## Virtual Polywell

### Virtual Polywell

I'm ever so slowly getting code to run. I now have a plot of one coil, close to the axis. Red is x, green is y and blue is the z axis. The magnetic vectors don't have directions. It is possible to add, but I'd rather work on getting the other coils added, increasing the compute volume and start adding electrons.

The 3D to 2D transform has been fun. I can see why graphics folks have a blast. Not to mention games. All I'm doing is checking math in a visual way. Each vector is the average of an 8 x 8 x 8 set of values. So it's a nice way to quickly tell when I'm totally screwed up (which happens way too often if I don't check every darn step of the way).

I'll post more when I get it.

The 3D to 2D transform has been fun. I can see why graphics folks have a blast. Not to mention games. All I'm doing is checking math in a visual way. Each vector is the average of an 8 x 8 x 8 set of values. So it's a nice way to quickly tell when I'm totally screwed up (which happens way too often if I don't check every darn step of the way).

I'll post more when I get it.

It's hard to see but at least the field near the coil is obviously large and going around the coil as expected. It takes quite a while to compute the full volume, but once I get all the coils in and create the data table ("only" 400 some MB) it can be used as a simple lookup for electron density and ion density computations.

Seems like it'll be best to add one coil at a time and check the field in the region of interest.

I've made some progress lately in this direction as well, only taking a slightly different path:

http://www.mare.ee/indrek/ephi/interpolate/

Good work btw. I hope we can compare numbers some day.

- Indrek

Rather than try to follow individual electrons, I'm going to use a plasma/fluid approximation. I'll try different collision terms (starting with none) and see what happens.

I've got one more set of formulas to check, then I can build the data block for a set of 6 coils. I have one parameter which is the coil radius to distance from origin ratio. What I've shown and tested so far is that ratio = 0.9. It will be interesting to see how the electron density changes as a function of coil radius. I'm a long ways from getting that to work though.

Nice work on your stuff! I like the comparison to different computations. Some of them look pretty good!

The second plot is looking directly down the z axis direction on top of where the x and y coils meet (radius of coils set to 0.9 * distance from center)

And here's a plot totally skew, just to get an idea of how much data there is. Not useful, but fun to do!

Next step is to compute the static electric field of charged coils. That's going to take a while....

http://iecfusiontech.blogspot.com/2007/ ... -here.html

post to some nice MIT papers.

I believe if your simulation is working properly you should see bunching in the particle beams giving a natural frequency.

The MIT paper says the beams self organize and lock in with each other.

If you put one coil on each face of a cube, then slice it in half on each axis (xy, xz, yz planes cutting) you end up with 1/8th of the whole thing. Since it is totally symmetric, there is no need to compute more than that 1/8th (and in fact, you can probably do half of that and just reflect, but it's easier to loop over full grids).

Even a trivial particle density function with lots of assumptions about no collisions and no field interactions with the particle fluid (fluid!! not even particles!!) is a horrible task.

MIghty fun though, so I'll be beating my head on it for quite some time.

So off to the time domain with me. I'm beginning to understand why the text books don't cover this case at all.....

Are you saying that oscillation is inherent in the device?drmike wrote:I've at least proven to myself if not fully to a mathematician that a stable steady state fluid can not exist in an arbitrary static electric and magnetic external field. There's just no way the equations will have a solution that is sensible.

So off to the time domain with me. I'm beginning to understand why the text books don't cover this case at all.....

Some oscillations must be naturally there too, but I haven't "allowed" that yet. Once I have a fundamental base to work with, I can turn on the interesting stuff. I knew I was rusty, I'm still just getting the oil into all the right places....

http://www.mare.ee/indrek/ephi/pef2/

As the coils are also the accelerators - this again is a dynamic system, the electric field generated by the

coils is not static through the lifecycle of the potential well formation.

- Indrek

One of the things I'm trying to do is come up with "dimensionless parameters" so I can compute the fields once and then scale everything. That's easy to do with the electric and magnetic fields on their own - the scale parameter is just voltage or current.

If I use the Vlasov/fluid equations for charged particles, I come up with a couple of parameters. I rearrange things so the particle distribution is dimensionless, the velocity is dimensionless and position is dimensionless - but that means I've sucked dimensions out into a "fudge factor" which I've decided to call "containment parameter". "Confinement ratio" might work too, I don't know what to call it really.

I can't write math very clearly here, but the containment parameter is

2.*.PI..................2*m*V

---------- * sqrt( ------------) (dots are for spacing)

mu_0.*.I..................e

where mu_0 is permiablity of free space, I is current in the coils, m is the mass of the particle in question (electrons here), e is the charge on an electron and V is the voltage on the coil. This term is multiplied to the dimensionless electric field calculation and added to the u X B term (where u is dimensionless velocity and B is dimensionless magetic field) and that full result is the force vector.

Now, things get hairy trying to plot all this. I've got 2 dimensions for current and voltage, 3 dimensions for space and 3 dimensions for velocity. So to just get a feel for the "force volume" in a scalable way (i.e. dimensionless) is an 8 dimensional object.

I've got a few ideas percolating on how to show this thing. I think it'll be fun, but the goal is to get a good understanding of the physics. I'll let y'all know what I come up with!