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 Post subject: alpha Larmor radius
PostPosted: Mon Apr 06, 2009 1:20 pm 
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MSimon wrote:
As far as a practical reactor goes (assuming the physics argument get settled favorably) the first wall (esp for pB11) and thermal issues are uppermost in my mind.

I suppose I should saunter over to the design forum if these questions interest me, but ... If you are still thinking of p-B11 and direct conversion in a grown-up sized machine, how do you intend to get the alphas out when their Larmor radius is only a fraction of the machine size?


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 Post subject: Re: alpha Larmor radius
PostPosted: Mon Apr 06, 2009 3:27 pm 
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Art Carlson wrote:
how do you intend to get the alphas out when their Larmor radius is only a fraction of the machine size?


It probably helps that they shouldn't see much B field till they get to the edge.


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PostPosted: Mon Apr 06, 2009 4:06 pm 
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The alphas make about 1000 passes before they exit through the cusps. They leave at essentially full energy.


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PostPosted: Mon Apr 06, 2009 4:41 pm 
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rnebel wrote:
The alphas make about 1000 passes before they exit through the cusps. They leave at essentially full energy.
If the alphas only exit at the cusps, why are we worried about significant heat generation on the magnets? Does this "at the cusps" apply only to the lower energy pB11 alphas or to any charged product? If there is only the neutron flux to handle, the TSP becomes a tad easier.

Second question. If the magnet contains the other charged particles, why bother with the electrons? Wouldn't a NegMaGrid for ions be easier than the two stage PosMaGrid for electrons/ions?


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 Post subject: alphas require big gaps
PostPosted: Mon Apr 06, 2009 4:44 pm 
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rnebel wrote:
The alphas make about 1000 passes before they exit through the cusps. They leave at essentially full energy.

Good. That makes more sense than the picture I had in my head. It does suggest that you don't have too much room to play with in terms of either decreasing the size (That's a problem I would like to have!), decreasing the field (if that's necessary to get a grip on the wall loading in a large D-T machine), or making the coils fatter (for field strngth, cooling, or shielding). You will need a few tens of cm clearance on all the cusps to let the alphas through unimpeded.

(Good to hear from you again, Rick. I was starting to worry about your health.)


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PostPosted: Mon Apr 06, 2009 5:06 pm 
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Heh, I'd been assuming they flew more or less straight out. If most are being guided through cusps, that sure helps with the alpha sputtering problem.

Quote:
Wouldn't a NegMaGrid for ions be easier than the two stage PosMaGrid for electrons/ions?


I think you would lose way too many ions to the grid if it were a cathode in a cloud of ions. Percentage-wise, fusion-product alpha losses are probably more acceptable than fuel ion losses (it might help too that they aren't heading toward a cathode; maybe if I get ambitious I'll try the math) since they don't affect the fusion rate.


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PostPosted: Mon Apr 06, 2009 6:15 pm 
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rnebel wrote:
The alphas make about 1000 passes before they exit through the cusps. They leave at essentially full energy.


I was under the impression that with the fields being considered the alphas (in a pB11 machine) would leave directly through any non solid core orifice. Then they enter the decelerator - get neutralized - and are entrained in the gas flow and exhausted.

Roughly. There should be some edge effects and some spreading of the alphas. Meaning the heat fluxes from the alphas will not be strictly geometric. Should be close though. (within 20% - which is good enough for now).

Of course this does not consider the range of alpha energies. Only those alphas below drive energies should be retained. Operating at the resonance peak should shorten the tail. Operating at the cross section peak would be the least favorable in terms of ash retention.

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 Post subject:
PostPosted: Mon Apr 06, 2009 7:14 pm 
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"Alpha's exit through the cusps".

Now that's a bombshell. Is there good evidence for this? It completely changes the game, engineering-wise. That would have to be not only the central-point cusps but the quasi-lines and corner-cusps also I'm assuming? In which case those nubs are going to smack in the firing line of some massive heat loadings ... (Kiteman, you got that little nub-cusp-geometry-thing solved yet?;))

On the other hand if the alphas products are leaving without significantly impacting the magnets it makes the coil-can-cooling design slightly easier, doesn't it?


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 Post subject: Re: alpha Larmor radius
PostPosted: Mon Apr 06, 2009 7:36 pm 
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Art Carlson wrote:
If you are still thinking of p-B11 and direct conversion in a grown-up sized machine, how do you intend to get the alphas out when their Larmor radius is only a fraction of the machine size?
Seems like my innocent little question was a good one.


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 Post subject:
PostPosted: Mon Apr 06, 2009 8:08 pm 
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The ions also show some magnetic confinement under reactor conditions. Run the numbers. The ion Larmor radii are also smaller than the device size, as are the alpha particles' Larmor radii.


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PostPosted: Mon Apr 06, 2009 8:39 pm 
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Art Carlson wrote:
Art Carlson wrote:
Bussard loss model (as near as I can tell): P_loss ~ R^2. Q = P_fusion / P_loss ~ R^2 / R^2 ~ constant. That is, either the thing works or it doesn't, but it doesn't work any bit better just by making it bigger.

Looking at Bussard's Valencia paper, I find this claim:
Quote:
Tests made on a large variety of machines, over a wide range
of drive and operating parameters have shown that the loss
power scales as the square of the drive voltage, the square
root of the surface electron density and inversely as the 3/4
power of the B fields. At the desirable beta = one condition,
this reduces to power loss scaling as the 3/2 power of the
drive voltage, the 1/4 power of the B field, and the square of
the system size (radius).

Looking into Valencia again for this thread, I am reminded of how little Bussard gave us to go on. Toward the end of the same paper, namely, he also says
Quote:
Fusion power scales as the
fourth power of the B field and the cube of the size, thus Pf
= (k1)B^4*R^3, while the unavoidable electron injection drive
power loss scales as the surface area of the machine, thus is
proportional to R^2. Assuming the use of super-conductors for
the magnetic field drive coils, the electron losses are the only
major system losses. Then, the ratio of these two power
parameters is the gain (Qf), which is thus seen to scale as Qf
= (k2) B^4*R^3/R^2 = (k2) B^4*R.
Thus here he is (indirectly) claiming that the losses do not have any B dependence. Now we could say that B^0 and B^0.25 are both a weak dependence, so it doesn't matter much, assuming either is right. On the other hand, a contradiction is a contradiction and doesn't improve one's confidence.

For the drive voltage, he concludes that higher voltages are always better, but in fact the cross section will decrease above a certain voltage, so there is an optimum voltage that maximizes the Q. Therefore, for reactor studies, it is fair to eliminate V from the scaling altogether.

The worst is his size scaling. Note that his experimental results cover variations in B, V, and n, which makes sense. He then eliminates n by applying the beta = 1 condition (N ~ B^2/V). That's OK, too. But at that step he also throws in an R^2 dependence. This is not an experimental result, like the other terms, but his theoretical prejudice. He only had a couple machines to work with, that had hardly any variation in radius but did have significant other differences, so there is no way he could have experimentally determined the R scaling.

I suppose you can take Bussard's scaling (or one of them) as a working guess, if you want, but please remember that the only part with experimental backing - which none of us has ever seen - is that there is not a strong B dependence (under the conditions of his experiments).


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 Post subject:
PostPosted: Mon Apr 06, 2009 10:19 pm 
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KitemanSA wrote:
rnebel wrote:
The alphas make about 1000 passes before they exit through the cusps. They leave at essentially full energy.
If the alphas only exit at the cusps, why are we worried about significant heat generation on the magnets? Does this "at the cusps" apply only to the lower energy pB11 alphas or to any charged product? If there is only the neutron flux to handle, the TSP becomes a tad easier.

Second question. If the magnet contains the other charged particles, why bother with the electrons? Wouldn't a NegMaGrid for ions be easier than the two stage PosMaGrid for electrons/ions?


At first, when I read the 'second question' I thought the answer was obvous, but further reflection leads to more 'what ifs'.
First, the pos. charge on the magrid serves to acellerate the electrons from the low voltage electron gun into the magrid internal volume at high voltage/ energy. A high voltage electron gun with a grounded magrid would also work acording to Dr Bussard, but (I speculate) that a pos. charged magrid may aid electron recirculation.

With Dr Nebels statement of ~ 1000 cycle lifetimes for the alpha particles, the ion confinement time is apparently influenced significantly by the magnetic field. But, without the centrally located electron cloud, how much smaller would that number be? Or, inversely, how much longer is the fuel containment time due to the electron cloud? Since the deuterium mass/ charge= the alpha mass/ charge I'm guessing they both would have a similar lamar radius, protons smaller and boron11 slightly larger (?). Since the protons and boron ions would have significantly lower energy, presumably they would have an orbital radius smaller than the alphas, and be less likely to reach deep into the cusps, thus have greater lifetimes to allow for significant fusion to occur.

But, without the more centrally located electron cloud (produced by the continous injection of new high energy electrons that replace the slowing, periferalizing (is that a word?), and finally escaping electrons) there is no focusing/ converging force acting on the ions so they bounce around randomly- thermalized plasma.
Also, with the electron cloud confining the ions, presumably to a significantly larger degree than the magnetic field for the fuel ions, the fuel lifetime is 10- 1,000 times longer(?) than the alpha confinement that I presume is dominated by the magnetic field.

So the electrostatic confinement of the fuel ions by the electrons does several things- significantly increasing the containment lifetime of the ions, serving to foucus them towards a central region with resultant increase in fusion rate, and delaying thermalization of the ions.


Is a 1000 orbit lifetime for the alphas a problem in terms of ash biuldup?

In a p-B11 net gain sized reactor, if most of the alphas leave the magrid through the cusps at nearly full speed it would not only change heat load considerations as already mentioned, it would also change the design and efficiencies of an energy capuring grid.

If the alphas transfer some modest amount of thier kinetic energy to the fuel ions, would that lead to a decrease in the needed drive energy (sort of a partial ignition or supercharger effect)?

Finally, if fusion products from D-D fusion , like tritium (more likely to fuse in only 1000 passes) and He3 have similar lifetimes, could significant secondary fusions occur automatically?

I'm not sure if my logic is consistant or acurate, but that's my updated understanding of what is going on.

ps: A negative magrid would not only impead the injection of electrons, it would have no confineing effect or focusing effect on the ions that are inside the magrid. There is no electrical field inside a charged sphere, so the ions would not see the negatively charged magrid untill they passed outside of it. You would have essentially a shielded Hirsch- Farnsworth type fusor. The ions wouldn't be hitting the grid, but electrons from the cathode would be streaming away from the grid, directly to the walls. I'm not sure how the details would work out but it is an obvous solution that presumably have been done already if it worked. Then again, there is a link I saw recently where, based on the drawings, someone is proposing this.


Dan Tibbets

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PostPosted: Tue Apr 07, 2009 12:17 am 
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icarus wrote:
"Alpha's exit through the cusps".

Now that's a bombshell. Is there good evidence for this? It completely changes the game, engineering-wise. That would have to be not only the central-point cusps but the quasi-lines and corner-cusps also I'm assuming? In which case those nubs are going to smack in the firing line of some massive heat loadings ... (Kiteman, you got that little nub-cusp-geometry-thing solved yet?;))
I've said yes for several weeks now. Others may disagree.

See my plots on the "Optimal" design thread.


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 Post subject:
PostPosted: Tue Apr 07, 2009 12:34 am 
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Art et. al.:
A few comments on scaling laws….
To a certain extent we are in the same boat as everyone else as far as the previous experiments go since Dr. Bussard’s health was not good when we started this program and he died before we had a chance to discuss the previous work in any detail. Consequently, we have had to use our own judgement as to what we believe from the earlier experiments and what we think may be questionable. Here’s how we look at it:
1. We don’t rely on any scaling results from small devices. The reason for this is that these devices tend to be dominated by surface effects (such as outgassing) and it’s difficult to control the densities in the machines. This is generally true for most plasma devices, not just Polywells.
2. Densities for devices prior to the WB-7 were surmised by measuring the total light output with a PMT and assuming that the maximum occurred when beta= 1. We’re not convinced that this is reliable. Consequently, we have done density interferometry on the WB-7. We chose this diagnostic for the WB-7 because we knew through previous experience that we could get it operational in a few months (unlike Thomson scattering which by our experience takes more than a man-year of effort and requires a laser which was outside of our budget) and density is always the major issue with electrostatic confinement. This is particularly true for Polywells which should operate in the quasi-neutral limit where Debye lengths are smaller than the device size.
3. As discussed by several people earlier, power output for a constant beta device should scale like B**4*R**3. All fusion machines scale this way at constant beta. Input power scales like the losses. This is easy to derive for the wiffleball, and I’ll leave that as an “exercise to the reader”. This is the benchmark that we compare the data to.
4. As for Mr. Tibbet’s questions relating to alpha ash, these devices are non-ignited (i.e. very little alpha heating) since the alpha particles leave very quickly through the cusps. If you want to determine if the alphas hit the coils, the relevant parameter is roughly the comparison of the alpha Larmor radius to the width of the confining magnetic field layer. I’ll leave that as an “exercise to the reader” as well.


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 Post subject:
PostPosted: Tue Apr 07, 2009 12:53 am 
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So does any "reader" know how to determine this and would you be so kind as to tell me?

As to my "why bother with the electrons" question above, it finally filtered into my memory that folks have often said it takes 10,000 passes or more to fuse. And while 1000 is much better than the 100 or so from a typical fusor, it still isn't anywhere near 10,000. Oh well.

PS: Welcome back Dr. N!!


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