POLY-TOK?

[KitemanSA]

Has anyone investigated a hybrid polywell/tokamak machine?
Picture a tokamak with a toroidal poly-grid inside such that the reaction volume is toroidal but the magnetic fields press inwards more strongly as the reaction volume gets denser and presses outward more strongly. (IIRC., that means the poly-grid would provide a convex field?) The inner poly-grid would be comprised of simple rectangular coils (as close ot square as needful) arranged in a toroid, with larger units (with more windings) on the outer major radius, smaller rectangles, fewer windings on the inner, properly graded around the minor diameter. Imagine a medium resolution finite element model of a toroid.

At certain points around the circumference of the grid, quads of coils would be intensionally misaligned to allow injection ports thru the funny cusps.

Thoughts?

[ladajo]

I have been pondering the efficacy of going down from a six-sided to a four sided. Or, maybe a three sided.
The primary loss mechanism is the point cusps, thus a reduction in their count seems logical.
If you have a six sided machine, that is eight point corner cusps, and six ring center point cusps, making for a total of 14 point cusps.
A four sided machine presents four corner cusps, and four ring centers, for a total of eight point cusps.
This could drop point cusp losses by almost half...
As the research move from arguing, essentially, in magnitude reductions, a half reduction could be become significant.

[KitemanSA]

I have been pondering the efficacy of going down from a six-sided to a four sided. Or, maybe a three sided.
The primary loss mechanism is the point cusps, thus a reduction in their count seems logical.
If you have a six sided machine, that is eight point corner cusps, and six ring center point cusps, making for a total of 14 point cusps.
A four sided machine presents four corner cusps, and four ring centers, for a total of eight point cusps.
This could drop point cusp losses by almost half...
As the research move from arguing, essentially, in magnitude reductions, a half reduction could be become significant.

I was under the impression that the primary loss mechanism was the LINE cusp that, in a Polywell, should NOT exist. Properly built with square and triangular magnets, the point and bare funny cusps SHOULD recirculate cleanly.

[ladajo]

I think the issue with the line cusps is there is more statistical opportunity for gyro-radius 'matching' allowing particles to walk into and through the cusp. ???

[KitemanSA]

I think the issue with the line cusps is there is more statistical opportunity for gyro-radius 'matching' allowing particles to walk into and through the cusp. ???

I suppose that may be the mechanism, BUT there should not be any line cusps to begin with. The line cusps are the result of using toroidal magnets rather than the conformal square ane triangle magnets of the theoretical Polywell.

MAYBE, someone should build an actual cube-octahedral Polywell like Bussard first described. Then there would be point and funny cusps but no line cusps.

[ladajo]

Ok, however won't there be a cusp no matter given you are bringing opposing magnetic fields together at a 'joint', for lack of a better term. The shape of the magnet doesn't negate the fields opposing and creating a 'joint'. Maybe I am missing something here. Maybe I need to go back and look at what they meant when discussing "funny" cusps. We have cusps in the center of the magnets, at the apex of multiple magnets, and between the edges of two magnets (be they straight or curved). So, three types of cusps. And, testing and modelling indicates the largest leakage is occurring at the cusp between the edges of two magnets.
My reading of the current work gives me the impression that less cusps is better, which makes sense. Thus, my thoughts about shifting from a six sided cube to a four sided polyhedron gives less cusps. The shape of the magnets could be round, multisided straights, or even down to a triangle. Although, I suspect there may be uniformity issues in field strength at the 'corners' once you start moving away from a circle. The 60 degree corner of an isosceles triangle may present a weaker field at the resultant cusp than a circle, and as such could limit the 'squeeze' desired to close the cusp, given there is less to 'squeeze' in field flux. I am thinking of it like a bar magnet at the extreme, where maximum flux is seen on the sides, and minimum flux is seen at the poles, which creates that classic bar magnet field pattern, 'the stretched donut'. If you bend the bar, you get weakened flux on the convex side of the bend, and compressed flux on the convex side. Therefore, the inference is that circles are the best call to minimize the overall flux density variations around the magnet, thus provided the maximum flux for compression by the plasma, which in turn makes for 'tighter' cusps.
What is interesting here is that the (e-) leak mechanism is a function of the (e-) gyro-radius, which may relate to the lines of magnetic flux density. Makes me wonder if there is a resonance or matching connection between leakage rates for a given (e-) gyro-radius and the magnetic flux line density. And, how gyro-radius varies in relation to plasma compression as well as the flux density variance due to changes in plasma pressure.
In general, gyro-radius increases with higher plasma pressures given a corresponding increase in temperature or a compression of a confining magnetic field. So it follows there are likely resonant points of increased leakage when gyro-radius equals multiples of the magnetic field flux lines density allowing the (e-)s to find more escape opportunities at those points via coupling to the lines of flux. In my mind it is like a filter screen of parallel fibers and the oscillating (e-), as it changes frequency (gyro-radius), finds a matching gap width between the fibers and passes through to become leakage. At the end of the day, keeping the filter tight and gyro-radius big seems to be the path to least leakage, along with avoiding a resonance condition between the two. A tight filter wants dense flux and anything to eliminate cusps or reduce their count is a good call. Also, it follows that the longer the 'straight' length of the fibers, the more likely a resonant (e-) to the fiber separation distance will find a gap. So, with that in mind, maybe reducing the number and length of magnet to magnet edge boundaries is also a good call.
This EMC2 paper gets into it a bit:
https://www.frontiersin.org/journals/as ... 00074/full

[KitemanSA]

Ok, however won't there be a cusp no matter given you are bringing opposing magnetic fields together at a 'joint', for lack of a better term. The shape of the magnet doesn't negate the fields opposing and creating a 'joint'. Maybe I am missing something here. Maybe I need to go back and look at what they meant when discussing "funny" cusps. We have cusps in the center of the magnets, at the apex of multiple magnets, and between the edges of two magnets (be they straight or curved). So, three types of cusps. And, testing and modelling indicates the largest leakage is occurring at the cusp between the edges of two magnets.

In a proper Polywell, there are no “edges” between “two” magnets. It is all one magnet. The triangular and square “edges” have current flowing in the same direction, thus are one magnet, not two opposing.

My reading of the current work gives me the impression that less cusps is better, which makes sense. Thus, my thoughts about shifting from a six sided cube to a four sided polyhedron gives less cusps.

For polywell to work, every vertex must be between 4 faces, a 4 sided polygon only has 3 faces meeting at each vertex. Won’t work.
Ummm, FEWER cusps is not the real issue, It is lower cross section that makes the difference. Line cusps have a lot of area. That is why we should shrink the line down to a point-like funny cusp.

The shape of the magnets could be round, multisided straights, or even down to a triangle.

The point is to have the edges of ALL adjacent magnets carrying current in the same direction. The WB series with the round magnets did not. BAD implementation of the basic polywell design.
[/quote]

[KitemanSA]

If you bend the bar, you get weakened flux on the convex side of the bend, and compressed flux on the convex side. Therefore, the inference is that circles are the best call to minimize the overall flux density variations around the magnet, thus provided the maximum flux for compression by the plasma, which in turn makes for 'tighter' cusps.

I suspect the second “convex” was ment to be “concave”.
Indeed, if you look back at prior discussions, you will find I often used the term “square planform” meaning take the 4 corners of the “square” and draw “great circle” lines between them. Each line would then be concave toward the center of the sphere and would cause the inside flux to be greater than the outside.
None-the-less, I still suspect that having 12 point and 12 funny cusps would have less uncontrolled leakage than 12 point and 12 line cusps.
The issue isn’t any single magnet, it is the MagGrid. With circular magnets on 6 faces, the resulting triangular faces are in even worse shape than with square planforms where the circles are in the WB series. Those tortured triangles would have even weaker point cusps that the MagGrid I have described and would have the detestable line cusps.

[ladajo]

No matter how I arrange faces, given the magnets are polar, to have aligned/coupled seams, you need to alternate the fields (Clockwise/Counter-clockwise). This still results in both edges and points where the fields oppose and don't couple.
The linked paper helps show what I am talking about. Granted, it speaks to mechanical stability as the goal. Which is really about the "motion" (torque) in the motion-flux-current model. It still helps understand the magnetic fields not being able to being all aligned (coupled) when you bend them into a 3d shape (polyhedron). There are going to be cusps.

https://archive.bridgesmathart.org/2017 ... 017-79.pdf

[KitemanSA]

No matter how I arrange faces, given the magnets are polar, to have aligned/coupled seams, you need to alternate the fields (Clockwise/Counter-clockwise). This still results in both edges and points where the fields oppose and don't couple.
The linked paper helps show what I am talking about. Granted, it speaks to mechanical stability as the goal. Which is really about the "motion" (torque) in the motion-flux-current model. It still helps understand the magnetic fields not being able to being all aligned (coupled) when you bend them into a 3d shape (polyhedron). There are going to be cusps.

https://archive.bridgesmathart.org/2017 ... 017-79.pdf

Why are you showing solid magnts. We are talking electro-magnets.

This links to a graphic of a cube-octahedron.
https://en.wikipedia.org/wiki/File:Cubo ... olored.svg

The square faces are EMs pointing one way, the triangles are EMs pointing the other. Let us assume the squares are clockwise. The triangles would thus be counter-clockwise. Along each edge, the current is flowing in the same direction. Only the vertices have conflicting flows. Each vertex in the cube-octahedron has 4 edges connected, an even number. Polywells won’t work without even numbers of edges meeting at the vertices. In this case, numbered clockwise 1 thru 4, 1 & 3 would then have current flow in one direction (say into the vertex) and 2 & 4 would have current flow in the other. The field disappears. That is what makes the cusps “funny”. But with realistic construction, i.e. the hard angles at the vertices actually being slightly rounded, there is a gap at each vertex so no metal to be grounded against. Thus, the “naked” funny cusp.

The flux flows from the center of the squares thru the centers of the triangles. Between each pair of congruent centers is a quasi-flat field. The centers of each face are point cusps. the vertices are funny cusps. The edges have uni-directional flow, thus NO cusp.

I am puzzled about the confusion!

[ladajo]

From a field perspective, magnets are magnets. How the fields interact remain the same.
You went where I was headed, the edge cusps can couple with that arrangement. And, as noted, the point cusps at the 'merge' will not. And, the center cusps on each coil will also still exist.
For the coupled edge cusps, the lines still don't mix. they just complement, and as such can be compressed better by the plasma pressure. There still remains (be it smaller) opportunity for an (e-) to resonate with gyro-radius to field lines spacing and walk it's way out. I still think overall, there is a sweet spot to be found, not that it will guarantee success, where the number of cusps, their coupled / non-couple (as I call it) orientation, and plasma pressure will have the optimized minimal loss rate. I don't think there is a likely chance of multiple configurations providing best confinement. I think it will play out to be one optimized version, which probably looks to minimized cusp counts.
I did not sleep at a Holiday Inn last night, nor play a Plasma Physicist on TV. I reserve full rights to be completely wrong.

[KitemanSA]

For the coupled edge cusps, the lines still don't mix. they just complement, and as such can be compressed better by the plasma pressure.

There seems to be a fundamental misunderstanding of what YOU mean by “edge” cusps. There is no lit that I have every seen that defines such.
There are point, and line, and AFAIK uniquely in a proper Polywell, “funny”.

So, what are “edge” cusps? And if you mean LINE cusps along the edges of a true Polywell, there are none.

[ladajo]

Yes, I mean the Line cusps found at the parallel field edges on the sides of the cube, vice the point cusps found at the corner faces where three or more fields interact, or the point cusp found in the center of the 'donut', where the toroid interacts with it's own field.

I do not agree with your argument that two complementary fields merge at a 'line/edge'. They do not merge, there is a cusp construct. While the two fields are oriented in the same direction they retain individuality in the flux lines. This is why the (e-)s can still couple to the flux lines and begin the leakage hopping across the lines based on resonance between their gyro-radius, flux line spacing, and reflective properties created by the electro-static effects from the diamagnetic layer current (with a thickness at the gyro-radius range). That said, the edge/line cusps are not the primary leakage, it is the corners and center "Point" cusps. The edges are negligible based on physical observations and sims.

I think the piece you are missing is the interaction between the magnetic field flux lines and the diamagnetic current in the sheath around the plasma. The loss points at the cusps is where the diamagnetic current is the least, which allows the (e-)s to couple to the field lines and then escape. At the line/edge cusps, there is more diamagnetic current in play than the points. There is also a relationship with the (e-) gyro-radius, sheath thickness, and field flux lines density. It seems to me that when these all align (resonance if you will) the (e-) can find the door and cross the sheath to the flux and leak. The line cusps on the 'edges' of the cube are the much lessor loss (to an almost none), and the corner cusps are the dominant by far. This was seen in both the test article and the sim work. I call it "Spikey-Ball", as you may remember. The loss rates are similar between the corner cusps and the coil center cusps, both "point" cusps. The original (old) thinking was the line cusps (edges) would be the dominant problem, and is the reasoning behind looking to 3D polyhedral constructs. The loss rate for the line cusps is low enough it can be dropped from the confinement efficiency calculation, and loss rates become based on the 14 points for the six sided cube (6 centers + 8 corners). This is my rationale for considering how to reduce the number of corners and centers. Each point cusp is the manifestation of an ambipolar field, and as such becomes a bi-directional gateway. We can squish them (Beta =1) or reduce the number of them in efforts to seek better confinement if my understanding is correct.

The Coils in WB-8 were charged, however this was determined to not be needed, and very hard to technically manage, and only potentially useful for P-B11 aneutronic pursuits. They were not able to achieve High Beta with WB-8 as it displayed low confinement to the point that (e-) injection was essentially peeing into the wind.

WB-X focused on the core mechanisms for conditions needed to achieve DT net, with emphasis on getting to High Beta. The bottom line is that they hadn't fully sorted the base mechanisms of magnetic fields / (e-1) injection and establishment of a sufficiently pressurized (-) plasma to gain High Beta (Magnetic containment of (e-) plasma), then driving a well with enough efficiency and sufficient for (+) fuel containment (negative potential well depth), and fuel acceleration (heating) for fusion conditions (power generation). WB-X approached the problem by use of two opposing plasma guns to flood the core during startup to achieve High Beta before (e-) leakage could prevent the startup cycle from reaching Beta=1. Slamming the inside of the core to close the holes with a rapid pressure build of the plasma before the startup (e-) source ran out of (e-)s. WB-8 max input for (e-) was 150kw. WB-X max input was on order of 500 to 700MW pulse. More or less like setting off an (e-) bomb inside the magnet containment field to 'instantly' (~15us) pressurize it to Beta = 1 during start-up. The resultant High Beta lasted about 5 us, which correlated to about 700 "bounces" of a given (e-). WB-8 demonstrated about 7 "bounces" for an (e-). The outcome of WB-X was physical validation of 'Step1': Establish High Beta Condition for (e-) Plasma Magnetic Containment. WB-X also demonstrated that there is a 'sweet spot' for field strength between too low and too high for enhanced confinement. It is important to note that before and during startup, the field lines are 'in the core', and the act of start-up quickly establishes the plasma with a sheath of diamagnetic current which forms the 'wall' that excludes the field lines from penetrating the plasma, and allows the building plasma pressure to push and compress the field lines out from the core. That layer becomes, essentially, the wall of the balloon being inflated.

[KitemanSA]

Yes, I mean the Line cusps found at the parallel field edges on the sides of the cube, vice the point cusps found at the corner faces where three or more fields interact, or the point cusp found in the center of the 'donut', where the toroid interacts with it's own field.

I do not agree with your argument that two complementary fields merge at a 'line/edge'. They do not merge, there is a cusp construct. While the two fields are oriented in the same direction they retain individuality in the flux lines.

I am puzzled about you line of thought. It seems you think there is a line cusp between every wire in a magnet coil!
Since that is obviously absurd, there must be a breakdown in communication.

I am not sure what you mean by “two complementary fields”.
Again, in the cuboctahedron linked above, the silver bars at the edges between each square and triangle represent a combined coil from each. Since the current in the squares coils all flow in one direction (assume clockwise) and the current in the triangle coils all flow the other, the current in every pair of adjacent square + triangle coil segments will flow in the same direction. It is ONE COIL.

The effect is the the field flux enters the volume thru the point cusps in the squares and exits thru the point cusps in the triangles and crosses the combined coil segments as if they were one coil, because in effect, they are.

Are you envisioning both shapes carrying current in the same direction, like EVERY shape flowing clockwise? That would do what you describe, but that is NOT the polywell design.