Near Spherical Magrid

[rjaypeters]

Tetrahedron with bowed grid:

[happyjack27]

it is not identical to the mag field topology of wb-6. wb-6's mag field topology is roughly that of a cuboctahedron [img src=http://upload.wikimedia.org/wikipedia/c ... hedron.gif]

yours is that of a cube w/line cusps all along the edge. wb-6 only has a few very short line cusps right at the vertexes. as do the other designs here.

the idea behind the straight-segment coils is that it makes these line cusps even shorter, while more evenly distributing the magnetic field strength about the sphere.

sure, technically you can go from yours to a wb-6 without breaking or joining any field lines (actually there would be quite a bit of that, on the individual field line level). but at beta=1 the geometric differences in the mag-field are going to become topological differences, in a clinical sense.

the advantage of removing adjacent coils is that it completely eliminates most of the line cusps. but that's something you can only do when there's an even number of faces at each vertex. like in the base-ball seem design. just remove the blue coil. (even if that was a north-out coil while the red was a north-in coil) looks the same to the plasma, except for fewer escape routes.

happyjack:

two problems:

Reading your comments here I think you, and others, may have missed the point of this exercise.

The field goes the same direction for all the faces (out or in) and the opposite direction out (or in) in the small line cusps gaps between the coils.

It is an identical mag-field topology to WB-6 (7, 8?) but the field coming through the line cusps have been squeezed to their minimum (order of a gyroradius length scale). I.e. the smallest gap between the circular coils of WB-6,7 becomes the gap for the whole length of the line cusps of those machines (which is the same length for this configuration).

The rationale being, if the line cusps are the problem squeeze them up as much as possible. Obviously, they cannot be sealed shut completely or that would be a different field topology altogether.

What is clear from the morphology of the mag-field is that by a simplified conservation of flux-tubes the same flux through a central-point cusp is to be expected issuing from its attendant (surrounding) line cusp. (hat tip to Art Carlson on this one)

An analogy would be if you squirt a jet of water at a surface on the perpendicular. The mass flux of water through the diameter of the jet (central cusp) is the same mass flux of the water through the thin annular ring exiting the impact area (line cusp), regardless of the diameter of surrounding ring (length) you choose to analyse.

[D Tibbets]

Reading your comments here I think you, and others, may have missed the point of this exercise.

The field goes the same direction for all the faces (out or in) and the opposite direction out (or in) in the small line cusps gaps between the coils.

It is an identical mag-field topology to WB-6 (7, 8?) but the field coming through the line cusps have been squeezed to their minimum (order of a gyroradius length scale). I.e. the smallest gap between the circular coils of WB-6,7 becomes the gap for the whole length of the line cusps of those machines (which is the same length for this configuration).

The rationale being, if the line cusps are the problem squeeze them up as much as possible. Obviously, they cannot be sealed shut completely or that would be a different field topology altogether.



What is clear from the morphology of the mag-field is that by a simplified conservation of flux-tubes the same flux through a central-point cusp is to be expected issuing from its attendant (surrounding) line cusp. (hat tip to Art Carlson on this one)

An analogy would be if you squirt a jet of water at a surface on the perpendicular. The mass flux of water through the diameter of the jet (central cusp) is the same mass flux of the water through the thin annular ring exiting the impact area (line cusp), regardless of the diameter of surrounding ring (length) you choose to analyse.

The first part of your comments make sense to me, it seems similar to what I argued above. But, the last part does not make sense in light of claimed efficiencies. Perhaps you point is valid in an imaginary system.
If a ring magnet was made of of an imaginary thin crossection , then the outer line cusp might have a surface area similar to the central point cusp, because the point cusp has significantly weaker opposing magnetic fields, while the line cusp is much longer. This, along with the next magnet being placed very close to the reference magnet (the line cusp is much longer, but also much narrower than the point cusp), and no deviation in the distance between the magnets (no curving of the magnets, ie: square coils with sharp 90 degree corners. I can see this imaginary system having equal point cusp and line cusp areas. This picture does reinforce my current belief that the corner areas of the magrid dominates the line cusp losses. Otherwise, higher order polyhedra (which introduce increasing line cusp lengths (I think)) would leak more if the corners did not dominate losses (I think the corner areas would decrease). If this is real and significant, it would improve confinement. Or, the anticipated gains might be completely due to increased quasi sphericity.

But, in the real world (especially when the need for several gyroradii spacing of the magnets was realized) the situation is much different.
The spacing increases the effective width of the line cusps. And the crossection of the coils is not infinitely small. The minor radius of the WB6 coils was ~ 17% of the total diameter. This effectively moves the maximum B-field area towards the center of the coil (point cusp) and away from the line cusps. As the B field strength drops with the square of the distance, this effect is considerable. In a super conductor where there may only be a few thin windings, this effect may be less pronounced(?).

I have wondered if making the coils thicker- especially in the direction towards the center (oval shape instead of circular crossections) would help much. As the point cusps are already considered to be a minor loss area, the benefits may be small. Other concerns about crossectional area exposed to cross field transport, x-rays, neutrons, etc may cause more problems than any minor gains.

[EDIT] The original 4 grid spherical layout that started this thread. would suffer from longer point / face cusps. I assumed it would not be a severe penalty compared to the anticipated gains from reducing the corner cusps. One thing that I have considered is varying the crossection shape of the magnets to mitigate this somewhat. The internal volume of the coil would not change, but the shape would. Near the poles, the coil would be thicker in the direction towards the point cusp, while the coil would be thicker away from the center of the Wiffleball in the regions near the equator of the coil ( the two corner cusps are considered as the poles). This would presumably decrease the point cusp area, perhaps increase the corner cusp area, but the balance may be beneficial, again depending on the relative leakage rate through the cusps, along with other possible concerns, and optimizations.

Dan Tibbets

[icarus]

happyjack:

sure, technically you can go from yours to a wb-6 without breaking or joining any field lines (actually there would be quite a bit of that, on the individual field line level). but at beta=1 the geometric differences in the mag-field are going to become topological differences, in a clinical sense.

Have got experimental data or, at minimum, a numerical simulation to back the beta=1 assertion up? Would be interested to see how you get such an insight.

Or else you have just said that , "yes they are topologically identical". Nuancing a confluence of 3 line cusps into "the spreading out of a funny cusp" is technically meaningless, unless there are other physics taken into account besides mag field topologies (cusp plugging or pinching, enhanced mirror effect, etc).

I didn't see anyone definitively saying which is worse or better (are you? it is not clear), I thought the thread was just investigating different configurations of mag fields. I've got no favourites, in fact, I have grave reservations about any "good" solutions ever being discovered for reasons other than scientific or technical.

[icarus]

Dtibbets:

The first part of your comments make sense to me, it seems similar to what I argued above. But, the last part does not make sense in light of claimed efficiencies. Perhaps you point is valid in an imaginary system.
If a ring magnet was made of of an imaginary thin crossection , then the outer line cusp might have a surface area similar to the central point cusp, because the point cusp has significantly weaker opposing magnetic fields, while the line cusp is much longer.

I specifically said 'flux', which implies a volume flow rate, i.e., particle velocity along the field lines also needs to be considered .... not just area, when comparing line cusp to central cusp fluxes. (To the first order, they balance, what goes in must come out.)

[krenshala]

Has anyone made a new(er) model of the dodecahedral magrid? I know it was one of the shapes Bussard thought would work better (at least, according to what I read ).

[D Tibbets]

Dtibbets:

The first part of your comments make sense to me, it seems similar to what I argued above. But, the last part does not make sense in light of claimed efficiencies. Perhaps you point is valid in an imaginary system.
If a ring magnet was made of of an imaginary thin crossection , then the outer line cusp might have a surface area similar to the central point cusp, because the point cusp has significantly weaker opposing magnetic fields, while the line cusp is much longer.

I specifically said 'flux', which implies a volume flow rate, i.e., particle velocity along the field lines also needs to be considered .... not just area, when comparing line cusp to central cusp fluxes. (To the first order, they balance, what goes in must come out.)

Now you are confusing me even more. Certainly, at steady state, the flux of charged particles in must equal the flux out. But this is a net effect and consists of the sums of the flows through all of the cusps (and if cusp/Wiffleball confinement is good enough, the cross field transport also has to be considered). It does not imply that all of the cusps must be equal. An analogy would be a bucket of water with equal numbers of small and large holes. and one facet supplying water. The bucket will only fill till the water is draining out as fast as the water comes in, but most of the water would be leaving via the larger holes. Certainly with a spherical symmetrical geometry the cusps opposite of each other would be expected to leak at the same rate if they are the same type of cusp. But if a point cusp faces a corner or liniar (funny cusp), the flows may not be even. This is one reason I wonder if nonsymetrically arranged magnets (eg:inverted triangles) can support a near spherical plasma.

Dan Tibbets

[ladajo]

Dan,
I see it more as a bucket with holes as well as evaporation and birds that drink.
Flux in does not equal Flux out. It is loss mechanism dependant.

[happyjack27]

happyjack:

sure, technically you can go from yours to a wb-6 without breaking or joining any field lines (actually there would be quite a bit of that, on the individual field line level). but at beta=1 the geometric differences in the mag-field are going to become topological differences, in a clinical sense.

Have got experimental data or, at minimum, a numerical simulation to back the beta=1 assertion up? Would be interested to see how you get such an insight.

it's not that hard to picture. you weill have much bigger loses out of the centers of the coils, in addition to the losses out of the line cusps. and the plasma will be les table because it's not as convx to the plasma.

[quoteI didn't see anyone definitively saying which is worse or better (are you? it is not clear), I thought the thread was just investigating different configurations of mag fields. I've got no favourites, in fact, I have grave reservations about any "good" solutions ever being discovered for reasons other than scientific or technical.[/quote]

things that are better:
1. more evenly distributed mag field (about the sphere)
2. mag field more concave to the plasma
3. shorter line cusps
4. cusps more equal, such that wiffleball closes them off evenly. this way its much harder for them to push any open. generally makes for a tighter and more stable wiffleball.

[rjaypeters]

Has anyone made a new(er) model of the dodecahedral magrid?...

Over in "magrid configuration brainstorming" since the magrids aren't "bowed."

[D Tibbets]

...

it's not that hard to picture. you weill have much bigger loses out of the centers of the coils, in addition to the losses out of the line cusps. and the plasma will be les table because it's not as convx to the plasma.



things that are better:
1. more evenly distributed mag field (about the sphere)
2. mag field more concave to the plasma
3. shorter line cusps
4. cusps more equal, such that wiffleball closes them off evenly. this way its much harder for them to push any open. generally makes for a tighter and more stable wiffleball.

#2 should be convex towards the center. The concave shapes is what leads to macro instabilities.
I don't think makling the magnetic fields even more convex towards the center improves macro stability. The critical thing is that they do not pass a perfect spherical surface and become concave towards the center. The closer you can come to this spherical surface without exceeding it, will possibly have advantages for central focus and confluence. Also, that apparently is accompanied by the cusp throat geometry becoming more spherical towards the center so that the charged particles are less likely to be fed into the cusps. This pressure induced effect on the magnetic surface is the whole point of the Wiffleball effect. Macro instabilities with concave surfaces is a different issue. I think the Wiffleball surface reflects natural competitive forces. Once a maximum density of charged particles is achieved, any additional input will open up the cusps and paticles will escape more quickly. Thus there is a feedback mechanism in place that limits the Wiffleball's maximum performance.
What worries me, is that if the fields are not symetrical, the weakest cusp configuration will open up (blow out) first and this will limit the Wiffleball trapping factor due to this weakest link. Other cusps might be stronger, but that is irrelevent to containment (within some limits). My main concern is that this irregularity compromises the extent of quasisphericity. Of course with inconsistent magnet shapes on opposite sides , there could still be overall average symmetry once all of the magnetic surfaces are considered. It might be more complexly lumpy, but that may not harm containment or quasisphericity, but I wonder if it could avoid both at the same time.

As far as the face center point cusps, they are much less leaky than the edge or line or corner cusps (at least in any real system). Read about opposing magnet mirror setups, equatorial cusps and mirror reflection to gain a better understanding.

Concerning flux flows being dependent on both cusp area and particle speed, that is certainly true. But, I don't see how it applies to a Polywell, as the charged particles are supposed to be well behaved over their lifetimes. The ions can be ignored as they are primarily contained electrostatically (and edge annealing keeps their radial speed on the edge within a narrow range). The electrons are claimed to maintain monoenergetic speeds (within limits). so they hit all of the cusps at ~ the same speed, so that is a constant. Even if the electrons were thermalized, their average speed at the cusp throats would be the same on average.

I should add that some of the electrons will be upscattered and therefor escape is actually desired, so that do not accelerate the thermalization of the remaining electrons. Still, these higher speed electrons likelyhood of escaping a cusp would be dependant on the cusp area, as the electon motions whether monoenergetic or thermalized are satistically most likely to hit the larger cusps.

Dan Tibbets

[WizWom]

Dan,
I see it more as a bucket with holes as well as evaporation and birds that drink.
Flux in does not equal Flux out. It is loss mechanism dependant.

Um... Gauss' law would say you're absolutely and totally wrong.

There are no magnetic monopoles, so net flux through a closed surface must be zero. That means if a field line goes in, it must come out.

[D Tibbets]

Having greater cusp leakage through selected cusps could direct the majority of fusion ions in one, or several, general directions. This was one of my arguments for the bowed 4 grid design, Assumeing the two corner grids lose several times as many ions as the combined stretched point cusps and line cusps (funny cusps) would allow for smaller collection grids or better directed thrust. One pole (corner cusp) could exaust fusion ions. The ions leaving the other pole could be used for direct conversion. Obvously this would result in less efficient conversion, but if you have enough excess efficiency in the fusion balance, such games could be played.

In this regard the escaping charged particles are already at high speed, probably much above that obtainable in a VASMIR, so it would be an unnessisary step. For more thrust, fuel ions could also be allowed to leave in a steady flow or pulsed. For even more thrust (with decreasing ISP) additional gas could be mixed into the reactor exaust. This may be better than allowing some of the fuel ions to escape if you wish to maintain a net positive usefull power output). Again, it depends on how much fusion excess beyond breakeven you have to play with.

Ignoring fusion (and having an alternate power source), an IEC type of reactor can be used as a high efficiency (high ISP) thruster , with efficiencies at least as good as ion engines, and with greater thrust. Such has been proposed by George Miley at the Univ. of Illinois at Urbana (?).

http://adsabs.harvard.edu/abs/2009AIPC.1103..164M

Dan Tibbets

[ladajo]

Dan,
I see it more as a bucket with holes as well as evaporation and birds that drink.
Flux in does not equal Flux out. It is loss mechanism dependant.

Um... Gauss' law would say you're absolutely and totally wrong.

There are no magnetic monopoles, so net flux through a closed surface must be zero. That means if a field line goes in, it must come out.

Yes you are correct, I was mixing ideas in my head regarding particles and fields, and not clear in my intent.