Nonlinear characteristics of relativistic Pierce diodes in stationary state

Abstract

Time independent states are explored theoretically for generalized Pierce diode (non-neutral plasma diode with ionic background), which is driven by a cold relativistic electron beam. The region between the electrodes is assumed to be filled uniformly with static ions. Injected beam is monochromatic, i.e., all the electrons are emitted with the same kinetic energy (relativistic). Relativistic effects are explored both for collisionless and collisional systems. The formulation of the model is based on the fluid-Maxwell's equations and it is solved by two methods: in the absence of any dissipative source, Eulerian description is employed, whereas to incorporate the effects of collisional drag Lagrangian formulation is found to be useful. The steady-state solutions are visualized through the “Bursian” and “Non-Bursian” branches in a parametric plane. It is observed that the magnitude of the maximum current density of a Pierce diode increases with the relativistic factor of the injected beam. Other factors like the density of background ions and particle collision also have significant influence on the space-charge-limited flow and other steady state properties. Obtained results are relevant to comprehend the working mechanism of many diode-based instruments such as thermionic energy converters, microwave emitter, Q-machines, etc.