Figure 7: Equipotential line plot of the electrostatic solution. Create the input script. Perform the finite-element solution. Analyze the results. Step 1 has already been performed, so click the tool marked 2 and pick ElectronDiode.EIN . EStat reads the geometry data in ElectronDiode.MOU , generates the set of finite-element coupled linear equations and solves them, all within a second. FP File Organizer shows that two new files have been created: ElectronDiode.ELS (a diagnostic text listing file) and ElectronDiode.EOU (the main solution file containing potential values at nodes). Click the 3 tool in EStat and pick ElectronDiode.EOU .
The program shifts to the Analysis menu and displays the default equipotential-line plot of Fig. 7 . This type of plot is useful for ex- perienced users because it shows complete information. Section 7.5 of the companion text Finite-element Methods for Electromagnetics describes how to interpret equipotential plots. There are many capabilities of the Analysis menu that you can explore. Let’s check out two of them. A plot of the magnitude of the electric field | E | is useful to pinpoint areas where breakdowns may occur in high-voltage systems. To create the plot, press Plots/Plot settings/Plot type in the menu and choose Element . Then press Plots/Plot settings/Plot quantity and pick | E | .
The resulting plot (Fig. 8 ) shows that the peak field in the electron emission region is about 442 kV/cm and that the maximum field on the insulator vacuum surface is about 40 kV/cm. A second activity is to find the capacitance of the system downstream from the insulator. We can determine this quantity from the volume integral of electrostatic field 11