Helix couplers for linear-beam devices

In this paper the interaction between electron beams and coupled helices is studied and generalized to include the effects of 1) space charge
QC
; 2) finite circuit loss
d
; 3) finite values of gain parameter
C
; 4) an unrestricted coupling parameter
k
, and 5) the effect of having a large positive value of the velocity parameter
b
such that the propagation constants are purely imaginary. A general determinantal equation including all these factors is derived from the coupled-circuit equations and the stream equation. Curves of the propagation constants for a variety of operating parameters are shown. Attention is called to the fact that a region of growing wave is found for large positive
b
for extremely tight coupling. The extent to which the "growing-wave island" is affected by the various operating parameters is also illustrated. Equations for the outer and inner helix
r-f
voltages are derived and from which curves of the propagating
r-f
powers along the helices are computed and plotted. Positions for maximum transfer of energy between the helices can be deduced and the extent to which they are affected by the various Parameters is discussed.