15th US-Japan Workshop on IECF

[D Tibbets]

Torulf2, I'm not sure what you are saying, the line cusp in the picture is obvious. The two magnets shown are opposing. It is not a solenoid arrangement. The solenoid arrangements are generally accepted as hopeless, due to poor magnetic curvature surfaces leading to macro instabilities.

In the picture 1/2 of a ring magnet is seen on the right, and a full ring magnet on the left. The plasma shows a point cusp with plasma exiting to the left, and a line cusp between the magnets with the plasma exiting in a line or cone between the magnets. If the magnets were the same diameter, this would be a classic biconic opposed magnet mirror machine. In the picture the right magnet would also have a point cusp exiting to the right. What is not shown (in my opinion) is a third magnet located further right. This would result in a picture mirroring what is seen. Copy the picture, flip it horizontally, and paste it on the right side of the original picture. Now you can see the two line cusps along with the two end point cusps. If the central magnet is removed, it would have one equatorial line cusp- the classic mirror machine. By having the central magnet the single equatorial line cusp is split into two, but importantly the width of these two line cusps are now much narrower,and the net result is better containment. If you assume magnets of very narrow width(horizontal width in the picture) or mathematical lines representing the magnets much like Bussard used in his modeling until WB6) the gain would be modest, perhaps halving the net losses from the line cusp component relative to a two magnet mirror machine. But with real magnets with real significant width/ thickness, the relevant magnetic fields are measured from the can surface, not the center line of the magnet. As such the gains from splitting the equatorial line cusp results in significantly greater gains in the confinement efficiency of the line cusp. The fatter the central magnet the better, within some practical limit. For example an oval instead of a circular magnet cross section. For other reasons increasing the diameter of the central magnet may also have benefits. Primarily by increasing the internal volume and by changing the direction/ angle of the two line cusps. This may have benefits in direct conversion grid layout outside the magrid, along with external direction guiding of the escaping plasma- such as for a rocket engine or transformer like energy conversion if the machine is pulsed. Also, having smaller diameter end magnets help to push the B fields to a common focus between the central magnet.

In the Polywell there are at least 6 point face cusps, and these may dominate the losses. In this design there are only two point cusps, so there may be significant gains. The line cusps are very similar to the truncated cube polyhedral shape for the Polywell. There are two end magnets with a central magnet. The difference is that in the Polywell this central magnet is actually a complex assembly of four seperate magnets, but still the result is the splitting of a single wide equatorial line cusp into two much narrower line cusps. In the Polywell the resultant line cusps are spiky, but otherwise the same concept.

Consider a 2 dimensional representation of a 3 D object., much like a globe of the Earth. Lay out the two end magnets withe the central magnets laid out side by side- 4 long. Now assign line cusps to the end magnets- it is circular with spikes towards the intersections of the central magnets. Because the central magnets are close to the end magnets at the intercepts, the line cusps look almost like 4 separate point corner cusps, but they are still obviously line cusps. This picture may reveal the similarity of the two designs.

The end result is similar, the magnetic fields still converge to a central minimum/ focus. Any line drawn through the center is still symetrical. The line cusp (corner cusps in the Polywell) losses could be made similar . And the face point cusps are reduced from 6 to two. I'm not sure if full volume could be maintained with the three ring design compared to the Polyhedral design ,but it would be close, especially relative to the net cusp losses. The magnetic fields remain symetrical. A line drawn through the center will always be symetrical. I think Wiffleball inflation is still valid. The internal volume is similar, so plasma volume and trapping is similar.
That is the problem with the two magnet opposing magnet mirror machine. The magnets could be moved very close together to minimize the line cusp losses, but this results in the internal volume also shrinking proportionately. That is the whole point of the Polywell- avoiding the volume shrinkage that occurs with line cusp loss minimization in a mirror machine.

Your mention of the plasma recirculating through the center along field lines could occur, but as it has been hashed out on this forum, and stated clearly in the patent application, this is intolerable. Due to up scattering the electrons and boosting their energy with each cycle, the electron temperature would be out of control and criticisms by Dr A. Carlson would apply- that is- extremely high internal electron potentials would be required to keep losses in check. Once the electron escapes outside the space between the magnets, if it is to be recirculated, it must first stop (be decelerated), and re enter through the same cusp. That way the electron energy upon reentry remains constant. Failing to stop the electron (up scattered) requires that the electron needs to be removed from the system (hit a wall), before it can circle around along a field line and reenter through another cusp.

Dan Tibbets

[paperburn1]

Your mention of the plasma recirculating through the center along field lines could occur, but as it has been hashed out on this forum, and stated clearly in the patent application, this is intolerable. Due to up scattering the electrons and boosting their energy with each cycle, the electron temperature would be out of control and criticisms by Dr A. Carlson would apply- that is- extremely high internal electron potentials would be required to keep losses in check. Once the electron escapes outside the space between the magnets, if it is to be recirculated, it must first stop (be decelerated), and re enter through the same cusp. That way the electron energy upon reentry remains constant. Failing to stop the electron (up scattered) requires that the electron needs to be removed from the system (hit a wall), before it can circle around along a field line and reenter through another cusp.

Dan Tibbets

Before you laugh and shame me off this forum, please remember I am an amateur.
A thought has occurred to me on plasma recirculating. We really do not need to have all the polygons symmetrical. Could it not be possible to have the re-circulation path end up at a magnetic "dead end" by using different sized coils and a odd number of coils leading to a point where the electron loses all its energy gained by its transit ? just a thought that came to mind.

also found this PDF, stuff we already know but interesting about funding and where the next round came from. search polywell.
http://www.dtic.mil/dtic/tr/fulltext/u2/a546511.pdf

[Torulf2]

I think the is 3coils 2 plasma volumes and the 2 line cusps are connected and some of the loses recirculate around the central coil.
Ass in my picture.

[ladajo]

Ass in my picture

I ass-u-me that you mean "as in my picture"

[D Tibbets]

I think the is 3coils 2 plasma volumes and the 2 line cusps are connected and some of the loses recirculate around the central coil.
Ass in my picture.

I disagree. There is one plasma volume, with a central focus (at the center of the middle magnet). I have modeled this with with a magnetic field tool. By adjusting the seperation, and the relative strengths of the end magnets versus the central magnet, a contrally minimal B field region is created, just like in the Polywell. By varing this ratio the central minimal B field can assume a torus shape or a dumbell shape. Such variations at appropiate frequencies might do some interesting things for the plasma behavior.

Again charged particles could circulate around any of the three magnets and re enter the internal volume. The same applies to the polyhedral Polywell. But this is undesired as pointed out in the EMC2 patent application. An electron that is not stopped and reversed through the same cusp continues on, probably trapped on a field line. The up scattered energy this electron has is retained, and once it loops around back towards another cusp, it is accelerated by the magrid and re enters the magrid at the accelerating voltage plus the retained up scattered energy. This causes a build up of electron energy in the machine beyond the potential of the magrid. This has various undesirable effects on Bremsstruhlung, etc. Also the average electron temperature would be pushed up and this would result in more relatively up scattered electrons which decreases same cusp recircultaion. It is a run away process. I think you would end up with a broader energy distribution of electrons (especially the high energy thermal tail) and an effective decrease in net containment for several reasons. This is why you want to intercept these escaping up scattered electrons. The non up scattered electrons will always (theoretically) stop and re enter the same cusp because the accelerating potential on the magrid is higher than the electron energy at the bottom of their potential well. I take this situation to imply that in WB6, if the recirculation was 90% effective then ~10 % of the escaping electrons were up scattered. And these were lost because they hit the Faraday cage before they could complete (reach the apex) of the external field line. This is a tolerable and necessary loss.

The system is three magnets only. Adding additional magnets cannot keep a single central focus, instead a stack of individual machines is created (sort of like Nebel's proposal to stack IEC cells to make a working reactor). The end face centered point cusps is reduced and this might have value, but it also begs the question of how you get electrons and/or ions into the machine.



As for the question about changing the geometry to have a preferred cusp for recirculation. I doubt that this is helpful from a containment perspective. Basically you want two things. Minimize cusp losses at any and all cusps. You cannot improve past this baseline. To purposely open up one cusp will result in overall worse containment. This may actually be useful, but only if you want to manipulate the plasma flow outside the magrid- for direct conversion schemes or rocket thrust, but you sacrifice baseline containment to do this.
The other issue is symmetry. You don't want the electrons entering from only one direction. True,they quickly scatter into a near spherical radial distribution, but still there would be a small (tiny, large?) deformation of the potential well. Also, any cusp does the recirculation, as the electrons escape they are decelerated by the evenly distributed magrid potential, reversed and re accelerated back through the same cusp. I do not see any advantage to opening up any one cusp. A confounding issue may be primary electron injection (from the E-guns). There may be a trade off between the cusp tightness (and thus losses) and injection efficiency. Some compromise may work best. As such those cusps that have an E- gun might benefit from being slightly more open.

Dan Tibbets