Abstract
This paper considers the transition from field emission according to the Fowler-Nordheim equation to the space charge limited regime. It extends previous works to the quantum limit and to the relativistic limit. These studies are fundamental to nano-scale emitters and relativistic diodes, key components for high power microwave generation. Related prior works include the transition of the Fowler-Nordheim equation to the Child-Langmuir law in the classical (non-quantum, non-relativistic) regime [1,2]. There have also been extensions of the classical Child-Langmuir law to the relativistic [3] and quantum [4,5] regimes. Geometric effects on the classical Child Langmuir law [6], on the quantum Child-Langmuir law [5], and on the Fowler-Nordheim conditions [7] have recently been analyzed. None of these previous works consider, either in the quantum or relativistic regime, the transition from the material-dependent Fowler-Nordheim equation to the material-independent Child-Langmuir laws for these regimes [3,4]. The simulation is performed using the one-dimensional OOPD1 code. For relativistic energies, the algorithm for injecting particles needs to be updated from the non-relativistic scheme. [8] The geometric effect [] and work function effect of the Fowler-ordheim equation will also be analyzed separately in these non-classical limits.
Published Version
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