Effect of Initial Conditions On Travelling Wave Tubes
Effect of Initial Conditions On Travelling Wave Tubes
W Sollfrey
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A natural method for treating semi-infinite systems is to apply the Laplace transformation. This approach will bring in the initial con- ditions in a direct manner, ■'■'he fields will be expressed as contour inte- grals, whose integrands will possess both poles and branch points. The residues at the poles will represent the discrete modes of the system and the integrals around the necessary bramch cuts will provide th? con- tinuous spectrum. The theory may be developed for arbitrary angular de-... pendence with no greater complications than arise in the symmetric case. We shall determine the current in the beam at large distances down the helix. Since the radius of the hole in the wall of the output waveguide through which the beam passes is a small fraction of the wave- length in the guide, most of the field in the helical section is reflected, and the major coupling to the output guide is by means of the a. C. Beam current. This current is expressed in terms of transfer coefficients which represent the current that would be generated by unit field, unit charge, or unit a.
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