In EStat and HiPhi, the term floating electrode refers to a fixed-potential region where ? is determined by capacitive or resistive division. In other words, the potential depends on the electrostatic solution and is not known in advance. For regions with non-zero volume, the standard method is to assign a high value of conductivity or relative dielectric constant (?r ยป 1.0).
I recently had an inquiry about how to find the self-consistent potential of a floating open region. Such a region consists solely of node assignments and has zero volume. In this case, it is not possible to assign special material properties. One resolution is to perform a series of calculations with different potentials assigned to the region and to look for the one with the lowest electric-field energy. This involves some extra work. In the next post, I will show how to automate the procedure using a Perl script.
The first picture below shows the geometry and equipotential lines of a test solution in cylindrical coordinates. The inner electrode has potential ? = 10,000 V and the outer boundary is grounded. There is a fine mesh grid at unknown potential in the intervening space. The goal is to find the grid potential determined by capacitive division for a rapidly-pulsed voltage. I made a series of 20 calculations with grid potentials from 2000 to 10,000 V. The top section of the first figure shows the distorted field distribution at 9200 V. I calculated the electrostatic field energy for each case. The second figure shows a plot of energy versus grid voltage. There is a minimum at 4000 V. The bottom section of the first figure shows the resulting smooth field distribution. Sample files for this example are available in the next post.
Please use these links for more information on EStat (http://www.fieldp.com/estat.html) and HiPhi (http://www.fieldp.com/hiphi.html).
