Evaluation of the Pierce Parameters C and Q in a Traveling Wave Tube

Summary form only given. This work provides a critical examination of the Pierce gain parameter C and the space charge parameter Q in a traveling wave tube (TWT). How to determine Q accurately remains an open question in TWT design. An accurate evaluation of Q in particular is important because a small change in Q can lead to a large change in the predicted gain. The threshold for backward wave oscillation in a TWT is also known to depend critically on QC. From a model dielectric TWT for which there is an exact dispersion relation [1], we identified the exact expressions for Q and C according to Pierce's classic 3-wave theory and his 4-wave theory that includes the reverse propagating circuit mode. In general, we find that both Q and C depend on the frequency and on the wavenumber k, and that they are different between the 3-wave and 4-wave theory. This allows a rigorous test on the various approaches that approximate Q and C. For the dielectric TWT model [1], we find that the spatial amplification rate, Im(k), may be most reliably calculated in both 3-wave and 4-wave theory if Q is evaluated by approximating k = k_beam, where k_beam is the wavenumber of the beam mode (frequency/beam velocity). The wavenumber dependence of C must also be carefully evaluated for accurate results. The implications of these findings for TWT design are explored.