Computer simulations of the chaotic dynamics of the Pierce beam-plasma system

The cold fluid theory of the Pierce beam-plasma system is modified by the incorporation of warm plasma effects. The controlling parameter a in the cold theory, where alpha = L omega(p)/V-0, L = diode width, omega(p) = plasma frequency, and V-0 = beam velocity at injection, is replaced in the warm theory by an effective value of a involving the thermal velocity. The theory is verified by means of a fluid simulation code; the phase states for a cold plasma, including the chaotic state, are recovered for a warm plasma, but with a shift in values of the bifurcation parameter. Furthermore, in order to include plasma kinetic effects, an extensive electrostatic particle simulation code is developed to model the Pierce system. Among the new physical effects arising in this particle model are the local and global thermalization of electrons by electrostatic waves, and blocking oscillations due to particle reflection and trapping. As the parameter alpha is decreased, the electric field at the injection point typically changes state as follows: blocking oscillation --> small fluctuations --> quasi steady oscillation --> prechaotic oscillation --> chaos --> blocking oscillation --> dc electric field. The mechanics of chaotic oscillations in the Pierce system are examined with particular regard to kinetic effects. (C) 1996 American Institute of Physics.