Near Spherical Magrid

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

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D Tibbets
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Near Spherical Magrid

Post by D Tibbets »

Duplicated as a new topic to seperate it from the many pages in the other thread.


viewtopic.php?t=289&postdays=0&postorder=asc&start=315


I have been considering the idea of bowing the magrid until the ends of the grids meet at the top and the bottom. Start with a WB6 truncated cube. Discard the top and bottom grids. Lengthen the side grids till they are ~ 2 times as tall as wide.* Then bow them inward until they almost meet at the top and bottom. You end up with a 4 sided near sphere shape. The advantages is that you only have 4 magnets instead of 6. It is more spherical. And, there are fewer cusps. There are 4 point cusps instead of 6. These point cusps may be larger, but I don't think they would exceed the area of the original 6 point cusps. There would be two corner cusps instead of 8. The resultant individual corner cusp area may be modestly larger (or not). But the number advantage would be significant. The side 'funny' cusps would be longer individually, but the total would (I think) be the same. So, I think you would have a ~ 4 X advantage in corner cusp losses, while the other cusp losses would be unchanged. I Think this might result is and ~ 4 x advantage in the cusp confinement dominated Wiffleball trapping facter ( the corner cusps are the most significant for losses).This may translate into a 4X density advantage and a 16X fusion rate advantage. Multiply that by the 3-5X advantage Bussard expected from a more spherical shape and the net gain might be ~ 45- 75X.

You would need perhaps two connecting nubs on each side of the magnets- one perhaps neat each end of the grid, but the total nubs in this case would be 8, compared to 12 in WB6. This represents a 1.5X gain in the exposed metal considerations, With separate stand off supports, the number of legs might be 16, instead of the 24 in a WB6 truncated cube design(4 per magnet)- the same gain.

With the two (top and bottom) corner cusps dominating the cusp losses (IE: the alpha escape routes), there may be advantage in designing a conversion system for a P-B11 reactor.


* I say ~ 2X the height for the prebent grids, because as the ends approach each other on the top and bottom, the opposing fields may displace each other to a degree. In order to get a near spherical shape to the internal B-field edge, the physical magrid shape may need to be elongated somewhat ( or perhaps even shortened a bit, depending on how close together they approach each other and the angles involved) . Perhaps as much as 1.5 times as tall as wide for the bowed physical grids would be required.

This closure angle and overall height (vs width) may be adjusted somewhat to maximize alpha collection advantages (make the end cusps more leaky) . This would compromise containment advantages somewhat, but if my estimates are real, you are starting with an ~ 4X advantage, so there is some wiggle room. If your priority is to maximize alpha (or other charged fusion ion) flows through the ends of the device (like in a rocket engine- use one side for direct conversion, and the other end for thrust) you could trade off size for this polar flow advantage. Even for stationary reactors this might give enough direct conversion engineering advantages that it is worth the larger size (especially as that would also ease other engineering concerns).

[EDIT] I don't think bowing the sides would have to result in concave towards the center magnetic fields. Though this concern might require the the prebowed length be be a little longer to prevent the deformations of the opposing fields on the ends resulting in this problem . Or instead of increased length, a shallower closure angle (say each side bowed inward ~ 88 degrees instead of 90 degrees); or a combination of both might be used.


As mentioned above, and as emphasized by
icarus wrote:The whole idea of bowing the coils to arc around a sphere is suspect in my consideration, unless I see a good simulation (or an experiment god forbid) of why it would help.

It seems at first glance to be creating the situation of having a field gradient away from the center of the device, exactly the opposite of what you want for stability of the plasma.
concern for the shape of the magnetic fields on the top and bottom of the grid might be addressed by varying the geometry as mentioned above and as shown in the illustrations. The red shading hopefully illustrates the magnetic field geometry and that the distortion of the face point cusps may not be as great as it might seem from the grids themselves. The magnetic field shapes in the other illustration shows an estimate of the correction needed to restore Wiffleball surfaces to near spherical geometry (instead of convex towards the center) on the top and bottom corner cusps regions.




Image

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Dan Tibbets
Last edited by D Tibbets on Mon Oct 18, 2010 1:35 am, edited 8 times in total.
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chrismb
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Post by chrismb »

...and if you have just two coils facing each other then it's called a 'mirror machine'. One might casually presume that two cusps would be better than 4 or 8.

Unfortunately, many mirror machines have been built but they loose electrons too fast through their two cusps for them to do anything much of interest....

D Tibbets
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Post by D Tibbets »

Did youread the post, and look at the other illistration? The minimum number of grids would be four. You might increase this to 6,8,etc if you wished. The illustration showing the opposing magnet grids are actually one limb of the bowed magrid on each side. Trying to draw the entire magnet grids would be very messy and unenlightening. A three dimensional computer graphic that shows the magnetic fields and grids; that can be rotated and zoomed in realtime would be useful, but is far beyond my efforts here.

The idea that this is a mirror machine is wrong. It has similar corner cusp and funny cusp geometry to WB6. The coil center cusps would be distorted some but I'm hoping this would not compromise them much (less than the benefit of removing 6 corner cusps).What has been described as a virtual magnet made up of the proximal portions of the real grids forms a discontinuous circular grid that forms a 'point like cusp' on the corners. This is one of the major points of the Polywell design , of which this is a warped example of. The question is whether the 'warps are tolorable, or even benificial.

Dan Tibbets
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WizWom
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Post by WizWom »

The advantage to the cubic vs the beach-ball idea is that the corner cusps in a cubic ar in a completely different direction than ANY of the electrically charged surfaces. In a beach-ball, the electrically charged surface near the poles will accelerate electrons nearly directly into the cusp, and then they'll be guided out by the magnetic fields.
Last edited by WizWom on Sat Oct 02, 2010 10:32 pm, edited 1 time in total.
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KitemanSA
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Post by KitemanSA »

WizWom wrote:In a beach-ball, the electrically charged surface near the poles will accelerate electrons nearly directly into the cusp, and then they's be guided out by the magnetic fields.
Gauss's Law?

hanelyp
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Post by hanelyp »

As drawn I see 2 line cusps circling the machine intersecting at the poles.

As for a mirror machine, 2 coils with poles aligned and field lines running the length of the machine would be a minimal mirror machine. 2 coils with like poles together and a cusp at the equator would be a minimal cusp machine. The illustrated configuration is more closely related to the latter.

D Tibbets
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Post by D Tibbets »

Again I repeat, the illistration is essentially a two dimensional crossection of one limb of two opposing magrids. The geometry is comparable to what you would have with a higher order polyhedra, except the bowing to a nearly circular shap is done with one magnet instead of devided amoung multiple straight magnets (with many more resultant cusps).

If the magnetic field distortions caused by the closely approaching magnets can be controlled as illustrated (by closure angle and stretching of the vertical dimension), there is little difference in the edge cusps compared to a planer slab sided Polywell. The only difference is the angle the opposing angles meet at compared to the angle needed to maintain convex magnetic surfaces towards the center. Because in WB6 geometry these edges are at 90 degrees from each other, the distortion (squishing) of the magnetic fields are easily maintained as convex. In a higher order pohyhedra, thes angles may be 60 degrees or 30 degrees, or smaller. With enough sides, a zero (or 180 degree) angle could be approached. At some point this also may reach the point where the squished magnetic field surfaces becomes concave towards the center.

The funny (or what would be a large equatorial cusp in a mirror machine) are present in all Polywell designs. The losses here in WB4 were significant, and probably even higher in WB6 (if you ignore the losses to the square and more exposed surfaces of WB4). This is where recirculation enters the picture.
The performance in the imaginary funny cusps and to a lesser extent the real linear cusps between adjacent magnets apparently works in Polywells because the area (width) is much smaller than in traditional opposing magnet mirror machines. The magnet edges are very close together in Polywells, while there is considerable separation in mirror machines (unless you wish very tiny internal volumes, which defeats the purpose). Also, since the edges are close the effective magnetic field strength on each side of the cusp is increased, (which I believe is why the effective cusp width is much less). You could do this with two opposing magnets in a mirror machine if you increased the magnet strength to equivalent levels, but this again would greatly decrease the internal volume aviable between the opposing magnetic coils. In a sense, the Polywell is a three dimensional version of a 2 dimensional very strong magnetic field mirror machine. In the mirror machine you can trade volume for confinement, while the Polywell avoids this tradoff.
[EDIT] I should add the Density increasing and cusp pinching Wiffleball effects inherent in the Polywell design that separates them from the opposing magnet mirror machines (keep in mind that the solenoid type mirror machines are a different beast). What I said above about the linear cusp width being much narrower in the Polywell should be abridged to include: because of the Wiffleball effect, the openings into the cusps, including the linier cusps are much reduced. Both the effective width and height of the openings into the center point and edge cusps are reduced, and the width of the openings into the linear cusps are reduced.

In any case if the funny/linier cusps work in WB6, they should work equally well in this configuration.

Concerning charged particle accelerations through these cusps, if there is better focus through the cusps (which I doubt because the magrid surfaces are curved and symmetrical in both this and WB6 designs) this design might produce a deeper potential well if there is better focus. As far as this happening to charged particles within the magrid, it is a non issue because (as already mentioned) you would have to ignore Gauss's law. As far as well focused electron beams (if that occurred) exiting on the opposite cusp with out scattering, I believe that issue has been explored in early Polywell research and to be found to be a non issue as the electron scattering/ divergence in the core quickly disperses the electrons into dispersing radial vectors. The only effect I see, is if the potential well is closer to the accelerating voltage on the magrid, it might effect somewhat the dynamics of selective (and desired) escape of upscattered electrons.
Also, in this design, I see the electron guns and possibly ion guns being placed on the side point cusps anyway, The end corner cusps would be left unobstructed to better facilitate fusion ion collection into a direct conversion array.

Dan Tibbets
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icarus
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Post by icarus »

Image

Image

Image

Image

ladajo
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Post by ladajo »

I like it, but no sharp edges allowed.
Can you round the corners?

icarus
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Post by icarus »

Can you round the corners?
Can do anything, it's a cartoon sketch. Probably also like to;

i) engineer a proper stand-off spacing to adequately 'zip up' the line cusps
ii) engineer a proper tube radius to sphere radius ratio
ii) design the can/tube cross-section to be conformal to the resultant mag-field (including for operational plasma whiffle-ball push back).

For now, it is just a thought-piece. The currents all flow around the coils the same direction, i.e., central-cusp mag-fields all radially-directed identically.

D Tibbets
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Post by D Tibbets »

Having 8 bowed grids, instead of the 4 (without the horizontal division) I suggested, that are show by the illustrations of icarus would also be more quasi spherical than the slab sided magrids. In this case there would be 6 corner cusps as opposed to the two in my suggestion or the 8 in the slab sided WB6. So there is still a corner cusp number advantage and a possible sphericity advantage without resulting in higher order polyhedron and associated increased numbers of corner and face point cusps. This may be superior if the center point cusps in the 4 grid version has too much distortion of the central point cusps. There are longer funny cusps than the 4 grid version. Where the trade off between the possibly more distorted point cusps in the 4 grid version and this 8 grid version's increased funny cusps lengths (along with twice the point cusps) would lie is uncertain. I think the the 4 grid version (where each of the 4 grids extends from the top to the bottom) has the same funny cusp lengths compared to WB6. This version would I believe, have 8 equivalent magnets contributing to the the funny cusps, verses the 6 magnets in WB6. IE: total funny cusp losses ~ 1.5X that of WB6. I don't know how these losses would compare with the presumed decreased losses in the corner cusps. If there is a net gain (before recirculation), increased internal densities might be possible. With good recirculation the electron losses may not be effected much, but it is the density gains and spherical convergence gains(?) that this geometry may allow.

This design would suffer the same corner cusp magnetic field squishing that might cause concave magnetic surfaces as described for the 4 grid version.

The other bowed example championed by Talldave [EDIT- actually I think I should have said KitemanSA] is difficult to compare as the funny cusps are replace by 'X-cusps' and even more point cusps. Only experiment or a good computer model would answer which is best (if any of them).

Dan Tibbets
Last edited by D Tibbets on Thu Oct 07, 2010 10:03 pm, edited 1 time in total.
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KitemanSA
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Post by KitemanSA »

Please clarify. Are the coils in icarus' sketches alternating or uni-directional?

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Post by WizWom »

I really think you want the corners NOT to be coplanar.
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ladajo
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Post by ladajo »

In WB6 & 7 the current flows are opposite in each adjacent coil.

icarus
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Post by icarus »

I really think you want the corners NOT to be coplanar.
Which corners and co-planar with what? (There are at least two sets of curves that could be construed as 'corners').

I'll assume you mean the sharp corners of the coils and coplanar with the tangent pane of the generating sphere, where four of them come together .... and then ask why not?

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