vi -w, (89) y y z y w h e r e &(x, z) is taken t o b e periodic in x a n d z, w h i c h are orthogonal directions of propagation.

C <<^ 1. Circuit Equations sin 0{y y 0' ) d& oj oi (19) D cos 0(y, 0^) (10^ Lorentz Equation -A

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