To check for breakdown conditions in high-voltage systems, it is useful to know the distribution of electric-field over surfaces of electrodes and dielectrics. Recently, a customer who has used the software for 10 years asked me if EStat had this capability. It took me several minutes of searching to answer the question. My conclusion is that perhaps this useful feature has been under-emphasized.
I added entries to the index of the EStat manual and decided to write this post. The figure below shows a plot of |E| for a cylindrical example. The solution volume is bounded on the right and top by the shaped inner wall of a grounded vacuum chamber. A high-voltage rod electrode with spherical tip is supported by an insulator on the left-hand side. The goal is to find the variation of electric field over the electrode and the vacuum surface of the insulator.
The Region command in the Analysis menu of EStat generates the listing. We could also set up analysis script like the following:
INPUT FieldList.EOU OUTPUT FieldList * Electrode REGION 2 * Insulator REGION 3 ENDFILE
EStat performs several activities in response to the command, including volume integrals of field energy, surface integrals of normal electric field to infer induced charge and surface integrals of the Maxwell stress tensor to determine force if the region is surrounded by air or vacuum. The code also calculates the electric field on element facets that lie on the region boundaries. It then goes to some effort to arrange them in a logical order. Here’s an example of the first portion of the table that appears in FieldList.DAT:
Identified 102 facets Maximum field value of 2.5310E+06 occurs at z = 1.6848E+01 r = 1.0876E+00 on the boundary with Region No 1
Z R D |E| Ez Er NBorder ===================================================================================== 1.6997E+01 1.0134E-01 0.0000E+00 2.5182E+06 -2.5174E+06 -6.3852E+04 1 1.6988E+01 2.9815E-01 1.9705E-01 2.5280E+06 -2.5210E+06 -1.8840E+05 1 1.6968E+01 4.9752E-01 3.9744E-01 2.4856E+06 -2.4663E+06 -3.0928E+05 1 ...
In this example, EStat does a very job of ordering the facet data. On the electrode, the list starts on the axis at the tip and travels along the surface to the left-hand boundary. For the insulator, the list covers the vacuum face, moving outward in radius. Each data line contains 1) the average coordinates of the facet and the distance from the start point, 2) the magnitude and components of the electric field and 3) the number of the region that shares the boundary facet.
An outstanding feature is that you can generate electric field listings along surfaces of arbitrary shape. For example, if you want to know the field along a curve in vacuum, divide the vacuum region into two vacuum regions separated by the desired path.
Here are links to input files for the example:
fieldlist.min
fieldlist.ein
fieldlist.scr
Please use this link for more information on EStat: http://www.fieldp.com/estat.html.
