Virtual Polywell

drmike · Post by **drmike** » Thu Nov 01, 2007 9:52 pm

For this kind of stuff I use C. It's been a long long time since I used FORTRAN! I've got a model of the B and E fields done, and I can post that code if you like. The formulas are in the "virtual polywell" write up I'm working on: http://www.eskimo.com/~eresrch/Fusion/fusion.pdf

I'm trying to get some really crude formulas so I can use those fields (stored in 400 MB files) so I can see if the fundamental polywell idea is stable. Since I'm more of a hardware guy than software, I'm pretty sure my code can be improved by an order of magnitude.

An "open source" virtual polywell could be a fun way to stay off the street at night

Solo · Post by **Solo** » Thu Nov 01, 2007 10:48 pm

Hey, that sounds like fun! I'd love to have a look at the code if you don't mind posting it somewhere. I don't know if I could be any help, but if I see anything I think I can take a stab at, I'll let you know.

drmike · Post by **drmike** » Fri Nov 02, 2007 3:42 am

OK! I put the code up in the same directory:
http://www.eskimo.com/~eresrch/Fusion/

There is no index.html, so it just shows up as a directory listing. The *.c files are the code I used to create the pictures in the "Virtual Polywell" pdf. I use GSLmath and pnglib, so feel free to substitute if you have alternative ways to do the same thing.

I'm absolutely certain the code is not efficient!! It's probably also got bugs, so fixing things so they are correct will certainly help. It _looks_ right, but that doesn't mean it is.

The force and plot force were just aids to help me see the magnetic forces and how they relate to particle motion. I have not documented that yet.

I just got a formula for the electron fluid electric field for a "static" assumption. I'll start writing that up over the weekend (with luck). Maybe over the next few weeks I can explain the math and we can begin to code it up for some really crude checks on how polywell works. It would definitly be a lot of fun!

Solo · Post by **Solo** » Fri Nov 02, 2007 4:04 am

Whoo boy! Looks like I opened my mouth too fast!

I guess I should have mentioned that I've only just had the first two semesters of C++ here at school.

I'll see what I can make out; I'll probably have a few questions for you once I figure out what to ask!

Thanks!

drmike · Post by **drmike** » Fri Nov 02, 2007 5:35 pm

Ask away! Sometimes "experts" make assumptions that are wrong, and simple questions expose it!

Solo · Post by **Solo** » Fri Nov 02, 2007 6:38 pm

looks like I'll need to download GSL and learn about it. Seems like it has some pretty powerful functions.

So I gather that you go through and use the GSL functions to integrate and find the field strength at a point due to each point of the coils, correct? That's a lot of computation, but I guess that's why we have computers, eh!

Ok, so in order to find out whether the polywell forms, we need to run enough electrons at once to see how they interact with each other and with the coils, right? Do collisions need to be accounted for? I guess that's where the terabytes figure comes in, huh.

I need to do some research on modeling methods, in terms of the physics mainly, and not so much in terms of the programming. Of course, programming limitations dictate what kind of approach works best.

One thought for simplification of the field calculations: if the coils are symmetrical then you only really need to calculate one field shape, and then just superimpose the same shape three times over the volume, but orienting the coil different ways and in the appropriate position each time. (This should work for the B-field, but with the E-field, you might have to be careful because they tend to interact I think, with the whole Faraday effect and whatnot.)

MSimon · Post by **MSimon** » Fri Nov 02, 2007 8:05 pm

Solo,

The problem is that everything interacts with everything.

Moving electrons (and ions) create magnetic fields. These interact with the "fixed" fields. Lorenz.

Then you have beams bunching. Ions/electrons entering and leaving the system. Slow electrons in the center.

I think I can build a quantum computer to solve the problem for $10 to $15 million including staffing. Hahaha.

Doing what simulations are possible until that quantum computer becomes available is a good start. It should give us a feel for the problems even if we don't get exact solutions.

drmike · Post by **drmike** » Sat Nov 03, 2007 4:00 pm

I've uploaded a new version (with a "part 2") of the "virtual polywell" at http://www.eskimo.com/~eresrch/Fusion/fusion.pdf which includes the thermal and spatial distribution assumptions I mentioned above. The math is pretty thick and so are the assumptions. But it gives me some clues on what to think about.

The first thing I noticed as I was finishing is that the electron temperature needs to be cold if there is no current flow. I want to change the assumptions and play with the math some more but I think it's important to add ions in at this point. The formulas don't change, they just get a lot more messy! And there are more of them.

I think the theory can be useful. But it would be really nice to have some real experiments to compare it with!!

dch24 · Post by **dch24** » Sat Nov 03, 2007 7:49 pm

Hi drmike,

fusion.pdf looks good. I'm a programmer (well, an EE), not a physicist, so I'm reading it to understand the program, not checking the physics or math. But I did notice: permeability is misspelled permiability on page 1, if you find that helpful.

drmike · Post by **drmike** » Sat Nov 03, 2007 10:46 pm

Yes, thanks! I've been really, really, really bad at spelling since I was a kid. I should check to see if texmacs has a spell checker, I'm usually more worried about the equations (and I make spelling typo's there too, so don't mind people telling me where the mistakes are!)

drmike · Post by **drmike** » Fri Nov 16, 2007 4:07 am

I've been having an argument with myself, and since I'm not really winning I figured I'd let more people in on it. The problem is simple: compute the orbit of a single electron in the polywell. In dimensionless parameters it is just

Du_x + b_z*u_y - b_y*u_z = - C_p* e_x
-b_z*u_x + Du_y + b_x*u_z = - C_p* e_y
b_y*u_x - b_x*u_y - Du_z = - C_p* e_z

Where D == d/d(nu) = dimensionless time derivative, b_j is dimensionless magnetic field, e_j is dimensionless electric field and u_j are the dimensionless velocities of the electron (see http://www.eskimo.com/~eresrch/Fusion/fusion.pdf for details).

The argument is whether to solve this numerically or analytically. They both have advantages. Analytically it's a huge mess, but possible to do since none of the fields I'm looking at are time dependent (even if they were slowly time dependent it'd be possible analytically). I haven't had a whole lot of time to grind through the analytical solution, but it'd be a blast to just _do_ it. But I'm not so sure I'll get any answers any time soon.

The reason this is important is find out if non interacting electrons will stay in the polywell. If the system is not stable for even single electrons, it is hopeless for lots of them.

Interactions and full fluid equations are much messier and it'd be pretty hopeless to do analytically. But I guess that gives me a good reason to do an analytical model - it gives a way to check the computer model for a pure numerical solution.

Hmmm... I guess arguing out loud helps!

tonybarry · Post by **tonybarry** » Fri Nov 16, 2007 11:51 am

Hello drmike,
One question I feel ought to be asked even though it's possibly a bit dumb ...
Why do you not constrain your simulation to two dimensions? Adding a third dimension just boosts computational requirements, for (possibly) no real gain in understanding.

Regards,
Tony Barry

MSimon · Post by **MSimon** » Fri Nov 16, 2007 1:04 pm

Electrons don't act right in two dimensions. The collision probabilities change drastically.

This really is a space and time problem not an area and time problem. And yes it makes the comps really long.

I'm still wondering if we can't devote spare cycles to the project.

If we can't outsmart the problem maybe we could beat it to death.

drmike · Post by **drmike** » Fri Nov 16, 2007 1:51 pm

The real orbit is a 3D spiral. The fields change in 3D along different planes, and the electrons orbit will take them across different planes.

Lots of 2D computations have been done with plasmas, and that's why tokamaks are where they are today. It's a hard problem!! And everytime you think you have some kind of understanding, real experiments prove you wrong.

I think we need both - a good theoretical foundation and good empirical knowledge that shows the limits of theory. At this point the computational feasability is within grasp, it's just a matter of having the ability to pay for it! Hopefully we can do some simple models that will convince the people with the deep pockets that it is worth while pursuing deeply.

Solo · Post by **Solo** » Fri Nov 16, 2007 8:04 pm

Kind of going with what MSimon was talking about in terms of manifolds the other day, would there be any way to deal with the magnetic and electric fields together using a relativistic description of the electrons? I've never heard of such a thing, so I'm guessing it's a dumb idea.

My thought was that maybe you could just have one value for the E and M fields combined at each point in space, from which you could compute the force on the electron, given its speed.

I ought to mess around with that idea over break.