Frequency dependent target response

[Aziz]

Hi all,

the latest cross section of a thick straight wire of short length indicates, that the amperes law doesn't work well at the endings and beyond of the wire. This effect is called the "edge effect".
One can clearly see the discontinuity of the magnetic field density at the wire endings. But the f|_|cking publications and text books doesn't say it explicity, that the amperes law doesn't work for finite lenght straight wires. I haven't found anything, that would help me.


The solution is simple but it costs more calculation time. I have to divide the entire wire element into more finer wires with lower diameter (thick wire model -> thin wire model). At the end, I can really model the frequency dependent inductance, frequency dependent resistance (and time constant), rectangular cross section wires, tube wires, thin foils, etc.
The target coil model can be modelled as a thick disc coil with rectangular cross section. I would only need one target model.

Unfortunately, the coil software must be redesigned at some certain parts. But I can answer some of my open questions and thesis.
Cheers,
Aziz

[Aziz]

Hi all,

finally, I see what is really happening to the "edge effect". Did you know, that surface currents through a finite length straight wire produces a zero B-Field inside the entire conductor (all current is flowing at the surface of the current). This is the reason, why the internal inductance gets 0. You probably never seen such accurate and good visualisations of the effects. I have to implement a lot of code yet.

Wire: 10 cm length, 40 mm thicknes, 1 A current
Surface current model. All current is flowing at the surface of the conductor.

You see no significant B-Field inside the conductor cross section. See at the edge effect and the continuity of the B-Field density.
For this simulation, I had to break the wire into many thousands of filaments.

Test passed! (Physics works )

Stay tuned... more to come later

Cheers,
Aziz

[Carl-NC]

Did you know, that surface currents through a finite length straight wire produces a zero B-Field inside the entire conductor (all current is flowing at the surface of the current).

This is only true for a perfect conductor (σ = ∞) or when f = ∞.

[Qiaozhi]

This is only true for a perfect conductor (σ = ∞) or when f = ∞.

It's called the Meissner Effect.

[moodz]

So if we immerse the coil in liquid nitrogen ...

[Aziz]

Hi all,

now let's look at the uniform current density for the same straight thick wire. The simple and fast algorithym produces discontinuities in the magnetic field at the endings and beyound that. This is owed to the fact that the amperes law isn't defined outside of the straight wire. Particularly beyond the endings. If I break down the piece of straight wire into many many wire filaments (2491 in the follwing example), I get finally the correct magnetic field everywhere. The discontinuity disappears.

Wire model consists of many many wire filaments:


Simple and fast wire model (only 1 wire filament):


Now the wire model with many many wire filaments:

Look at the above picture: There are minor differences.
It seems, that the amperes law is only valid for long wires (length much greater than the thickness of the wire). It lacks at the endings of the wire and beyond that (not defined).


The "edge effect" has not been investigated till now. Let's wait 10 - 20 years until someone publishes a paper. And a good formula for more accuracy.

Cheers,
Aziz

[Aziz]

Hi all,

I didn't have much time to make some codings. I will try the "mobile coding" method so I have bought a cheap and refurbished Microsoft Surface Pro 4 (Tablet PC, Windows 10, i5 core, 2x2.5 GHz). I payed ~127 EUR for it on Amazon. It's a nice Tablet PC with enough CPU power. I hope, I can code on it. My coil software works on it. But I am missing the special mouse functionality (left and right mouse clicks at the same time ). Zoom in/out via rotary wheel. And so on..
This is very strange to me. But I will try it.
Pity, it is quite big (12.3 inch screen) but very thin. The half of the size would be perfect for me. Anyway.

Cheers,
Aziz