ions in potential well

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

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jcoady
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Joined: Fri Jul 15, 2011 4:36 pm

ions in potential well

Post by jcoady »

How are the ions in the potential well supposed to travel in order for the polywell to work. Are the ions supposed to fall straight down into the well and collide at the bottom of the well. Or is it expected that they will follow an elliptical orbit and collide with other ions on some other elliptical orbit that intersects it. Here is an image depicting a mass moving in a 1/r^2 potential well.

http://dl.dropbox.com/u/5095342/PIC/Images/potwell.gif

Are the trapped electrons of the Polywell supposed to form a perfectly shaped potential well where the shape of the well curves is the same in all directions from the center of the well, or is it expected that the shape of the potential well curves are not necessarily the same for different directions from the center of the well. If the shape of the well is different in different directions then it seems that the ions will follow some sort of elliptical orbit when dropped into the potential well.

happyjack27
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Post by happyjack27 »

from my sims, http://www.youtube.com/user/happyjack27, the overall containment region of the ions tends to follow the shape of the electron core. as it approaches b=1 that becomes more spherical.

http://www.youtube.com/watch?v=BY0-1CGX ... ature=plcp

that cloud is made up of a superposition of many orbits at many energy levels and many radial velocity components. from my sims it appears that the the radial component never gets very large. their mutual repulsion tends to keep them at the same radial velocity, which the law of large numbers tends to keep at zero. this results in very good central convergence.

jcoady
Posts: 141
Joined: Fri Jul 15, 2011 4:36 pm

Post by jcoady »

I created my own PIC simulator for the polywell to experiment with. A PIC simulator is usually used for low density plasmas. For high density plasmas an MHD simulator is more appropriate. What I was seeing with my PIC simulator is that the magnetic grid would influence the location of the trapping electrons and in turn the location of trapping electrons would determine the shape of the potential well. The density of the electrons in the polywell varies with position, and this resulted in a potential well with different shape profiles depending on the direction from the center of the well. When I dropped an ion into this well I noticed that it would follow an elliptic path and not necessarily pass through the center of the potential well.

Here is a link to my web based 3D PIC simulator which uses a java applet in a web page. It runs best on with Firefox and google chrome browsers which support webgl. After the applet is up and running in the web page, which can take up to 20 seconds depending on your machine, you can press the start simulation button.

http://members.shaw.ca/johncoady/polywellPICApplet.html

After it has been running for a while, you can scroll down the web page and see profiles of the potential well start to form for a few directions from the center. After a large enough potential well forms, I would click on the "Drop neutral atom" button to drop an atom into the potential well at the configured location which would then ionize into proton "red" ball and "electron" green ball. A force is then exerted on the ion in the direction of the electric field at its location. This force may not be in the direction of the center of the polywell, it depends on the shape of the potential well ath that location, and it will be in the direction of steepest descent. As a result the ion would then follow an elliptical trajectory when moving in the potential well, the more transverse momentum it had the further away its path would be from the center of the well.

ladajo
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Joined: Thu Sep 17, 2009 11:18 pm
Location: North East Coast

Post by ladajo »

Somehting interesteing and related is the presentation at IEC 2011 where Madison showed that they thought they were getting more beam fusion than core fusion. The profile they mapped showed low fusion in the center. Joseph should be interested in this as it is a little similar to what he his thinking.

In any event keep pluggin away. And HappyJack is good to talk to as he has done a lot of good work using a graphics processor to run his models.

happyjack27
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Joined: Wed Jul 14, 2010 5:27 pm

Post by happyjack27 »

nice sim, jcoady!

what you describe is kinda what i'd expect from a single ion - i'd it expect it to take sort of a flower orbit. i forget what they're called.

but when you have a whole lot of ions, that in itself introduces new dynamics. their mutual repulsion gives them a sort of "viscosity" if you will (after all, does not viscosity in liquids come largely from incompressibility?), and you get sort of a "swarm intelligence" effect as i described.

so with many many ions (and electrons) the "orbits" look a lot more like a bunch of (fairly evenly distributed) straight lines passing very close to the origin. i mean, clearly they're still elliptical/sinousoudal, just the eccentricity of the orbits get _very_ high as these planets are rather anti-social. so sort of like a "spiky ball" if you will

http://www.dreamstime.com/royalty-free- ... ge13123245

though that image is a little decieving, actually, from my sims, at least. from my sims at least, after some time you get a full range of energy levels, i.e. distances that the orbits come out from the center. so a a spiky ball with the spikes at all different lengths.

there's debate on whether there's an "annealing" effect in real life that drives them towards the same energy level. there are a number of limitations in my sims, most notably particle count and sim time. (what you see in the videos translates in real time to something on the order of picoseconds, and each sim particle represents many orders of magnitude of real particles.) their could exist phenomena that my sims aren't able to show due to these limitations. the goal of my sim was merely to overcome some of the limitations i saw in other sims, not to not have its own set of limitations.

on that note, come to think of it, since my point charges represent millions of ions, their charge is that of millions of ions and their trajectory probably represents the average trajectory of milllions of ions, so take into account the central limit theorem.... well, the individual ions orbits might not be nearly as eccentric. i think the reasoning still applies, though, even if the result is not as pronounced.

what i was going for in my sim was more of a finite-element approximation of the em-field, both staticly and dynamicly; of the plasma dynamics, if you will. i suppose it does have its shortcomings (as just mentioned) when it comes to showing individual trajectories. then again, i could simply lower the particle representation ratio to 1:1 and that specific shortcoming would vanish.

D Tibbets
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Joined: Thu Jun 26, 2008 6:52 am

Post by D Tibbets »

Not based on sims, but on hearsay, A. Carlson insisted that the potential well would be square in the Polywell. And Bussard in his Google talk actually confirmed this- for the initial electron potential well. But once ions are introduced, their greater momentum, will drag some of the electrons towards the center and an elliptical potential well will form. *

In a low collision plasma, the ions would assume elliptical orbits, very few of them would pass through the center. If there is any confluence at all a vertual central anode will form. The magnitude of this effect plays a role in the shape of the potential well (double wells, etc), along with fusion rates, bremsstrulung issues, etc.
The conditionality of the plasma, while dependent on average density, confluence and associated MFP- the local collision effects compete with the space charge effects. Ideally the density throughout the mantle regions will be such that the MFP is greater than the radius of the machine (or is that the diameter?). Thus annealing is possible. The question is not one of pure radial or circular orbits but of average elliptical ion orbits of uncertain narrowness.

Using MHD analysis may be problematic as I believe it has been claimed that this is not the state in Polywells, IEC devices.

* A. Carlson claimed that bipolar flow occurred in the cusps, I assume through similar localized effects (the plasma would be closely coupled in this regard) and this wrecked any claimed ion containment greater than electron containment. My response is that this is an absolute view that is inappropriate. Because of momentum differences, an electron may be locally accelerated more (by a factor of 60) by a transient nearby ion (a Coulomb collision), and tend to tag along to a modest extent. But an electron traveling outward through a cusp (thanks to the overall negative space charge generated by the 1 ppm electron excess) will tend to tug an ion along by only 1/60th as much as the opposite relationship. Both of these localized actions- ion tugging on an electron and an electron tugging on an ion. oppose the general space charge effects. That an elliptical potential well forms but there is not bipolar flow in the cusps is because of the different momentum of the ions and electrons and while the plasma is not collisionless, but it is far from a closely coupled plasma.

Dan Tibbets
To error is human... and I'm very human.

ladajo
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Location: North East Coast

Post by ladajo »

Would not square be bad? Would it cause a bias for a maxwellian distribution? In any event, I think that all the profiles I have seen are not square, but curved. I think that is better in the sense that it helps unbalance the distribution.

D Tibbets
Posts: 2775
Joined: Thu Jun 26, 2008 6:52 am

Post by D Tibbets »

ladajo wrote:Would not square be bad? Would it cause a bias for a maxwellian distribution? In any event, I think that all the profiles I have seen are not square, but curved. I think that is better in the sense that it helps unbalance the distribution.
I'm not sure what you are asking. My impression is that a pure electron plasma will quickly assume a square potential well.* This is the case unless you pump in electrons with radial velocities at shuch a rade that the radial thermalization is not reached and this is [perhaps one of the reaoning behind critisisms that intolorable electron currents are needed to maintain a radial electron distribution (this is a statric consideration that does not account for the dynamics between the electrons and ions). I believe that means that many of the electrons are as far away from the center as possible. This would imply that the electrons have nearly circular orbits, I guess that would be thermalized from a radial electron vector perspective. An ion outside the square well would be quickly accelerated till it passed the edge of the potential well then it would have a constant velocity, assuming there is not a central virtual anode formation. My impression is that this is not good, but this starting condition is a static situation that has almost nothing to do with the dynamic potential well that forms due to the electron- ion interactions. A complex potential well shape is possible, anything from a smooth elliptical well, to various wells with shoulders and a central peak (virtual anode). If there are knobs that can modify the relationships to an ideal configuration is one of the issues of viability, or at least optimization. As Bussard repeatedly stressed, people thinking in static terms are missing the boat.

* A pure electron plasma would also be much less dense that the mixed plasma (neutral to the sixth decimal place) in a working Polywell. Perhaps no more than ~ 1/1,000,000 as dense- that would fit with the ~ 1ppm density difference in the ion and electron population (assuming a 1 Z ion like deuterium) in a working Polywell. Otherwise the Coulomb pressure would not be containable.. If this is related to issues like the Brillion limit and other issues is beyond my pay grade.
Keep in mind that the ions have a much longer lifetime compared to the electrons and they are annealed to a low energy dispersal in the radial (and angular momentum?) renormalization spread. Thus the ions can repeatedly tug the electrons inward so that the electrons maintain a more radial component to their orbits than they would do on there own. And this is done without the energy cost mentioned above. This may also play into Bremsstrulung issues, though my understanding in this regard is fuzzy, I mean fuzzier. :wink:

Dan Tibbets
To error is human... and I'm very human.

happyjack27
Posts: 1439
Joined: Wed Jul 14, 2010 5:27 pm

Post by happyjack27 »

my sims show a pretty square potential well in an all-electron plasma.

the electrons are pushed by their r^2 repulsion to the shape that minimizes their local voltage gradient, but that's limited on the outside by the magnetic fields, which turn any outward accelleration around. so what you get is the electrons all running to the surface of a sphere. and so now that you got a fairly hollow sphere instead of a filled one, you get the electric field of a hollow sphere -- you get a square potential well.

remember that the electrons are going to do whatever they can to try to eliminate any potential wells. and they succeed in that in the closed little klein bottle that the magnetic fields make for them.

...also, regarding electron thermal distribution, from my sims the electrons are pretty cold. even if they start out hot, they tend to cool down over time. they eventually discover that their lowest energy configuration lies on a small surface ("stable manifold") at maximal distance from the other electrons, so their own little spot on it, and all paths lead to it. the few strays that get knocked or whatever outside of the core, however, get pretty hot.

though my sims doesn't take into account quantumn physics. that would be rather interesting. really from a quantum electrodynamics perspective they'd probably tend towards some infinite set of harmonic orthogonal orbits (err..waves) about the stable manifold. in which case they need not be so cold to be at minimum energy level. (which might lead to more bremstralg (sp?) losses) and you might get some interesting entanglement effects, which i'd imagine can only be good for electron confinement.

happyjack27
Posts: 1439
Joined: Wed Jul 14, 2010 5:27 pm

Post by happyjack27 »

here's some videos of elecron-only plasmsa in my sims using different magrid configurations, showing the shape of the core at various plasma densities and magnetic field strengths.

you can see it can range from quite hollow to fuzzy (and from anti-spherical to spherical) depending on how you set "the knobs" as dan says above. essentially i'm playing w/the "knobs" throughout the videos. ("net charge" and "amp turns")



http://www.youtube.com/watch?v=UUKEUXvM ... ature=plcp

http://www.youtube.com/watch?v=8GFmtQJrLq8

http://www.youtube.com/watch?v=ULfi1fr3 ... ature=plcp

http://www.youtube.com/watch?v=B3HIHfpx ... hA&lf=plcp

edit: another nice one: http://www.youtube.com/watch?v=OdR4LPbz ... hA&lf=plcp

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