Dodec Magnetic field?

Discuss the technical details of an "open source" community-driven design of a polywell reactor.

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93143
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Post by 93143 »

Do you even read my posts?
93143 wrote:Density times average outward flow velocity of electrons (proportional to sqrt(drive voltage)) times effective cusp area (proportional to gyroradius^2) times electron specific energy (proportional to drive voltage) times recirculation loss fraction (constant due to geometric similarity).
93143 wrote:I believe drive voltage is an independent parameter unrelated to the scaling laws
93143 wrote:B^2 is plasma density.
93143 wrote:The gyroradius is going to go down as B goes up.
(Specifically, gyroradius is inversely proportional to B.)

This stuff is standard plasma physics.

Assumption: Wiffleball trapping works like how it sounds, rather than just having all of the charge collect at the edge in a thin magnetized sheath that directly connects to the cusps via flux tubes. This is necessary in order for the concept of effective cusp area to make sense. The observed virtual well generation efficiency (80%+) seems to me to imply that this is true, and I've already made half a stab at explaining why I think it's physically plausible.

I can't remember why I think the cusp width scales with the gyroradius. It seems logical, and I think Art and Dr. B both thought this, but at this point I can't be bothered to check...

Result: Point cusp leakage is independent of both device size and applied magnetic field. It is similarly easy to show that line cusps leak as B*R, given the same assumptions.

Where's the problem? Except that I noticed a flaw in my analysis halfway through and changed my postulated loss scaling laws as a result - maybe that confused you?

icarus
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Post by icarus »

93143:

You are contradicting yourself.
average outward flow velocity of electrons (proportional to sqrt(drive voltage))
93143 wrote:
I believe drive voltage is an independent parameter unrelated to the scaling laws
It is most certainly not
This stuff is standard plasma physics.
or else everyone would know how it was going to work and scale, not to mention generally recognised "standard" plasma physics is done in Tokomak-type environments.

If you would write out for each of your given variables what you think the scaling law is we can begin to discuss if/why your might be wrong/right. At present, it is a disparate bunch of "I said this/that" and it doesn't really hang together coherently, unless I was to be some kind of cyber-psychic, You make it sound like it is so obvious it should only take a couple of lines, please indulge me once more (and keep the unnecessary comments about my confusion to yourself if you wouldn't mind)

Here they are again, your variables, how do they scale?

1) plasma density
2) average outward flow velocity of electrons
3) effective cusp area
4) electron specific energy

93143
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Post by 93143 »

icarus wrote:93143:

You are contradicting yourself.
average outward flow velocity of electrons (proportional to sqrt(drive voltage))
93143 wrote:
I believe drive voltage is an independent parameter unrelated to the scaling laws
What I meant (my phrasing was extremely bad) is that it's independent of B and R, which are what we're assessing scaling laws with respect to. Actually it just occurred to me that this probably isn't true...
Here they are again, your variables, how do they scale?

1) plasma density
B^2. This is standard plasma physics, is it not? Magnetic pressure at a given plasma temperature and beta value results in a density x?

Expanding on my realization above: if the drive voltage (corresponding to plasma temperature) is increased by some factor, the plasma pressure at a given density increases by the same factor, so the magnetic field has to increase by the square root of that factor or else the density drops by that same factor. Right?

Given this, we have a first-order inverse scaling of density with drive voltage, resulting in point cusp losses scaling inversely with drive voltage while being unrelated to anything else...?
2) average outward flow velocity of electrons
sqrt(drive voltage). This one is pretty simple. Drive voltage gives you the energy of the electrons at the edge of the wiffleball. Even if they aren't moving mostly radially, the characteristic radial velocity should still scale with the square root of the average kinetic energy. This isn't cross-field diffusion; it's a low-field direct leakage path.

The average velocity counting electrons entering the cusps as well as leaving is much lower and depends on the loss fraction, but we don't really care about that.
3) effective cusp area
gyroradius^2 or 1/B^2 for a point cusp, R*gyroradius or R/B for a line cusp. Seems reasonable and the idea has some heritage, unless I've misremembered... basically the idea is that the magnetic field can't close the cusps beyond a certain point, determined by the electron gyroradius. Art thinks it will have something to do with a hybrid gyroradius in accordance with his quasineutral cusps argument, but either way the scaling is the same.
4) electron specific energy
Drive voltage. Again, dead simple.

You have to make an assumption about how the cusps work in order to assess loss scaling this way, and as Talldave pointed out, cross-field diffusion doesn't require a cusp to leak through, but I think it's reasonable to say this could be one part of what's going on.

I seem to be at least partially in scratch-paper mode... this is why my research notebooks are so hard to read...
Last edited by 93143 on Thu Mar 26, 2009 9:50 pm, edited 1 time in total.

icarus
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Post by icarus »

Oh yes, you make it sound all so simple. Probably you are being too simple.

You must realise that those are some huge leaps of faith that you have just put forward? (Some might unkindly call it wishful thinking). The loss scaling is the big question of this device, to say it is simple strikes me as arrogant, if not ignorant.

Drive voltage is another variable that must be taken into account for cost, engineering and physics so saying that "scaling matters only for B and R" is being willfully ignorant I think. What about arcing, power supply cost and other limitations on drive voltage, are they not as real as magnetic field and reactor physical size limitations?

Now that the stakes are in ground, and the evasive hand-waving has subsided, it is time to look at the devil in the details.

Maybe we can verify your unbelievably simple power loss scaling law for Polywell and then investigate where the dodec configuration will come into it.

EDIT: you have massively edited your previous post with expansions, changes, etc so I don't know how much of my above is relevant, I'll wait until you have a "final" version until I make another reply.

93143
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Post by 93143 »

There are things I have stated are simple, and there are things I have not stated are simple. The overall loss scaling over the range required is one of the latter.

I have addressed the idealized cases of point cusps and line cusps, making certain assumptions about how the wiffleball behaves. It almost certainly does not behave exactly like this. In addition, I have ignored cross-field diffusion, the geometric effects on cusp leakage spreading (and thus, possibly, loss fraction) of growing the reactor while shrinking the cusp, the effects of increased velocity distribution relaxation on cusp behaviour at larger reactor sizes, etc.

Dr. Bussard said R^2. I'm trying to figure out why. I'd just wait for the results, but an increasing number of people seem to be unnecessarily pessimistic and unwilling to wait and see what's actually going on here. If I weren't busy with my Ph.D. research I would put some real effort into trying to counter Art's theoretical arguments, but as it is, handwaving is the best I can muster. Deal with it.

Also, my previous post is finished, so go ahead.

EDIT: I don't know why I got so worried about the drive voltage thing all of a sudden. It's still independent of B and R; it just affects the density on its own, which you can account for separately. The basic B and R scaling laws won't change, unless there's a second-order effect caused by the change in plasma temperature that alters the exponents...

TallDave
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Post by TallDave »

Talldave: I thought intercept area WAS a cusp loss, since that's how the electrons get to the unshielded metal. If the point cusps really do have constant leakage at a given drive voltage, that then implies that cross-field diffusion dominates at net power - but that's not plausible because Bussard was very insistent that net power was impossible if the fractional intercept area was above a certain maximum. So line-like cusps and/or flux-tube leakage mechanisms look more plausible. Unless I've missed something...
Ah, OK, that makes sense. The interconnects intercept a certain portion of the electrons recirculating in the cusps. Obvious in retrospect, I guess I just hadn't really thought about it that way before.

KitemanSA
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Post by KitemanSA »

TallDave wrote: Ah, OK, that makes sense. The interconnects intercept a certain portion of the electrons recirculating in the cusps. Obvious in retrospect, I guess I just hadn't really thought about it before.
They don't need to. Pair them, move them aside (away from the point of closest approach of the "real" magnets, run current thru them, they are protected and no loss channel.
Easy!
Last edited by KitemanSA on Fri Mar 27, 2009 4:29 am, edited 1 time in total.

hanelyp
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Post by hanelyp »

93143 wrote:Dr. Bussard said R^2. I'm trying to figure out why.
Let's see if I can come close.

Point cusp area scales 1/B^2.
line and funny cusp area scale with R/B.
In both cases losses through the cusp ~ pressure*area. or B*R for line and funny cusps. point cusps have proportionately less area with larger scale, so become insignificant for a large polywell.

Cross field diffusion losses, if I guestimate correct, is area*pressure/B*thickness of the magnetic shield. again B*R. I'm sure I'll be corrected here if an accepted model says otherwise.

Subtracting losses from the B^4*R^3 fusion scaling, I get a net gain of B^3*R^2.

KitemanSA
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Post by KitemanSA »

hanelyp wrote:
93143 wrote:Dr. Bussard said R^2. I'm trying to figure out why.
line and funny cusp area scale with R/B.
Why should the funny cusp scale with R/B? They seem more like point cusps to me. Not the quasi-linear varient we get with the truncube non-Polywell, but a real one from a recticube.

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Post by TallDave »

They don't need to. Pair them, move them aside (away from the point of closest approach of the "real" magnets, run current thru them, they are protected and no loss channel.
Easy!
Hrm. There must be something preventing that, or Bussard and Nebel wouldn't have made them that way (in the latter case, twice).

I'm guessing the reason is either that the current flow or engineering dictates they be at the corners, or has to do with the fact the interconnects carry the Magrid's large positive charge, and the funny cusps were the least disruptive place to put them.

KitemanSA
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Post by KitemanSA »

TallDave wrote: Hrm. There must be something preventing that, or Bussard and Nebel wouldn't have made them that way (in the latter case, twice).

I'm guessing the reason is either that the current flow or engineering dictates they be at the corners, or has to do with the fact the interconnects carry the Magrid's large positive charge, and the funny cusps were the least disruptive place to put them.
DrB specifically said he did it out of the need to build quickly. He also thought that the current thru them would provide a degree of protection. He also stated that he thought they should perhaps be electrically isolated.

The current task at EMC2 seems to be to do something about them.

DrB wanted to make the MaGrid more rectified polyhedral which would have greatly shortened the linear nature of the funny cusp, but would have put the cross-over in that configuration in a higher flow area. Moving them aside takes them out of the short funny cusp and allows the magnetic protection to work better. No prob, Bob.

PS: Structurally, the two separated crossovers would be as strong and stable as a single one.

hanelyp
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Post by hanelyp »

KitemanSA wrote:
hanelyp wrote:
93143 wrote:Dr. Bussard said R^2. I'm trying to figure out why.
line and funny cusp area scale with R/B.
Why should the funny cusp scale with R/B? They seem more like point cusps to me. Not the quasi-linear varient we get with the truncube non-Polywell, but a real one from a recticube.
If funny cusps scale more like point cusps than line cusps, that would make the polywell work better. However, even assuming the cusp scaling I did the polywell gain scales fairly well. More worrying would be a compelling argument or experimental data to suggest losses scale worse than estimated.

TallDave
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Post by TallDave »

DrB specifically said he did it out of the need to build quickly.
Do you have a cite on that? This was the only thing I could find:
Poorly
shielded areas, such as the interconnects between spaced
corners of the coil systems, can be minimized by careful
design to minimize area and avoid sharp corners, and by use
of internal B fields produced by current carriers through the
interconnects. And the main MG transport losses can be
controlled by use of the well-developed transport models and
equations obtained from 13 years of EMC2 experimental
research. In general, the impedance can be controlled
successfully, but only with proper care in design and
construction of the devices.
It seems odd that Nebel's team would have done the same thing if it would have been trivially easy not to, and it would eliminate a large source of losses. They didn't follow WB-6 exactly anyway (you can see the separation in WB-7 is a little larger) so they weren't completely averse to modifying the WB-6 design. Also, why would the new WB-7.1 contract be looking at "high-temperature coil joints" if it wasn't still an intercept issue?

I'm guessing again the reason is interconnects at other places either create current flow problems, open holes in the line cusps, or simply represent a greater poorly-shielded intercept area (because they would have to cover a larger area). I suppose it's possible, though, that they just didn't consider it important enough to fiddle with at this point.

But I am struck by the fact the interconnects appear to have been put in the places where they would require the smallest size.

KitemanSA
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Post by KitemanSA »

TallDave wrote:
DrB specifically said he did it out of the need to build quickly.
Do you have a cite on that?
Actually, no, because I chose my words poorly, incorrectly even. He made a series of statements from which I inferred the statement. The statements include:
In the Valencia Paper, DrB wrote:This was hastily built and tested

Poorly shielded areas, such as the interconnects between spaced corners of the coil systems, can be minimized by careful design to minimize area and avoid sharp corners, and by use of internal B fields produced by current carriers through the interconnects.
In the Final Report, DrB wrote:Detailed design here will lead to optimization of the spacing to maximize overall performance. Insufficient time was available to undertake such detailed design analyses for WB-6, and the dimensions chosen were based on general considerations of gyro radius effects in the flow channel.
...
With these design features, the WB-6 device was hastily constructed in August/September 2005…

In WB-6 these corners were separated to avoid this problem, but less well-shielded interconnects still existed between coils, which offered higher loss flux regions than for the direct cross-field transport to the B-field-conformal coil containers.

These supports were inevitably an electron loss, but their location outside the mid-plane of the overall magnetic field kept these losses to a minimum, and the high field at the inter-coil spaces helped to keep the local density gradients high so the impact losses would be low.
TallDave wrote: It seems odd that Nebel's team would have done the same thing if it would have been trivially easy not to, and it would eliminate a large source of losses. They didn't follow WB-6 exactly anyway (you can see the separation in WB-7 is a little larger) so they weren't completely averse to modifying the WB-6 design. Also, why would the new WB-7.1 contract be looking at "high-temperature coil joints" if it wasn't still an intercept issue?
It is my understanding that the WB7 was to be a replica of WB6. Why they made it wider set I can only guess, but based on the quotes above I suspect that DrB had other fish to fry. Not that he didn't think it was a issue, as you seem to be stating above, it is still an issue; just not a TOP issue. I suspect that if presented with an opportunity to test a "square" plan form Polywell with interconnects where they are vs a toroidal Polywell with split interconnects, he would chose the former because it provides the more significant advantage. But he does state that the interconnect issue must be taken care of with carefull design and seems to express the "we did the best we could" attitude. I believe my design provides the square plan form he wanted and takes care of the interconnect issue carefully, and presents many other benefits besides.
TallDave wrote: I'm guessing again the reason is interconnects at other places either create current flow problems, open holes in the line cusps, or simply represent a greater poorly-shielded intercept area (because they would have to cover a larger area). I suppose it's possible, though, that they just didn't consider it important enough to fiddle with at this point.
Not important enough to fiddle with AT THIS POINT is my guess too. The WB6 had way WAY too little time to fiddle with much at all, and WB7 was supposed to be a repeat of it.
TallDave wrote:But I am struck by the fact the interconnects appear to have been put in the places where they would require the smallest size.
Without good magnetic protection, small size may have been an incidental consideration. I suspect it was simplicity rather than anything else. Build it FAST! was the mantra I suspect.

TallDave
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Post by TallDave »

He made a series of statements from which I inferred the statement.
That's OK, happens to me a lot too.
Without good magnetic protection, small size may have been an incidental consideration.
He seemed pretty adamant about minimizing unshielded areas.

The more I think about it, the more I'm convinced Bussard was working under the premise that you can't hide the interconnects and they will suck up electrons wherever you put them, so you just have make them as small as possible, which by geometric coincidence puts them at the funny cusps. I'm not 100% sure what he means by "outside the mid-plane." That could refer to being at the cusp, or maybe he just means they're far back enough to not get hit by most electrons.

Also, if they could put them somewhere there was no electron flux why would they be testing high-temperature coil joints?

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