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That just canceled by the displacement current. the conduction current finite and an the distinguishing characteristic between This result infinite beam. There now remain to be considered Eqs. 30. Utilizing Eq. 30, Eq. 29, Eq. 25 is By utilizing Eq. 31) reduced to = dz Now, Eqs. 32) v0 equations that govern wave propagation for one-dimensional (infinite) beam in confined flow. 32 are the fundamental is is essentially the equation of motion. 31 beam velocity. 32 forces) modulates the velocity. tinuity equation and shows how the velocity modulation couples to the The next task is current modulation.

Normal mode form. First, define several new quantities. 34) me0 is ft, a up is the frequency at called the plasma frequency. It which plasma of uniform density p0 will oscillate under the action of the space-charge repulsion forces. 35) constant and ft the "electronic" = = - propagation constant. 36) COUPLED MODE AND PARAMETRIC 42 The d-c electron velocity V0by ELECTRONICS is constant and is related to the d-c potential ~v02=\e\V0 Further, recall that J0 = pqV 0. Now introduce these definitions (Eqs.

12. raphist's Equations," Bell System Tech. , 34, pp. 995-1044 (September 1955). W. W. Mumford, "Directional Couplers," Proc. IRE, 35, 160-165 (February 13. 1947). S. E. 14. IRE, H. J. Miller and W. W. Mumford, 40, 1071-1078 Riblet, 1307-1313 "A (September "Multielement 1952). Directional Couplers," Proc. Mathematical Theory of Directional Couplers," Proc. IRE, 35, (November 1947). 15. R. Kompfner, "Experiments on Coupled Helices," AERE Rept. No. G/M98 (September 1951). 16. R. Kompfner, "Coupled Helices," presented at IRE Annual Conference on Elec tron Tube Research, Stanford, Calif.

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