Uniform Field Gap (Rogowski profile) Electrode Design

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Summary:

I am trying to replicate the results found in papers for uniform field gap electrode designs but I'm not sure what some of the terms mean or if I am getting the correct results.
Hi,

I am interested in designing an electrode that reduces the peak e-field intensity at the edges of the electrode. I've read some papers and it looks like there are quite a few. I'm not really familiar with the terms, so I decided to start off with what looks like is one of the simpler ones.

I am following a paper called "Electrode Design for Testing in Uniform Field Gaps" found at https://ieeexplore.ieee.org/document/4113920.
N. G. Trinh, "Electrode Design for Testing in Uniform Field Gaps," in IEEE Transactions on Power Apparatus and Systems, vol. PAS-99, no. 3, pp. 1235-1242, May 1980, doi: 10.1109/TPAS.1980.319754.

If you cannot access it, just let me know.

I have put all of the equation into matlab but I'm not sure how to get the section of the electrode defined by the -x direction in the paper. It looks like what I'm getting is the circular section, shown in Fig. 1b, and the rogowski equipotential like for x<0. I'm also trying to figure out Ro because I don't see it defined in the paper anywhere. I also need to know the height to place the plan electrode section. I thought it would be A/2, but it looks way out of place when I draw a horizontal line at that height.

I am trying to get this so so I can also try the Bruce electrode profile shown in Fig 1c.

From here, my plan is to do an if loop to place the points of a the plane section, rogowski equipotential line, and circular section in a file which I could import into my CAD program to actually build this profile and simulate the e-field intensity with it. Any help and suggestions is much appreciated. This is my first attempt at anything like this so I hope I'm approaching it right in the first place.

I've included a screenshot of my matlab code in case it is off all together. I've also uploaded screenshots what I see when plotting the equipotential line, circle, and plane section.
 

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So I've still been working with this and haven't had much success. For anyone who may view this post, do you think it may be in the wrong forum? Should I consider moving it to a place other than electrical engineering? I know this is definitely riding that like between electrical engineering and more traditional physics.
 
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Baluncore
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Should I consider moving it to a place other than electrical engineering?
You will get a different response from Classical Physics. But is that what you need?

I don't believe these electrode profiles are as critical as is made out.

The initial breakdown in air is not along a straight line. It is along a curved path or "arc" that includes more air molecules in series. Unfortunately I can't find the reference immediately.
Paschen's law comes into it.
https://en.wikipedia.org/wiki/Paschen's_law#Conclusions,_validity

The edges of the electrodes is where the breakdown would normally occur. It appears that Rogowski may have been trying to optimise a situation that was not relevant. Minimum in-gap variation with maximum fall-off at the edges is akin to a filter optimisation problem.

An even electric field is therefore not critical, it is the edges of the field, and the rate the electrode area can become involved by UV ionisation, that decides the dynamics. Larger area electrodes have lower inductance, but due to skin effect, the current flow does not enter the electrode perpendicular to the surface, but follows the surface of the electrode around the outer edge. That rounded corner has lower inductance than a sharp corner. Should you be analysing DC field prior to breakdown, or AC current as breakdown current begins to flow.
 
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You will get a different response from Classical Physics. But is that what you need?
Not necessarily, but I was thinking maybe this leaned further over to physics. There have been a number of works I've found on this, but it's not nearly as extensive as other topics.

I don't believe these electrode profiles are as critical as is made out.
I think the electrodes are critical to actually knowing the e-field intensity when you experience breakdown in air. Although breakdown occurs at various e-field intensities following Paschen's curve, you need to know what your E-field intensity is in order to build any type of curve like that. The goal with creating a uniform field electrode is really to ensure that the peak e-field intensity is in the middle parallel region of the electrode so E=V/d can be used. The edges of the electrode should be lower, therefore less important to breakdown.

Rogowski worked on an electrode where the ends of the electrode curve up to follow the field lines; hence my other posts asking how to determine the equation for a field line. There are other profiles such as Bruce, Borda, Harrison, Cheng, etc. that have worked to refine this by making more defined profiles and aiming to create and even more uniform electric field in the center with a lower intensity toward the edges. My problem here is trying to take those equations and plot them in matlab to visualize the same profile.

Should you be analysing DC field prior to breakdown, or AC current as breakdown current begins to flow.
I wanted to study both actually. I would like to determine parameters for breakdown in different environments which is finding the critical breakdown field. The first step would be to get an electrode design that I can test. Unfortunately, I can't measure the e-field intensity along the electrode but that's where simulations will be helpful in ensuring I have an electrode that will work for my purpose.

For these tests, I'll be using electrical detection methods. I have a partial discharge checker to build the PRPD, so I can see with decent resolution when I start to have corona. I'll also be using an HFCT and a silicon photomultiplier. Acoustic will hopefully be added in the future.
 

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