When solving the Laplace equation numerically via computer simulation, in order to determine the field values at the surface of a shape model that represents a field emitter, it is necessary to define a simulation box and, within this, a simulation domain. This domain must not be so small that the box boundaries have an undesirable influence on the predicted field values. A recent paper discussed the situation of cylindrically symmetric emitter models that stand on one of a pair of well-separated parallel plates. This geometry can be simulated by using two-dimensional domains. For a cylindrical simulation box, formulas have previously been presented that define the minimum domain dimensions (MDD) (height and radius) needed to evaluate the apex value of the field enhancement factor for this type of model, with an error-magnitude never larger than a “tolerance” ${\epsilon }_{\mathrm{tol}}$. This MDD criterion helps to avoid inadvertent errors and oversized domains. The present article discusses (in greater depth than previously) a significant improvement in the MDD method; this improvement has been called the MDD extrapolation technique (MDDET). By carrying out two simulations with relatively small MDD values, it is possible to achieve a level of precision comparable with the results of carrying out a single simulation using a much larger simulation domain. For some simulations, this could result in significant savings of memory requirements and computing time. Following a brief restatement of the original MDD method, the MDDET method is illustrated by applying it to the hemiellipsoid-on-plane and hemisphere-on-cylindrical-post emitter shape models.

中文翻译：

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场发射体静电学：用于高精度计算场增强因子的高效改进仿真技术

当通过计算机模拟对拉普拉斯方程进行数值求解时，为了确定代表场发射器的形状模型表面的场值，需要定义一个模拟框，并在其中定义一个模拟域。该域不能太小以至于框边界对预测的字段值产生不良影响。最近的一篇论文讨论了位于一对分离良好的平行板之一上的圆柱对称发射器模型的情况。这种几何可以通过使用二维域来模拟。对于圆柱形模拟盒，先前已经提出了公式，用于定义评估此类模型的场增强因子的顶点值所需的最小域尺寸 (MDD)（高度和半径），${\epsilon }_{\mathrm{托尔}}$. 此 MDD 标准有助于避免无意的错误和过大的域。本文讨论（比以前更深入）MDD 方法的重大改进；这种改进被称为 MDD 外推技术 (MDDET)。通过使用相对较小的 MDD 值执行两次模拟，可以获得与使用更大的模拟域执行单个模拟的结果相当的精度水平。对于某些模拟，这可能会显着节省内存需求和计算时间。在对原始 MDD 方法进行简要重述之后，通过将 MDDET 方法应用于平面上的半椭球体和圆柱柱上的半球体发射器形状模型来说明 MDDET 方法。