Carlson and Nebel

Discuss how polywell fusion works; share theoretical questions and answers.

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kcdodd
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Post by kcdodd »

hanelyp wrote:Running a tokomak in IEC mode (magnet confinement of electrons, electric confinement of ions) would be an interesting experiment. No cusps for electron leakage, but magnetic contours less favorable to stability.
Quit frankly I dont really understand how you can hope to make a stable confined plasma in a tokomak to begin with. Its a uniform field, how do the electrons/ions know where the center is "supposed" to be?
Carter

StevePoling
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electron distributions?

Post by StevePoling »

Indrek,

If I understand your picture correctly, an ion sitting in that region of outer darkness will be most strongly accelerated toward the red regions. However, once it gets into the green it'll feel the spacial separation of the four red regions and when it gets close enough, it'll be steered toward one of the four.

Presumably, other ions will feel likewise and the best ion-on-ion action will take place in the red spots. If so, the alpha radiation should originate from these red spots, too.

I sort of get the feeling the electrons clump into those red areas like a panicked stadium crowd rushing a limited number of gates. The clumping gets worse and worse until the electrons are turned around and try another gate. I don't pretend to understand this, but I am guessing that this wiffleball behavior is when all the electrons tell their friends the gates (cusps?) are "so crowded nobody goes there anymore."

You know, all my thinking is way too Newtonian about this. This all looks like classical statistical mechanics. I'm thinking of these electrons and ions as little billiard balls. Has anybody thought to look at this through quantum mechanic lenses? Are the wave equations way to gnarly to consider?

Indrek
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Post by Indrek »

No Steve. The red region near the coils is at +10KV. The black is ground (0V). The red-yellow-green-black transitions form the potential gradients.

The ions want to move from the higher potential to the lower potential. The idea for fusion is that the ions are added at the edge of the middle lower potential area and so are drawn towards the middle low potential and oscillate into it gaining kinetic energy and slowing as they move away from it - until they stop and start falling back in again. So back and forth a 1000 times until they collide and fuse.

You can think of it in terms of elevation and the ion as a billiard ball. Red is higher ground, black is lower ground - the ball wants to roll downhill.

But in this picture they can oscillate only with so much energy because if they have more they'll end up outside the system through the faces, and then go downhill towards the wall and will be lost.

The problem is that the effective energy they can oscillate at is too low for fusion.

- Indrek

TallDave
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Post by TallDave »

The Chacon paper is probably the best description of ion behavior.

StevePoling
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Post by StevePoling »

I got the sign wrong, eh? If those red spots are at way high + voltages, then they must be caused by clumps of positively-charged ions.

Let me run at this again. The electrons are spiraling along field lines, then the field lines clump into those "red" areas whereupon they reverse direction. A few get through the cusp to swing around and recirculate, but as long as there aren't too many we can ignore them. This leaves the bulk of the electrons oscillating between cusps. I'd love to see a map of electron density as we add more and more electrons to this mix and they start "pushing" the magnetic field lines outwards.

Meanwhile, there are fuel ions circulating, much more massive and oppositely charged. They're attracted to the electrons via coulomb forces, but the electrons are small and easy to miss. (But if the ions do manage to hit an electron, oops, it's a quanta of brehmsstrahlung loss.) Hopefully, the electrons who are more agile, will be moving much faster, too fast to make a run at the positive ions, hit them and cause brehmsstrahlung loss.

Am I correct to presume there's a soup of slower-moving ions and faster moving electrons? If these guys are all just bouncing around randomly, like air molecules, I think that's the maxwellian distribution of Rider's critique. The counter-argument that there's a "drifting maxwellian" distribution makes me think Dr. Bussard expected the bulk of ions and/or electrons have a pattern of circulation. Or he intended to impose one (somehow) upon them. Or is the non-uniformity of ion distribution as seen by those red spots what he had in mind?

I'm feeling like a really dull student right now. Sorry if this has become tedious.

charliem
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Post by charliem »

Steve, I think that Indrek's last graphic is just the E-field not densities. The red regions are at a high possitive potential, but not from the ions in them but from the electrons inside the machine.

According polywell theory ion density should maximize near the machine center (light yellow), and minimize in those peripheral red regions. About speeds ion maximize it also at the center, and minimizes it near the magrid, while electrons do the opposite.

Moreover, ions movement should be roughly radial.

StevePoling
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Post by StevePoling »

Indrek wrote:No Steve. The red region near the coils is at +10KV. The black is ground (0V). The red-yellow-green-black transitions form the potential gradients.
Where's the +10KV come from? I thought it came from a mob of positively charged fuel ions, but charliem just said otherwise. If they're from the electrons inside the machine, how do you get + V from negatively charged electrons? Potential is relative, but you said the black area was 0V, so, because I see no black stripe in the gradient from the red spots to the center, the center has to be +V, too.

Is my association of voltage/E-field with charged particles stupid and the E-field derives from some kinky cross-product action in the magnetic field that I've forgot from the physics I took 30 years ago?

kcdodd
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Post by kcdodd »

I think that is indreks point: the electrons do not make a very deep well. It is lower then +10k in the center, but still very much higher then 0. So in indreks model ions will only see maybe a few hundred volts drop (cant tell from the scale exactly) toward then center.

One question I have for indrek is if the simulation is run to the maximum electron density. In other words, a density where electrons stop going into the core, or blow out the core whichever is first. Because higher densities would possibly mean deeper wells then it's showing?
Carter

Indrek
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Post by Indrek »

The coils are directly charged at +10KV - like the grid in a fusor - using transformers and wires and stuff.

The force the ion experiences is not dependent on the particular voltage number (or color) but rather at the rate of change in the potential at the point where the ion is.

The force the ion experiences is calculated as F=-grad(V)*q - where grad(V) is the rate of change in potential at the given ion position. Anyways I suggest you google these concepts and try to remember your schooling.

But there is clearly a lack of clear explanation on the net on how polywell is supposed to work. With all the people around noone's really bothered to write a simple two-page clear explanation. So we end up with this over and over again.

Perhaps someone respectable in the know person would be willing to make something like that. So we can avoid this. I'm willing to make/contribute graphics/video if any are needed or desired off my site.

kcdodd: it took me couple of days to run a single simulation. I was severely CPU constrained so I never got to try all the possible parameters.

In that picture the potential is from 0..+10KV with 32 levels, so one level is at around 312V.

- Indrek

Art Carlson
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Post by Art Carlson »

Indrek, what physics is your model based on? 1-fluid/2-fluid MHD, PIC, ballistic ions, Boltzmann electrons??? What does the 3-d structure look like? Is the central well a well in all directions, or could it be that it is even shallower (or non-existent) in the directions of the corners of the cube?

Art Carlson
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Post by Art Carlson »

Concerning questions from several authors about tokamak physics:
The radial electric field in a tokamak is a very important parameter that is thought to influence the confinement by up to a factor of two. What's important is actually the gradient in the field (the curvature in the potential). The picture is that the EXB drift is then dependent on radius and tears convective cells apart before they can get very big. Unfortunately, the plasma pretty much chooses its own potential profile, and there is very little that can be done about it from the outside. One thing that influences it is fast ions from neutral injection that are lost quickly when they are on certain orbits.
An essential feature of a tokamak is that the field is not uniform, but it twists as it goes around the torus. The field lines sort themselves into flux surfaces. The particles tend to stick to these surfaces, and that is how they know where the center is.

Indrek
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Post by Indrek »

The short answer would be: none of the above. Probably.
As I'm not really sure what ballistic ions or boltzmann
electrons are ;). I am a product of google and wikipedia
and I am an amateur so probably I did something unconventional,
probably something very wrong. For my dayjob I program
web pages and internet applications (mostly low level
big P2P applications - Skype).

But I do need someone telling me the truth about this so
please don't hold back. If you even bother to continue
from this point on.

I managed to reduce the calculation space using inherent
symmetries in the polywell:

http://www.mare.ee/indrek/ephi/symmetry/
http://www.mare.ee/indrek/ephi/symmetry2/
http://www.mare.ee/indrek/ephi/symmetry3/

The electric field of the coils and surrounding static
elements is calculated using this method:

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

The magnetic field from the coils is precalculated using
the analytic equation for a ring of current (equation
given at the end of this document, seems the Dolan fusion
book is down):

http://www.mare.ee/indrek/ephi/efield_r ... charge.pdf

And during simulation through bicubic interpolation:

http://www.mare.ee/indrek/ephi/interpolate/
http://www.mare.ee/indrek/ephi/interpolate2/

I track individual electrons and at each step I recalculate
the magnetic and electric fields they see.

I calculate the fields from each individual moving charge,
summing them up. From a distance I use an aggregating grid
though (for charge and current approximations).

From close by I model individual moving electrons as
spheres of charge, and calculate the fields they generate
and their derivatives, as detailed here:

http://www.mare.ee/indrek/ephi/savart.pdf
http://www.mare.ee/indrek/ephi/vsphere.pdf

I put these calculated values into a grid so that I can apply
tricubic interpolation on them. The tricubic interpolation
algorithm I use is this:

http://www.lekien.com/~francois/papers/LeMa05/

Once I have this interpolation grid I move electrons ahead
by one step. For that I use the Runge-Kutta-Nystrom 4 with
adaptive step size:

http://www.mare.ee/indrek/ephi/nystrom.pdf

Additionally I keep the interpolation grids of two previous
steps and use them together with the latest to do Lagrange
extrapolation during the RK4 steps:

http://en.wikipedia.org/wiki/Lagrange_polynomial

Using my quad core 2.5GHz pentium I managed to calculate
one step in 5-10 seconds. One step is 1e-11 seconds (there
are up to 256 adaptive substeps done as well).

Getting anywhere like this took couple of days of calculation
so I didn't really get very far ;)

One thing I failed to do was to check my model against
known plasma behaviour. Mainly cause I don't know much
about known plasma behaviour ;) A beam of electrons
dispersed, that was about my only check for correctness.

I should probably go and try out PIC instead. But I kind
of got bored of all this for a moment there.

So here you are. For more information you can see
my ephi homepage:

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

- Indrek

rcain
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Post by rcain »

Hi Indrek

Love your page http://www.mare.ee/indrek/ephi/ and the stuff on it.

I've seen some of these images already you posted on this forum, but its nice to see them all together.

One suggestion, if I may, could you add some further explanations around them, particularly, placing them in context with the attainment of fusion itself in a BFR? - just for thickos like me.

A question also: "Videos of electron paths inside the cube polywell" (pw3d_small.flv and pw2d_small.flv) - there seem to be both 'red' electrons and 'green' electrons.

I thought at first, you had both electrons (to form the wells), then +ve ions injected, but then realized that a) they were moving at about the same speed (which wouldn't be the case), and b) that they changed colour.
(though i did also think i spotted like-repelling like and unlike attracting, so I was doubly confused).

please could you explain to me exactly what is going on in this simulation?

rcain
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Post by rcain »

hanelyp wrote:Running a tokomak in IEC mode (magnet confinement of electrons, electric confinement of ions) would be an interesting experiment. No cusps for electron leakage, but magnetic contours less favorable to stability.
erm, how about the other way around - tok in a wiffleball - a spinning plasma (or perhaps just a spinning virtual cathode). By my current (limited) understanding, wouldn't such improve both confinement and density?

I think its called charged-sheath effect (magnetohydrodynamics).

There's a nice vid of one here... http://www.youtube.com/watch?v=9hqN8lmupDo

And a bit of research here (though I cant get to it) ... http://www.iop.org/EJ/abstract/0741-3335/40/3/005

I'm sure the Tok folk know all about this stuff.

Could it be induced by phasing the coils on the WB machine (along with POPS perhaps), or possibly by instantiating just the right amount of asymmetry at startup?

Or maybe its been ruled out already?

MSimon
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Post by MSimon »

Phasing the POPS coils has been mentioned around here (or was it at NASA spaceflight) as a way to get the plasma spinning.
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