The gyro-TWT in a cylindrical waveguide of linearly-tapered cross section w
as analyzed for the gain-frequency response, using the Pierce-type gain equ
ation. The taper in the waveguide cross section was adjusted for wide devic
e bandwidths, either by changing the taper angle, while keeping the interac
tion length to be constant, or by changing the interaction length, while ke
eping the initial and final radii of the waveguide constant. Tapering led t
o the prediction of wide bandwidths, though at the cost of gain, as compare
d to a non-tapered device. The range of the DC background magnetic flux den
sity relative to its grazing-point value was identified as a crucial parame
ter for large gains, with appreciable bandwidths, and minimum mode mixing i
n a tapered device, the latter in general facing more mode competition than
a non-tapered device.