New post - Conformal Mapping Example, the Eccentric Coax

https://comphysblog.wordpress.com/2020/06/28/conformal-mapping-1/

This post is different from all my others. Rather than stepping through solving a problem with FEniCS, I step through solving a problem with the mathematical method of conformal mapping.

I introduce the method by solving the far easier problem of a pair of slanted parallel plates with a potential difference.

After that I get to the main point of the post: finding the characteristic impedance of a coaxial cable where the centre conductor isn't in the middle; where the cylinders are eccentric. Although the process has quite a lot of algebra, the final solution is simple and very usable.

I've really enjoyed doing this example, because I think it's a great demonstration of using analytical methods to solve a problem with strange boundaries. These days we'd probably just solve this kind of thing numerically, but the analytical solution gives insight and a formula that can be used over-and-over.

I'll add a numerical comparison in the coming days.

What is everybody's view of the FCC project?

The opinions on YC seemed pretty critical in general. While I see some validity to the point that it's a shot in the dark, I also think that shots in the dark might be the best way to go. We know there are problems with our current model of the universe and aren't sure how to resolve them, maybe it'll give us some direction. The final price tag €21B sounds like a lot, but that is spread over a number of years and across multiple governments. Finally, if we don't fund a large project now, then 50 years into the future when we need a big collider for something specific we won't have the skills or expertise to build one. To me, that seems like reason enough to build something.

My latest post is about using boundary conditions to assume symmetry in a finite element electrostatics problem.

To demonstrate Neumann boundaries I solve the Laplace equation for a coaxial geometry using 1/4 of the cross section. I then find the fields of a differential pair transmission line using half the cross section and a Dirichlet boundary.

This is all done with FEniCS, the open source finite element solver. #physics #python #opensource #ham #radio #fenics

https://comphysblog.wordpress.com/2019/07/15/assuming-symmetry-with-boundary-conditions/

Here's the electric potential and field overlaid for a uniform cylindrical charge distribution created using FEniCS, an opensource finite element solver. Although this is a simple analytical problem, this technique can be used for much more complicated geometries.

Next up: linear dielectrics, I've tested in both 2D and 3D and I'm ready to write it up =] surprisingly easy!

After a couple of months without a new post I've started writing about simulating charge distributions, rather than just boundary value problems. I'll explain how #FEniCS can calculate the electrostatic fields of arbitrarily shaped charge densities, which are specified with mesh subdomains. These will have hard edges for now but I want to look into having more general charge distributions.

I've also run 3D simulations for calculating capacitances between arbitrarily shaped conductors and 2D linear dielectrics. I need to do some more testing & comparison with other FEA tools/ analytical methods before I publish any posts. Seems to be going well though!

I was reading the help files of a well-known commercial microwave FEA package and it suggested calculating characteristic impedance from the power and voltage rather than finding the current directly.

This way doesn't require surface normals or line integrals which my previous methods did, so it's probably better (easier to do anyway). I've added this into my TEM mode post - https://comphysblog.wordpress.com/2018/09/06/tem-mode-analysis-with-fenics/

@aparrish always happy to try and help with maths :)

This blog is dedicated to physics and computing, with a current focus on solving electromagnetic problems using open source tools.

I work in particle beam diagnostics and am a PhD student studying the interaction of particle beams with their surroundings as well as the associated dynamics.

I'm Interested in anything related to particle accelerators, beam dynamics, detectors, electromagnetism and computing for science. I also enjoy tennis, fountain pens, fantasy & sci-fi books and board games.

Joined Aug 2018