Remind me - why 10T field?

[D Tibbets]

I was also going to weigh in on the topic that I think the wiffleball (ie high beta) may not be a good idea. I think that if beta is increased to the point of making a wiffleball it will become more unstable and lead to larger anomalous transport of electrons, which defeats the purpose of the wiffleball approach. So, in order to increase density and reaction rate higher fields would be needed to suppress it.

Certainly, if Beta exceeds one the containment will become worse. But maintaining Beta below one (how close to one do you need to be to create an effective Wiffleball?) also harms containment. I don't know how tight the control needs to be. Certainly operating at low beta has two disadvantages. Obtainable densities would only be comparable to that obtained in similar Beta level Tokamaks (actually probably lower densities as the Polywell would presumably be operating at higher average temperatures). The Polywell might still have the advantage of monoenergetic ions so the power density might be ~ 60 X greater (dissecting Nebel's 60,000 X power density into a presumed 1000X density advantage, and a 60X monoenergetic fusion ion temperature advantage). Once the difference between D-T and D-D fuels is incorporated , the machines would be ~ equivalent in energy density and thus fusion yield per unit volume. This means the Polywell would be as big or bigger than the Tokamak*.
The other problem is that losses in this cusp machine are tolorable in large part only because the Wiffleball containment is ~ 1000 times better than a simple cusp machine. Energy input costs would not scale as ~ r^2 but as r^2 * 1000. Breakeven could probably never be reached even with machines much bigger than Tokamaks. [EDIT] Actually at low Beta, perhaps the polywell would have confinement similar to mirror confinement seen in Penning traps. Better (perhaps a factor of 1/20th that of a Wiffleball) but still ugly.

How would the containment and density behave in a machine with a Beta of 0.5? I have not seen any indication of the performance, except that cusp confinement only contains a charged particle for few passes, mirror confinement for perhaps as much as 60 passes, and Wiffleball for several thousand passes. How does the containment scale as you increase Beta towards one? If the graph is linear, then some intermediate value may serve. But I suspect the graph would be logarithmic, with much of the gain coming as you approached closely to Beta= one.


* I have heard that there are some efforts to design a high Beta tokamak like machine. This would presumably have significant power density advantages over low Beta tokamaks and thus large size advantages also.

[EDIT 2] Also, keep in mind that Polywells are supposed to be MHD stable, unlike tokamaks because all of the magnetic fields are convex towards the center, at least until Beta exceeds one. This eliminates most if not all of the concerns about stability.

Dan Tibbets

[TallDave]

I was also going to weigh in on the topic that I think the wiffleball (ie high beta) may not be a good idea. I think that if beta is increased to the point of making a wiffleball it will become more unstable and lead to larger anomalous transport of electrons, which defeats the purpose of the wiffleball approach. So, in order to increase density and reaction rate higher fields would be needed to suppress it.

High beta is very desirable. We need the WB, without it PW is no better than ITER (see Rick's comment linked below). That's why the WB-8 loss scaling is so, so important.

Bussard appeared to believe, based on his slew of machines, that cross-field transport scaled at something like B^.25. If he was right, there's something here worth pursuing. If he was wrong, there probably isn't.

Amnyways, icarus identified the problem with Chris' question: it calculates based on ion pressure. PW is run electron-rich to confine ions; ion pressure should be minimal.

Dan,

Nebel actually said 62,500 -- without any ion focussing. This confused me until I realized what the square root was. That power advantage is just the density advantage (250) squared.

viewtopic.php?p=4940&highlight=62500#4940

[D Tibbets]

TallDave, Thanks for the link. Ir remembered the ~ 60,000 advantage, but not the rest of the post. This non convergent situation is apparently what was used in the simulation last year as a flat ion density profile was reported. Several orders of magnitude improvement over this could significantly decrease size and size loss scaling to impressive amounts. In this case the engeenering concerns of magnet case thermal loading would be the limiting factor on size, even if the thermal loading came only from bremsstrulung radiation (I think).
Also, if this energy density is dependent only on the density, where does the drive energy come in? With D-D fusion the crossection increases ~ 100 fold between 10-100 KeV. Still, at 100 KeV the fusion rate would be only ~ 1 % of the D-T fusion rate at optimal temperatures (ignoring thermal vs nonthermal considerations). So the density advantage would be result in ~ 600X advantage. If the thermal conditions of monoenergetic fuel ions is applied to Polywell , while only the high energy thermalized tail applies to tokamaks, the advantage would move back towards the 60,000 X level.

Dan Tibbets

[TallDave]

Also, if this energy density is dependent only on the density, where does the drive energy come in?

Power rises as, roughly, density squared, with constant drive depth. The precise equation is around here somewhere. It's considerably more complicated than that but as a BOE calc density squared is okay.

Still, at 100 KeV the fusion rate would be only ~ 1 % of the D-T fusion rate at optimal temperatures (ignoring thermal vs nonthermal considerations). So the density advantage would be result in ~ 600X advantage.

D-D versus D-T, you mean? Well, PW can burn D-T too (the only reason we wouldn't is that tritium is expensive, so if PW works well it might be cheaper to do without). If the thing works the way we hope, it will have 62,500x more power than ITER at equivalent conditions, and possibly more than 1 million times once optimized with POPS, ion convergence, etc.

Heh, I just realized something re p-B11: IEC has a huuuge advantage in that the +5 boron atoms gain 5x the energy for a given well depth, whereas toks have to actually produce the exceedingly high temps to fuse them. I'd never considered the issue from that angle before.

[D Tibbets]

...

D-D versus D-T, you mean? Well, PW can burn D-T too (the only reason we wouldn't is that tritium is expensive, so if PW works well it might be cheaper to do without). If the thing works the way we hope, it will have 62,500x more power than ITER at equivalent conditions, and possibly more than 1 million times once optimized with POPS, ion convergence, etc.

Heh, I just realized something re p-B11: IEC has a huuuge advantage in that the +5 boron atoms gain 5x the energy for a given well depth, whereas toks have to actually produce the exceedingly high temps to fuse them. I'd never considered the issue from that angle before.

Yes I did mean D-T. I'm guessing that since Polywells have internal magnets, there would be more obstructions to achieving profitable tritium production from a lithium blanket. Perhaps with enough neutron boosters like beryllium or lead...

I think the P-B11 reaction in tokamaks is moot as the bremsstrulung losses would be insurmountable. Perhaps D-He3 might be possible in an advanced tokamak, there the advantages of the Polywell (He has a Z of 2)would still exist, but not to as great of an extent.

Which brings up another point. In a Polywell, what potential well depth would be needed to reach the ~100-120 KeV energies where the D-He3 fusion crossection is actually higher than that of D-D fusion? If P-B11 is a little too far, D-He3 reactors might have higher energy densities (smaller size) than D-D reactors. Smaller size and much less neutrons would make it more attractive as a space ship power source. The He3 would have to be supplied by terrestrial (or lunar) D-D Polywells or be mined from the moon. Or, Bussard's idea of a D-He3 1/2 catylized reactor might be the smallest of all. The tritium and He3 from the primary D-D reaction is fed back into the reactor for additional fusion. More neutrons, but also, significantly more power. Of course all the equipment to collect and process the tritium and He3 would have to be included, along with greater neutron shielding, and thermal radiators... Then, there is the question of how you convert the fusion energy into electricity, though with a dilluted fusion product rocket, that need would be minimized. Power for magnetic nozzles and general ehip electrical needs would be all that was needed, and partial direct conversion of the charged fusion ionsmight suffice. The neutrons would be entirely waste heat, except for some small (?) portion being used to preheat the diluent fuel.

Dan Tibbets

[chrismb]

So what are the edge conditions supposed to be; what is the mag field strength, beta, electric field, density and electron and ion temps. Can anyone actually put some figures to these, or am I now about to witness either a blank of responses, or a load of pontificating subjective and inconclusive hot air about what may or may not be what is intented and envisioned.

[MSimon]

So what are the edge conditions supposed to be; what is the mag field strength, beta, electric field, density and electron and ion temps. Can anyone actually put some figures to these, or am I now about to witness either a blank of responses, or a load of pontificating subjective and inconclusive hot air about what may or may not be what is intented and envisioned.

I have personally done the experiments. And I can tell you.... Oops. I just got a call. Maybe later.

[Aero]

Heh, I just realized something re p-B11: IEC has a huuuge advantage in that the +5 boron atoms gain 5x the energy for a given well depth, whereas toks have to actually produce the exceedingly high temps to fuse them. I'd never considered the issue from that angle before.

So does that mean that when the p energy is 100KeV, that the B11 energy is 500 KeV? And what does that do to the Barns? Collision cross section?

[Aero]

So what are the edge conditions supposed to be; what is the mag field strength, beta, electric field, density and electron and ion temps. Can anyone actually put some figures to these, or am I now about to witness either a blank of responses, or a load of pontificating subjective and inconclusive hot air about what may or may not be what is intented and envisioned.

I have personally done the experiments. And I can tell you.... Oops. I just got a call. Maybe later.

Chris, while we are waiting for MSimon, maybe you would be more specific.
Define a point on the edge where you want the conditions to be known, as follows:

Use a radial coordinate system where the full radius of the Magrid = 1, and let pi()/2 degrees = 1. That is, angles go from 0 to 1 over the range of 0 to 90 degrees. Given radial coordinates originating in the exact center of the Magrid with each axis centered through the bore of the respective magnets, at what azimuth and elevation does your edge point lie? At what percent of full radius do you think the edge lies? Using this coordinate system, I think that there are cusps at (0,0,1), (0,1,1) (1,1,1 (0,0,-1), (0,-1,-1), and (-1,-1,-1) as well as off at half angles. So your next task is to identify a point on the edge so we can avoid the cusp arguments.

Your question seems to be a simple one, but it is not so simple I think. As for me, I would be very interested to know at what radius the edge lies as the azimuth sweeps through the angle from 0 to 1. That is, can anyone plot the radius of the edge points as the azimuth sweeps from the point (0,0,1) to (1,0,1)? You see how confusing it is, (1,0,1) is not in my list of cusps, but shouldn't it be?

[chrismb]

(0,0,1) and (1,1,1), on the basis that I would hazard a guess the conditions at every other steradian angle at WB=1 will be between those two [types of] locations.

[Aero]

(0,0,1) and (1,1,1), on the basis that I would hazard a guess the conditions at every other steradian angle at WB=1 will be between those two [types of] locations.

I don't understand. Did you choose to name the radial coordinate "WB?" If I understand correctly, you have chosen a great circle arc from a point cusp to an adjacent point cusp. Doesn't that arc pass through a nub and a funny cusp?

I really do think chrismb"s question is a good one, and difficult. Correct me if I'm wrong, but won't every great circle arc from one point cusp to an adjacent point cusp always pass through a funny cusp? And isn't the edge of the WB located at infinity at every cusp? That is, at the cusps, the magnetic flux flows parallel to the radius vector, and generally parallel to the electrostatic force field. At some point along the arc, (hopefully, along most of the arc) the magnetic flux flows perpendicularly to the radius vector and generally perpendicularly to the electrostatic force field. (Generally, because the wiffle ball can not be treated as a point source of electrostatic forces.)

Anyhow, if we had a 2-dimensional graph of the edge radius along this great circle arc, we would probably have the answer to Chrismb's question. That is, I speculate that the edge radius is a function of mag field strength, beta, electric field, density and electron and ion temps fit in there somehow. It becomes more complex as a cusp is approached. A good task would be to post a sketch of the edge radius along the great circle arc so we could talk to it.

[TallDave]

So does that mean that when the p energy is 100KeV, that the B11 energy is 500 KeV? And what does that do to the Barns? Collision cross section?

1 -- Yes. 2 -- It just means we don't need a well nearly as deep as the fusion temp. I just think it's kind of neat that IEC devices naturally lend themselves to advanced fuels that way. The +5 does nothing for a tok.

[TallDave]

So what are the edge conditions supposed to be; what is the mag field strength, beta, electric field, density and electron and ion temps. Can anyone actually put some figures to these, or am I now about to witness either a blank of responses, or a load of pontificating subjective and inconclusive hot air about what may or may not be what is intented and envisioned.

I have personally done the experiments. And I can tell you.... Oops. I just got a call. Maybe later.

I have those numbers right here... darn, it's MSimon on a conference call. Gotta run for now.

[hanelyp]

In a Polywell, what potential well depth would be needed to reach the ~100-120 KeV energies where the D-He3 fusion crossection is actually higher than that of D-D fusion?

Related, since the D-D collision energy in a polywell would be less than D-He3 collision energy for the same well depth, how much might that favor the D-He3 reaction?

[chrismb]

If I understand correctly, you have chosen a great circle arc from a point cusp to an adjacent point cusp. Doesn't that arc pass through a nub and a funny cusp?

Sounds good to me! I was really just after those conditions at those points, but info on what is going on across the WB would be a bonus.

I mean - at this stage I'd be happy with any numbers from any point on the WB. Anything. Anything at all, then I'll be happy with it as a starter and we can go from there!

I thought these things were known. It seems inconceivable that all these conversations have gone on, but actually no-one has ever wondered what the ion and electron denisities are at the edge, and the electron temp.

(Incidentally - beta certainly does apply to both electrons and ions, else what'd keep the electrons in! It is nothing like 'ion pressure [alone]' as implied somewhere. That is nonsense. beta is e.kB.(Ti+Te).2uo/B^2)