In the last decades, numerical simulation has become a precious tool to assist the design and study of electron sources based on regular arrays of field emitters. Simulations of field emitter arrays (FEAs) require 3D treatment to account for the interactions between neighbor emitters. Therefore, modeling the thermal evolution of FEAs involves high computational resources due to the multi-physics approach and time dependency. The present paper proposes an algorithm which gives a fast prediction of the self-heating of a large array of N axisymmetric field emitters. It consists in finding for each emitter the equivalent 2D axisymmetric situation yielding the same electron current at 300 K as in the 3D array. The 3D modeling is thus efficiently split into N simulations in 2D, with a significant computation time reduction by at least one order of magnitude. The proof of concept uses 3 x 3 arrays of ideal emitters. Our results show a correct prediction, within a few percent, of the array thermo-field current and maximum temperature-two quantities of high interest for thermal failure and breakdown voltage considerations. The algorithm paves the way for including thermal effects in future optimization studies of realistic FEAs. Published under an exclusive license by AIP Publishing.
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