Nonlinear dynamics of electron flows with density gradient in spherical diodes

Abstract

A variety of Pierce diodes formed by a pair of grounded concentric spheres with electrons streaming radially are investigated with particle-in-cell simulations and analytical models. The electrons flow parallel or antiparallel to a density gradient in convergent or divergent diodes, respectively. The existence and stability ͑or instability͒ of laminar steady states with space charge and nonuniform velocity that are possible for a given set of diode parameters, are crucial to determine the outcome of the numerical experiments. The dispersion relation for the stability of the initial constant velocity states and the concomitant energy flow balance are examined in relation to the nonlinear dynamical evolution. Spherical diodes have properties that are common to a dual pair of diodes with reciprocal ratios of collector to emitter radii. Stable oscillatory electrostatic states, associated with Hopf bifurcations, are observed in the simulations. The breakdown of the laminar electron flow has completely different physical characteristics in divergent and convergent diodes.

Stationary to nonstationary transition in crossed-field devices

“…The fact that we can always find stationary solutions in this parameter region for the thermal case does not a priori guarantee that the system will not present a turbulent (nonstationary) character. In fact, the stationary solution may be unstable 15 or very sensitive to small oscillations in the system in such a way that it may not be actually attained in practice.…”