基于物理的对数形式描述半球-圆柱柱结构中静电场增强，用于高场应用
Physics-based logarithmic description of electrostatic field enhancement in hemisphere-on-cylindrical-post structures for high-field applications
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中文总结 AI 辅助
本文针对半球-圆柱柱结构，提出一种对数形式的解析近似公式来计算顶点场增强因子，在ASR为1至1000范围内最大误差仅0.15%，显著优于旧有近似。
中文摘要 AI 辅助
静电（ES）场增强在尖锐导电结构中起着核心作用，涉及避雷保护、电晕放电、真空中的电击穿（例如在粒子加速器中），以及更广泛的场发射电子器件的技术应用。研究这种静电效应的典型几何模型是半球-圆柱柱（HCP）模型，其条件为结构立于大面积横向范围的平面导体上，且结构与对电极之间存在大间隙。一个主要关注的参数是顶点场增强因子（AFEF）（顶点静电场/背景静电场）。对于该结构（及其他结构），AFEF 的公式可写为 AFEF = ASC × ASR，其中顶点锐度比（ASR）由（柱高/顶点曲率半径）之比给出，而顶点锐度系数（ASC）取决于柱形状。对于 HCP 模型，目前尚无 ASC 或 AFEF 的精确解析公式（很可能不存在）。本文发展了一个紧凑的解析近似公式，用于 ASC 进而用于 AFEF。该紧凑公式具有对数风格的结构，而非先前近似中使用的幂风格结构。与 HCP 模型的精确有限元分析相比，在计算可访问的 ASR 范围 1 到 1000 内，该对数风格公式的最大误差幅度为 0.15%，显著优于旧有的近似公式。
英文摘要
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.
发表机构
- Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）
- Department of Exact Sciences and Education, Universidade Federal de Santa Catarina（圣卡塔琳娜联邦大学精确科学与教育学院）
- Quantum Sciences Group, School of Mathematics and Physics, University of Surrey（萨里大学数学与物理学院量子科学组）
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