Some closed-form expressions for relativistic cross-field electron trajectories
Equations for nonrelativistic cross-field motion are first repeated from prior work, in a form suitable for piecewise trajectory calculation in fields that need not be constant. They are then extended into the middle relativistic range, using a new method of expressing the relativistic cyclotron frequency in terms of the fields and the starting conditions. The extended equations are found to include second harmonic terms, but not third harmonic. Accuracy is tested by comparison with Runge-Kutta integration of the relativistic equations of motion, and is found to be adequate for many engineering purposes up to peak velocities in the region of 0.6 c, corresponding to cross-field tube operating voltages on the order of 400 kV. Speed is similar to or a little better than R-K integration on a per-step basis, but is substantially higher when the fieldsallow large step sizes to be taken, since the closed-form expressions have no inherent step size limitation. The tests covered conditions appropriate both to gyrotrons and to relativistic magnetrons.
Peniotron oscillator operating performance
Performance results are presented for two 8 GHz peniotron oscillators operating in the funda mental rotational mode. To form the rotating hollow beam, a non-rotating hollow beam is generated by an immersed Pierce-type gun, and the beam is caused to rotate at cyclotron frequency by a field reversal. The resonant cavity consists of a section of waveguide with a double pair of ridges, short-circuited at each end. The first device tested was loosely coupled to the external load, and the second was much more tightly coupled to increase circuit efficiency. Observed performance is in quite good agreement with calculated performance. Extension of the peniotron to higher frequencies and to amplifier operation is discussed.
Time‐Dependent Computer Analysis of Electron—Wave Interaction in Crossed Fields
A time‐dependent analysis of crossed‐field interaction has been formulated for computer calculation. The computer program has achieved, for the first time, accurate and complete simulation of the magnetron oscillator, magnetron amplifier, and smooth‐bore magnetron. We believe that crossed‐field interaction of the distributed‐emission type is finally predictable. The computer results are reliable enough to serve as design information. They also indicate that the nature of the interaction is turbulent in the sense that the operation of these devices borders between order and disorder under certain conditions.The techniques used in this analysis are applicable to a wide range of problems dealing with other types of electron—wave interaction, and to plasmas.