Finite Element Analysis of the Uncertainty Contribution from Mechanical Imperfections in the LNE's Thompson-Lampard Calculable Capacitor

Thompson-Lampard type calculable capacitors (TLCC) serve as electrical capacitance standards, enabling the realization of the farad in the International System of Units (SI) with a combined uncertainty on the order of one part in $10^8$. This paper presents an electrostatic finite element (FEM) simulation study focusing on the mechanical imperfections inherent in the developed second generation TLCC at LNE and their influence on the combined uncertainty of the practical realization of the farad. In particular, this study establishes the acceptable tolerances for deviations from perfect geometrical arrangements of the TLCC electrodes required to achieve the target relative uncertainty of one part in $10^8$. The simulation predictions are compared with corresponding experimental observations which were conducted with the help of the sub-micron level control of the standard's electrode geometry. In the second generation of the LNE's TLCC, the uncertainty contribution from mechanical imperfections was reduced by at least a factor of 4, as demonstrated by the present FEM analysis. Combined with other improvements, the standard's overall uncertainty meets the target level.