Harmonic Content in the Beam Current in a Traveling-Wave Tube

In a klystron, charge overtaking of electrons leads to an infinity of ac current on the electron beam. This paper extends the klystron theory of orbital bunching to a traveling-wave tube (TWT). We calculate the harmonic content of the beam current in a TWT that results from an input signal of a single frequency. We assume that the electron orbits are governed by Pierce’s classical three-wave, linear theory. The crowding of these linear orbits may lead to charge overtaking and, therefore, harmonic generation on the beam current, as in a klystron. We analytically calculate the buildup of harmonic content as a function of tube length from the input, and compare the results with the CHRISTINE code. Good agreement is found. Also found is the surprisingly high level of harmonic contents in the electron beam current, even when the TWT operates in the small signal regime. A dimensionless bunching parameter for a TWT,
$X={(2P_{\rm{ in}}/(P_{b} C))}^{1/2}$
, is identified, which characterizes the harmonic content in the ac beam current, where
$P_{{\textrm {in}}}$
is the input power of the signal,
$P_{b}$
is the dc beam power, and
$C$
is Pierce’s gain parameter.