Theory of the Amplitron

The Amplitron device is analyzed from a normal mode viewpoint based on predominance of the reentrant character of the stream; the analysis is therefore valid for devices with short electron recirculation times and moderate signal levels. The nature of the space charge deduced from the above hypothesis is that of a rotating set of identical spokes having equal angular spacing in the interaction space. The induction effects of this space charge configuration upon the delay line are calculated, accounting for the periodic nature and the short length of the delay line. It is found that both forward-and backward-traveling waves are appreciable and must be considered. The fields in the interaction space are resolved into Fourier component traveling waves. The amplitude of the synchronously interacting wave is related to 1) the input signal, 2) the forward-traveling wave resulting from space charge induction, and 3) the backward-traveling wave resulting from space charge induction. Use is made of the phase relation (adiabatic theory) between the space charge and the synchronously traveling wave to obtain a consistent solution determining the phase relation between the input wave and the space charge. The above relationship between the space charge and the input signal allows the calculation of complex (vector) gain of the Amplitron. It is thus shown that the Amplitron is a nonlinear, or saturated, amplifier. A limit to the gain is observed; the backward-traveling wave is essential in determining it. Phase-dependence on operating RF level, or RF phase pushing, is noted; this type of phase variation does not exceed 90°. Calculations as a function of frequency show the bandwidth to be expected. It is found that conditions may lead to oscillation; feedback mechanisms reside in the backward-traveling wave and in the stream reentrance. The degree of input mismatch of the operating tube is discussed.