How can I simulate dielectric breakdown?

[seang]

Are there any programs around which will do this? I initially thought of Sonnet, but after some thought, I began to doubt that it would model dielectric breakdown. Any ideas at all? I've searched the web, and I can find some electrical (spice) models for it, but nothing geometric.

Thanks,
Sean

 

[NoTime]

I'm not sure of what you mean by geometric.
Why won't the spice models work for you?

 

[TheAnalogKid83]

I'd say to try matlab, you can program nonlinearities and conditions into what are normally continuous models.

 

[seang]

No Time:
I need a geometric simulation. I'm trying to model a spark plug kind of thing, you know?
I need to be able to say: If I apply a voltage at one end of the spark plug, what will the voltage be on the other side? How will the charge be distributed across the tip of the spark plug?

The Analog Kid:
You're right, but I don't think I have the skill level to build a dielectric breakdown model in MATLAB (3d, mind you). I'll check if one already exists.

Is there much formulae for dielectric breakdown? In my classes, we just heard things like If there's a lot of voltage, you can break a capacitor, etc. If there are formulae which model dielectric breakdown on a geometric basis, I'd sure like to know about it.

 

[f95toli]

Comsol (used to be called Femlab) or a similar package would work. As a matter of fact I think it would be pretty easy if all you need is to calculate the potentials.
However, full FEM solvers tend to be pretty complicated, you need to know what you are doing and preferably understand at least the basics of how FEM solvers work.
That said, Comsol itself is actually quite user friendly, so the user interface etc will not cause any problems.

If 2D is enough (axial symmetry?) the PDE toolbox in Matlab might also work. I know there are also some free 2D FEM solvers that can handle EM problems, but I have never used any of them.

 

[seang]

Comsol (used to be called Femlab) or a similar package would work. As a matter of fact I think it would be pretty easy if all you need is to calculate the potentials.
However, full FEM solvers tend to be pretty complicated, you need to know what you are doing and preferably understand at least the basics of how FEM solvers work.
That said, Comsol itself is actually quite user friendly, so the user interface etc will not cause any problems.

If 2D is enough (axial symmetry?) the PDE toolbox in Matlab might also work. I know there are also some free 2D FEM solvers that can handle EM problems, but I have never used any of them.

Thanks alot, that should help out quite a bit. Yeah, a 2D simulator is what I had in mind at first (that's what Sonnet is)...

The thing I've having problems with is, once dielectric breakdown occurs, you can't really apply the rules of electrostatics/dynamics, can you? I mean planar simulators assume that the energy is moving from trace to trace via electromagnetic waves (maxwell's equations and stuff.), don't they?

In other words, you'd probably have to write out the PDE which governs wave propagation (in COMSOL, or similar) in order to be able to solve the problems. But I'm having trouble finding equations which govern arc behavior, which is what I'd need, I think.

 

[NoTime]

No Time:
I need a geometric simulation. I'm trying to model a spark plug kind of thing, you know?
I need to be able to say: If I apply a voltage at one end of the spark plug, what will the voltage be on the other side?

Zero? I suppose you could use other reference systems, but that just makes things more complex. If your measurement device needs to be remote rather than connected to the electrode you may need to contend with IR losses.

How will the charge be distributed across the tip of the spark plug?

Generally evenly, but there is going to be concentrations at surface imperfections in the tip where breakdown eventually initiates.
The big determinant of the breakdown characteristics is the gas mixture between the electrodes.
Unless you are modeling very short time intervals your parameters are
Breakdown voltage
Breakdown resistance
Quench voltage

A small neon bulb might be easier to study than something like a car sparkplug due to the low voltages involved. Plus by controlling currents you can get a visual on breakdown initiation and propagation.

 

[physic2physic]

Sparkplug

Are there any programs around which will do this? I initially thought of Sonnet, but after some thought, I began to doubt that it would model dielectric breakdown. Any ideas at all? I've searched the web, and I can find some electrical (spice) models for it, but nothing geometric.

Thanks,
Sean

Hi Sean,
I am right working on the same thing, and I would be so grateful if we can share the ideas.
thanks,

 

[Zapitgood]

There is a freeware electrostatics simulator called BELA that I have used to simulate
field distribution in high voltage conductors but I don't think it will determine the
breakdown, just the field strength. I doubt a simulation would be very accurate anyway as the breakdown mechanism is fairly complex with many factors (temperature/pressure/humidity/ion collision factor) Do a search for Townsend breakdown .

 

[Zapitgood]

Here is a link to BELA

http://femm.foster-miller.net/wiki/HomePage

 

[SquibblyWibbl]

Sorry I'm replying to this post a little late. If you want to simulate dielectric breakdown there is only one really good (and efficient) way and that using a a fuse network. Treat the air as a network of fuses (this is just like using finite difference of the e-fields, see Kirkpatricks paper from, I think, 1972). Fuses are then removed as the current through them becomes too large (either stochastically or deterministically). Have a look for a paper by Phil Duxbury (sometime in the late 80's in either PRL or PRB) who did a model of this and a later paper by S. Zapperi (I think Science 1995). As the fuses are linear the solution of the e-field at each iteration is simply solving a sparse system of linear equations (conjugate gradient always works well). And its fast!