Nonlinear theory of helix traveling wave tubes in the frequency domain

A nonlinear helix traveling wave tube (TWT) analysis in the frequency domain is presented for a sheath helix surrounded by a conducting wall. Dielectric- and vane-loading of the helix are included as is circuit tapering and external focusing by either a solenoid or a field produced by a periodic permanent magnet (PPM) stack. The electromagnetic field is treated as a superposition of waves where the amplitudes and phases vary slowly in z. The field equations are solved in conjunction with the three-dimensional Lorentz force equations for an ensemble of electrons. Beam space-charge waves are included using a superposition of solutions of the Helmholtz equation. The dc (direct current) self-fields of the beam are also included. The simulation is compared with linear theory as well as a time-domain simulation, each of which is applied to an example of a tube built at Northrop-Grumman Corp. The frequency- and time-domain simulations are in substantial agreement. The advantage of the frequency-domain formulation is a shorter run time than for the time-domain simulation. Hence, the frequency-domain simulation can more easily treat beam thermal effects and multiple waves with closely spaced frequencies.