Influence of the non-regular deformed boundary of a TEM-waveguide to the field distribution

在拟议的 DFG 项目中，申请人希望对具有不规则变形横截面和传播方向随机缺陷的圆柱形波导中的电磁波进行建模和仿真。我们将重点关注 TEM 波导（两个电导体），因为只有存在两个电导体，TEM 波才能传播。由于制造工艺的原因，实际波导的横截面通常不均匀。所有真实表面都具有随机缺陷并且与理想几何形状不同，例如表面粗糙度。将分析表面粗糙度和几何形状的变化对电磁场分布的直接影响。谢尔库诺夫通过将麦克斯韦方程组转化为一组常微分方程，引入了更一般的波导中电磁波的传输理论。通过将横向电磁场分量展开为一系列正交基函数，导出了无限微分方程组，即所谓的广义电报员方程 (GTE)。该项目的主要目标是开发一种系统方法来分析 TEM 波导由于制造过程中的公差而导致的几何尺寸。基于 Schelkunoff 的概念，麦克斯韦方程组将被转换为 GTE，并且可以分析不规则变形的 TEM 波导的电磁场。特别关注同轴 TEM 波导不规则变形表面的建模。边界条件描述了表面的缺陷，我们假设这些变形没有规则。因此，将边界条件解释为随机变量是有用的。除了推导不规则变形 TEM 波导的所谓广义电报员方程以及这些微分方程组的数值解之外，另一个主要重点是验证同轴 TEM 波导上的模拟。现场传感器探头校准的目的是用可测量的量来充分描述由于几何缺陷而引起的不确定性。由于制造工艺而导致的表面粗糙度对场分布的影响目前尚不清楚。目前还没有考虑制造工艺造成的公差对电磁场分布的影响，但在测量过程中必须给出测量不确定度。因此，该项目的目的就是研究这个问题。

In the proposed DFG-project the applicant wants to model and simulate electromagnetic waves in cylindrical waveguides with irregularly deformed cross-sections and random imperfections in the direction of propagation. Great emphasis will be put on TEM-waveguides (two electric conductors), because TEM-waves can only propagate, if there are two electric conductors. Practical waveguides are usually not uniform in their cross-section due to the manufacturing process. All real surfaces have random imperfections and differ from the ideal geometry, e.g. surface roughness. The direct effect of the surface roughness and the changes of the geometry on the electromagnetic field distribution will be analyzed. Schelkunoff introduced a more general transmission theory of electromagnetic waves in waveguides by transforming Maxwell’s equations into a set of ordinary differential equations. By expanding the transvers electromagnetic field components into an orthogonal series of basis functions, an infinite system of differential equation is derived, the so-called generalized telegraphist’s equations (GTEs).The main objective of the project is to develop a systematic approach to analyze TEM-waveguides with regard to their geometrical dimension due to tolerances in the manufacturing process. Based on the concept of Schelkunoff, Maxwell’s equations will be converted into GTEs and the electromagnetic field of an irregularly deformed TEM-waveguide can be analyzed. Special attention is placed on the modelling of the irregularly deformed surface of the coaxial TEM-waveguide. The boundary conditions describe imperfections of the surface where we assume that there is no rule for these deformations. Consequently, it is useful to interpret the boundary conditions as random variables. Besides the derivation of the so-called generalized telegraphist’s equations for the irregularly deformed TEM-waveguide and numerical solution to these differential equation systems, another main focus is to verify the simulations on a coaxial TEM-waveguide. The purpose of the calibration of field sensor probes is to fully describe the uncertainties due to the imperfections of the geometry with measurable quantities. The effect of surfaces roughness due to the manufacturing process on the field distribution is not generally known. So far the effect of tolerances due to the manufacturing process on the electromagnetic field distribution is not considered, but the measurement uncertainty must be given during the measurement process. Thus, the aim of this projects is to investigate this problem.