Abstract
The characteristics of field electron and ion emission change when the space charge formed by the emitted charge is sufficient to suppress the extracting electric field. This phenomenon is well described for planar emitting diodes by the one dimensional (1D) theory. Here we generalize for any 3D geometry by deriving the scaling laws describing the field suppression in the weak space charge regime. We propose a novel corrected equivalent planar diode model, which describes the space charge effects for any geometry in terms of the 1D theory, utilizing a correction factor that adjusts the diode’s scaling characteristics. We then develop a computational method, based on the particle-in-cell (PIC) technique, which solves numerically the space charge problem. We validate our theory by comparing it to both our numerical calculations and existing experimental data, either of which can be used to obtain the geometrical correction factor of the corrected equivalent planar diode model.
Highlights
The current extracted from an electron emitting cathode or an ion emitting anode can be increased by applying higher electric fields, increasing the emitter temperature or irradiating it with light
The value of the corrected equivalent planar diode (CEPD) correction factor ω, which is calculated by fitting to the PIC results as described in section III A, varies on the emitting surface, mainly due to the variation of the current density distribution ξ( ̃r)
We have developed a three-dimensional theoretical model, describing the scaling laws of space charge limited charge emission at high electric fields
Summary
The current extracted from an electron emitting cathode or an ion emitting anode can be increased by applying higher electric fields, increasing the emitter temperature or irradiating it with light. The space charge (SC) effect plays a very significant role in all forms of electron and ion sources [3,4,5,6,7,8,9] and is of paramount importance for the understanding of the ignition of vacuum arcs [10,11,12,13]. In order to calculate the SC effects one has to solve self-consistently three coupled problems: the Poisson equation, the continuity equation, and the electron emission equation. This is possible by utilizing various numerical methods, such as Particle-In-Cell (PIC) [14,15,16], molecular dynamics [17], or the point charge method [18]
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