New Mars

So was Bussard correct?
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"The answers are going to be kind of nuanced," Nebel said.
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"I've been very pleased, frankly, with the sorts of things we've been getting out of it," Nebel said.
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"We're looking at power generation with this machine," Nebel said. "This machine is so inexpensive going into the 100-megawatt range that there's no compelling reason for not just doing it. We're trying to take bigger steps than you would with a conventional fusion machine."

It's fun to daydream, isn't it? And it's easy, too, as long as you don't know too much.

There's more reasons than you can shake a stick at that this won't work. For starters, you can forget about aneutronic fusion. It's not just the temperature, Bremstrahlung is almost to certain radiate more energy than you produce by fusion no matter how good your confinement is. Even if you somehow manage to get a decent power balance, for a given plasma pressure and fusion power, a p-B11 reactor would have to be about 1000 times bigger (and more expensive) than a corresponding D-T reactor.

The next thing to worry about is the electrons. The magnetic configuration has not only lines of radial field from the center to the edge, which is bad enough judging from the experience with mirror machines, it also has lines of *zero* field along which the electrons will gush out. The idea of recycling electrons lost through the cusps won't work because they will come out almost parallel to the field but hit the return cusp with a large perpendicular velocity component they picked up going around the bend.

And the ions? The device is conceived to utilize a bi-modal velocity distribution, which will be destroyed very quickly by the two-stream instability. The anisotropy of the velocity distribution is also know to be a big problem, again from experience in the mirror program.

We haven't even started to talk about energy loss to the grids, the consequences of tiny field misalignments, charge-exchange ion losses, energy coupling between electrons and ions, and whether the potential distribution envisioned is even possible at a non-trivial ion density.

Since they managed to sweet talk somebody into giving them money, let them finish and publish their results, but let's not stop looking for ways to save energy and trying to develop other, less sexy but more reliable energy sources.

Just a few comments for Mr. Carlson

1. The theory says that you can beat Bremstrahlung, but it's a challenge. The key is to keep the Boron concentration low compared the proton concentration so Z isn’t too bad. You pay for it in power density, but there is an optimum which works. You also gain because the electron energies are low in the high density regions.

2. The size arguments apply for machines where confinement is limited by cross-field diffusion like Tokamaks. They don't apply for electrostatic machines.

3. The Polywell doesn't have any lines of zero field. Take a look at the original papers on the configuration. See :
Bussard R.W., FusionTechnology, Vol. 19, 273, (1991) .
or
Krall N.A., Fusion Technology. Vol. 22, 42 (1992).

Furthermore, one expects adiabatic behavior along the field lines external to the device. Thus, what goes out comes back in. Phase space scattering is small because the density is small external to the device.

4. The machine does not use a bi-modal velocity distribution. We have looked at two-stream in detail, and it is not an issue for this machine. The most definitive treatise on the ions is : L. Chacon, G. H. Miley, D. C. Barnes, D. A. Knoll, Phys. Plasmas 7, 4547 (2000) which concluded partially relaxed ion distributions work just fine. Furthermore, the Polywell doesn’t even require ion convergence to work (unlike most other electrostatic devices). It helps, but it isn’t a requirement.

5. The system doesn’t have grids. It has magnetically insulated coil cases to provide the electrostatic acceleration. That’s what keeps the losses tolerable.

6. The electrostatic potential well is an issue. Maintaining it depends on the detailed particle balance. The “knobs” that affect it are the electron confinement time, the ion confinement time, and the electron injection current. There are methods of controlling all of these knobs.

TallDave responded to the statement, "That was about 15 orders of magnitude short of break-even." with the comment, "True, but no [one] expects break-even from a machine of this size and budget. The power scaling law is roughly radius ^ 7 (r^3 for the volume of ions x B^4 for the power increase from density created by the magnetic field, which scales roughly with the radius), so a machine about 1.5M in diameter would in theory be able to produce something around 100MW of net power."

Scaling is a tricky business. If you want to buy 14 orders of magnitude with R^7 scaling by increasing the volume a factor of (100)^3 and the field a factor of (100)^4, the ion gyroradius will shrink relative to the machine by a factor of (100)^5 = 10^10. Considering it is critical to the concept that the ions be practically unmagnetized, I'd say you have a problem (even if you think you the improvement you need is much more modest.)

The scaling laws quoted by TallDave and Dr. Carlson are the power output scaling laws. The B**4*R**3 scaling is just the “constant Beta” scaling which applies to every magnetic confinement device (that I know of) and is theoretically founded in something as simple as force balance. It works for Tokamaks, Reverse Field Pinches, Spheromaks, etc. This one I’m not worried about.
The one you have to worry about is the input power scaling, because that one is related to the plasma losses (or transport). This one answers the question of “How much power do I need to supply to the device to maintain constant Beta”. Theoretical modeling of transport has a much poorer track record than plasma equilibrium has. These scaling laws are where the major risks for the larger device reside. The major saving grace is that for the Polywell is that the projected average densities are ~ 2 orders of magnitude higher than they are in Tokamaks so the energy confinement times don’t have to be all that good. (It’s the product of the density and the confinement time that’s important.)
Our contention is that since our projections for a power producing device only require a machine like the one TallDave described, we might as well build the next one in that size range and accept the risk. The machines just aren’t all that expensive. Also, there are a multitude of things that can be done to improve confinement (such as pulse discharge cleaning, pellet injection, etc.) that have been successful in the magnetic confinement program that can be instituted if our projections fall short. This approach will minimize the development time and lead to a lower costs for the overall program.

Although there is a sign difference in our end assessments, Dr. Nebel and I are otherwise on the same wavelength. With a mess of caveats that we could discuss for weeks, I also like to start by considering a B**4 * R**3 scaling for the power output, although usually energy confinement scaling is the tough one. It seems that Bussard himself suggested scaling the field at the same rate as the radius, resulting in an overall R**7 scaling of power output, but I have never seen a justification for this (maybe Dr. Nebel can provide one). My argument is that the polywell concept requires unmagnetized ions, that is, an (appropriately averaged) ion Larmor radius that is a fixed samll fraction of the machine radius, so (at constant energy) the field should actually *decrease* in proportion to the radius. This would result in output power going *down* as the machine gets bigger. (@seedload: In simple words, it falls short now, and the scaling laws say it will fall even farther short if you make it bigger.) Nebel argues that, if you're going to spend money at all, you should spend enough. This applies to many programs (from ITER to the war in Iraq), and I agree with the philosophy. But if it were my money, I would want the theoretical scaling cleared up before I made a decision.

I never had the chance to discuss the B ~ R arguments with Dr. Bussard nor have I run across it in the files, so we have stuck with the B**4*R**3 scaling. I know where that one comes from. I suspect that the B~R scaling is a constant hoop stress scaling for the coils. We are doing detailed magnet designs so this isn’t really an issue with us.
As for the ion confinement, operating in the “wiffleball” mode (electron beta ~ 1) will push the magnetic field into the boundary. This mode was achieved experimentally a long time ago, so we know this works. Only the highest energy ions will enter this edge region. What this effect should do is to just slightly lower the effective potential well depth for the ions.
If this is an issue, then we can operate the WB-7 in the same dimensionless parameter regime as the large device where the magnetic and electrostatic forces have the same ratio. Since all real physics depends on dimensionless parameters, this should give some useful insight. Plasma simulation is also a possibility.

B~R scaling: It looks like Bussard really was thinking about a fixed current density and a fixed ratio of conductor size to machine size. The statements I found were too brief to judge whether they are correct, but it could well be that the engineering constraints work that way, at least up to some maximum field on the order of 10-20 T. That notwithstanding, I am still worried about the physics of the scaling. There are statements from Bussard that the ions must be unmagnetized, and a calculation by Krall about how big the field can be before the ions get knocked off center. On the other hand, maybe that is not really so important. (Dr. Nebel has suggested that the convergence of the ions is not as important as previously assumed.) Can someone supply some numbers? Above all, what is the (maximum) field strength envisaged for a polywell power reactor? From that we can calculate the ion Larmor radius, the electron larmor radius, and the Debye length.

Zero-field cusps: Apparently my assumptions about the coil geometry were those used in the first machines. Bussard eventually discovered the problem himself. If I understand correctly, the current designs have coils which do not touch each other. I'm still chewing on the implications of this. For example, do the point cusps at the corners start to trun into line cusps that wind around the machine? Bussard himself seemed to think that it is essential that the cusps be points.

Dr. Carlson:

The peak fields for the reactor designs (at least for our reactor designs) are in the 5-10 T range. however, these are work in progress.

I was planning to take this up with Dr. Nebel directly, but since there seems to be so much interest at a reasonable technical level, I'll give it a go here.
About that whiffle ball. It seems the picture is a spherical region with a fairly sharp transition from being field-free inside to being plasma-free outside. Clearly, the field must be parallel to the spherical surface nearly everywhere and, equally clearly, it can't be parallel absolutely everywhere. That's why the whiffle ball needs holes (cusps), although they may be very small.
Two cusps would be fine with me. Then it would be a sort of mirror machine (presumably axially symmetric). But the polywell is supposed to have 14 holes (6 faces plus 8 corners). I believe there is topologically no way to do this (with some exceptions that don't seem relevant) without having points on the surface where the field vanishes. In addition to the cusps, where the field converges and then takes a dive, there must be points where the field lines in the neighborhood are hyperbolic.
If you think I'm wrong, just try to draw a picture of the field lines around 4 or 5 of those whiffle ball holes.

Dr. Carlson;

I don't know exactly what to say, but we have run Gauss meters all over the face of the cubes and through the corners and we don't see any low field regions. The fields peak near the conductors and fall off near the coil centers, as you would expect. If you can identify where you think the field will vanish, we can measure it and see next time we break vacuum.

"The peak fields for the reactor designs (at least for our reactor designs) are in the 5-10 T range"

Taking a magnetic field of 8 T and a (perpendicular) deuteron energy of 100 keV, I get a gyroradius of 8 mm. In a machine of radius 1.5 to 2 m, the ions will be highly magnetized. Is this now considered unimportant? What about Krall's calculation of the deflection of an ion falling in to the center?

Taking again 8 T and adding the assumption of a high beta plasma with T = 100 keV (perhaps being sloppy with factors on the order of unity), I get a density of 1.6e23 m^-3, and a Debye length of 6 nm. That suggests to me that the plasma strongly fulfills quasi-neutrality, so that it is a dangerous proposition to consider electron and ion transport separately. An MHD picture would be more appropriate, like in a tokamak.

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"The fields peak near the conductors and fall off near the coil centers, as you would expect."

I am making two claims.

(1) The field must be radial at the midpoints of the sides of the cube. I assume you either see this or haven't checked yet. I believe that the field will be smaller there than at the corners, in which case these points will be more important for electrons losses than the corners. What relative field strengths are actually observed?

(2) The picture of a wiffle ball cannot be accurate. "Whiffle ball" suggests a spherical, high-beta plasma, surrounded by a low beta magnetic field, with the exception of a small number of "holes" where the field lines converge and become radial. But what happens at the midpoints of the sides of the cubes? The tangential field must vanish by symmetry, so they can be neither part of the solid ball, nor can they be holes.

Dr. Carlson:

The 8 mm gyroradius isn't a big deal since few of the ions will ever access that region of the device.In the middle the gyroradius is infinite which is where the ions spend their time.
The plasma is quasi-neutral (but not neutral) and the particle losses are ambipolar. MHD is not a good idea (just like it isn't for a Field Reversed Configuration) becasue there is a field null at r=0 and the wuiffle-ball effect (expansion of the plasma against the field) makes this low field region fill almos the entire plasma. Besides, the field line curvature is good everywhere so MHD stability isn't an issue.
I don't have the field magnitudes from the edge vs. the center of the coils at my fingertips, but the ratio of the field at the cusps in the corners vs. the cusps in the faces is about a factor of 2.
As for the midpoints on the faces of the cubes, since the adjacent conductors have currents in opposite directions they add between the conductors. Between the conductors should be the strongest fields in the entire system.

Nebel's answers have not changed my mind, but they are interesting enough to keep me talking. I think, however, that http://www.talk-polywell.org/bb/viewforum.php?f=3 is a more appropriate and more convenient forum. Anyone who wants to follow this discussion should move over there.

The Emc2 team has been ramping up its tests over the past few months, with the aim of using WB-7 to verify Bussard's WB-6 results. Today, Nebel said he's confident that the answers will be forthcoming, one way or the other.

"We're fully operational and we're getting data," Nebel said. "The machine runs like a top. You can just sit there and take data all afternoon."

So was Bussard correct? Will it be worth putting hundreds of millions of dollars into a larger-scale demonstration project, to show that Bussard's Polywell concept could be a viable route to fusion power?

No answers just yet Nebel said it's way too early to talk about the answers to those questions. For one thing, it's up to the project's funders to assess the data. Toward that end, an independent panel of experts will be coming to Santa Fe this summer to review the WB-7 experiment, Nebel said.

"We're going to show them the whole thing, warts and all," he said.

Because of the complexity, it will take some interpretation to determine exactly how the experiment is turning out. "The answers are going to be kind of nuanced," Nebel said.

The experts' assessment will feed into the decision on whether to move forward with larger-scale tests. Nebel said he won't discuss the data publicly until his funders have made that decision.

Nebel does sound positive

Glad to see you folks following this story.

Everyones waiting to see the results in August.

All the Polywell Fan Bois hang out here:

http://www.talk-polywell.org/

Dr Nebel does too.

So, how big would a 1 Terawatt reactor have to be?

I can't believe that I can't wait for August.

So, how big would a 1 Terawatt reactor have to be?

# Todd H. Rider, "A general critique of inertial-electrostatic confinement fusion systems", M.S. thesis at MIT, 1994.
# Todd H. Rider, "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium", Ph. D. thesis at MIT, 1995.
# Todd H. Rider, "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium" Physics of Plasmas, April 1997, Volume 4, Issue 4, pp. 1039-1046.