Physics-based logarithmic description of electrostatic field enhancement in hemisphere-on-cylindrical-post structures for high-field applications
Abstract
Electrostatic (ES) field enhancement at sharp conducting structures plays a central role in lightning protection, corona discharge, electrical breakdown in vacuum (for example in particle accelerators), and more generally in technological applications of field electron emitters. A canonical geometry for studying this ES effect is the hemisphere-on-cylindrical-post (HCP) model, in the regime where the structure stands on a planar conductor of large lateral extent, and a large gap exists between the structure and the counter-electrode. A parameter of major interest is the apex field enhancement factor (AFEF) (apex-ES-field/background-ES-field). For this (and other) structures, a formula for the AFEF can be written in the form AFEF = ASC x ASR, where the apex sharpness ratio (ASR) is given by the ratio (post-height/apex-radius-of-curvature), and the apex sharpness coefficient (ASC) depends on the post shape. For the HCP model, no exact analytical formulas for the ASC or the AFEF are currently known. (Quite possibly none exist.) This paper develops a compact analytical approximation for the ASC and hence for the AFEF. This compact formula has a logarithmic-style structure, rather than the power-style structure used in previous approximations. When compared with precise finite-element analyses of the HCP model, over the computationally accessible range 1 to 1000 for the ASR, this logarithmic-style formula has a maximum error-magnitude of 0.15 percent, which is significantly better than older approximations.
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BibTeX
@misc{assis2026physicsbased,
title = {{Physics-based logarithmic description of electrostatic field enhancement in hemisphere-on-cylindrical-post structures for high-field applications}},
author = {Thiago A. de Assis and Fernando F. Dall-Agnol and Richard G. Forbes},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32974},
eprint = {2609.32974},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32974},
}
RIS
TY - UNPB
TI - Physics-based logarithmic description of electrostatic field enhancement in hemisphere-on-cylindrical-post structures for high-field applications
AU - Thiago A. de Assis
AU - Fernando F. Dall-Agnol
AU - Richard G. Forbes
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32974
UR - https://arxiv.org/abs/2609.32974
AB - Electrostatic (ES) field enhancement at sharp conducting structures plays a central role in lightning protection, corona discharge, electrical breakdown in vacuum (for example in particle accelerators), and more generally in technological applications of field electron emitters. A canonical geometry for studying this ES effect is the hemisphere-on-cylindrical-post (HCP) model, in the regime where the structure stands on a planar conductor of large lateral extent, and a large gap exists between the structure and the counter-electrode. A parameter of major interest is the apex field enhancement factor (AFEF) (apex-ES-field/background-ES-field). For this (and other) structures, a formula for the AFEF can be written in the form AFEF = ASC x ASR, where the apex sharpness ratio (ASR) is given by the ratio (post-height/apex-radius-of-curvature), and the apex sharpness coefficient (ASC) depends on the post shape. For the HCP model, no exact analytical formulas for the ASC or the AFEF are currently known. (Quite possibly none exist.) This paper develops a compact analytical approximation for the ASC and hence for the AFEF. This compact formula has a logarithmic-style structure, rather than the power-style structure used in previous approximations. When compared with precise finite-element analyses of the HCP model, over the computationally accessible range 1 to 1000 for the ASR, this logarithmic-style formula has a maximum error-magnitude of 0.15 percent, which is significantly better than older approximations.
ER -