The Pierce diode with an external circuit. II. Chaotic behavior

The existence of the strange attractor discovered by Godfrey [Phys. Fluids 30, 1553 (1987)] in the neighborhood of α=3π for the Pierce diode is verified, and his numerical results are refined. The theory of Feigenbaum for the sequence of period-doubling bifurcations [J. Stat. Phys. 19, 25 (1975)] is tested with good agreement, despite the strong assumptions made by that theory. The evolution of this attractor is then followed as an external capacitance is introduced, producing a family of bifurcation diagrams. Examination of these diagrams produces one result that should be of interest to mathematical physicists: The existence of an unstable equilibrium in the neighborhood of the strange attractor is strongly implicated in both the existence and destruction of the attractor. The reversibility of the equations of evolution is also discussed, but no clear-cut conclusion is reached.