Particle simulations of the low-α Pierce diode

Abstract

The evolution of small initial perturbations of the uniform equilibrium of the ‘‘classical’’ Pierce diode [J. Pierce, J. Appl. Phys. 15, 721 (1944)] is studied using particle simulations. These simulations have been performed with the new bounded-plasma code PDW1 [Wm. S. Lawson (private communication)] and cover the parameter range 0<α<3π, where α=ωpL/v0. In the linear regime, three stages (initial transit, adjustment, and dominant eigenmode) are distinguished; oscillation frequencies, growth/damping rates, and potential profiles of the dominant eigenmode as well as oscillation frequencies of the next-to-dominant eigenmode are recovered and shown to agree quantitatively with recent analytical results. In the linearly unstable cases, the system evolves nonlinearly to a final state which may be either a new, nonuniform dc equilibrium, or a state of large-amplitude oscillations. In particular, for α=1.5π the character of the final state is found to depend on the details of the initial conditions.

Particle simulations of divergent and convergent radial electron flows in cylindrical Pierce diodes

“…2 Ͼx i Ј(x i ) 2 , for x i Ͼ1, and Ј(1) 2 , for x i Ͻ1. For a given value of x i , nonlinear solutions can be obtained with an increasing number of peaks and valleys as D increases.…”

“…The possibility of deterministic chaos arising in Pierce diodes was revealed in these works. At the same time, numerical simulations, 2,8,10,11 began to provide a comprehensive understanding of the nonlinear behaviour of the system, and contributed to the coming of age of the subject. Recent literature indicates a persistent interest in Pierce diodes, and shows new features ͑Ref.…”

Investigation of the complex dynamics and regime control in Pierce diode with the delay feedback

“…In this case the system may be described by fluid equations. It was also shown that in a narrow range of Pierce parameter the system may represent chaotic dynamics [4][5][6][7][8][9].…”

“…Pierce diode is one of the classical models of plasma microwave electronics [1][2][3][4][5][6][7][8][9]. This distributed model though is rather simple, demonstrates many features of the electron beam dynamics in different real electron devices.…”

Nonlinear dynamics of electron flows with density gradient in spherical diodes

“…However, topics like nonlinear steady-state oscillations and chaotic behavior of the system have been developed only in relatively recent times. 3,[5][6][7][8][9] In many electronic devices, thermionic cathodes with large curvature are used for practical reasons. 10 In fact, electronic devices with cylindrical and spherical electrodes were called ''Pierce electrodes'' ͑see e.g., Ref.…”