What does Maxewllian mean?

[alexjrgreen]

Our case is special: we have no data to go by.

Look up "Beam Power Tube".

[Art Carlson]

In other words, your set-up has to recover 99.96% of the energy your accelerator gives to your electrons.

Huh? Why? Shouldn't that depend on the size and density of the plasma?

Does the Lawson criterion really make sense applied that way to a Polywell? There is no ignition temperature as Polywells require constant input, and we get energy from neutrons with no concern over whether they keep the plasma hot (since we don't care about ignition). It looks like you're assuming a flat, neutral distribution (i.e. no well, no ion focus).

I would like to clarify that my latest calculation applies to a fusion reactor that just barely works, i.e. where the Lawson criterion is marginally satisfied. That is why the size and density do not specifically appear. And of course I am making a passle of assumptions and simplifications. You are welcome to present a calculation using a different set of assumptions. If those assumptions are not too wild, I expect that your answer will be within a factor of two of mine.

In the other direction are the polywells that have been built up to now. They are far from reactor conditions. I haven't run the numbers, but I expect that their confinement time is so bad that it is less than the electron equilibration time. Under those conditions, I would expect the electron velocity distribution to be non-maxwellian.

I might also mention that Todd Rider did a much more careful analysis than mine in a similar direction. His number are more trustworthy than mine, and his conclusion is the same: Making only a few reasonable assumptions, a fusion reactor that relies on a non-maxwellian distribution is not practical.

[TallDave]

Chacon's paper says that Rider is probably not correct in his assumptions. For one thing, Rider assumed square wells while more realistic parabolic wells, as it turns out, give very different results.

I would like to clarify that my latest calculation applies to a fusion reactor that just barely works, i.e. where the Lawson criterion is marginally satisfied.

Sure, but Polywells don't really have to satisfy the Lawson criterion because they never ignite. The charged products of the fusion reaction not only don't have to heat the plasma, they're basically irrelevant to continued fusion. I think we're applying a wrench to a screw there. A 3 MeV drive sounds excessive and I think it's a product of mixing equations from two unlike systems.

A better "Lawson-esque" question for a Polywell would be: how much fusion do we need to offset the required drive power? A Polywell that barely works would, say, require 1MW of drive power and produce 1MW of fusion power.

Here's a simple calculation: about .001 watts from WB-6. Scaling power at B^4*r^3 and losses at r^2, we come to net power at around 1.5M radius depending on how we scale B.

[Torulf2]

Do you not confuse the Lawson criteria and the C?
Even in a polywell its must be important for the fusion output, the ion density, the ion energy and the time the ions are in the well.

[TallDave]

Maybe. Not sure what you mean by C. Here's Wikipedia on the Lawson criterion:

In nuclear fusion research, the Lawson criterion, first derived[1] by John D. Lawson in 1955 and published[2] in 1957, is an important general measure of a system that defines the conditions needed for a fusion reactor to reach ignition, that is, that the heating of the plasma by the products of the fusion reactions is sufficient to maintain the temperature of the plasma against all losses without external power input.

Now, obviously much of that is irrelevant to a Polywell. Ion density, confinement, and temperature still matter, of course, but they have nothing to do with ignition, and a Polywell always needs external power input.

[Art Carlson]

The Lawson criterion is about the fact that it takes power to maintain a plasma, and that power has to come ultimately from fusion reactions. In the usual case of magnetic confinement of a D-T plasma, the trapping of charged fusion products can be considered a 20% efficient heating method: of the 17.6 MeV produced by a D-T reaction, 3.5 MeV is in the alpha particle. This is the basis of the numerical limit that Lawson derived.

A polywell is 100% driven, so you have to convert the energy coming out the plasma into a form that you can put it back into the plasma. The energy comes out in the form of fusion products (alphas and neutrons) and other losses. At a minimum, the "other losses" include the electrons that you are replacing to maintain a non-maxwellian distribution (if you think that's important).

To keep things simple, let's lump everything into a single efficiency eta that includes

• conversion of the energy of charged fusion products to electricity,
• conversion of the energy of neutrons to electricity, and
• recovery of electron energy as electrical energy (for example by being collected by an electrode near the potential of the source).

After that, the derivation of the condition for net (useable) energy output proceeds just the way Lawson did it. The only difference is that we have to use our eta instead of his 20%. In that sense, I probably made a mistake by a factor of 5, so that eta only has to be 99.8%, not 99.96%.

[Art Carlson]

Chacon's paper says that Rider is probably not correct in his assumptions. For one thing, Rider assumed square wells while more realistic parabolic wells, as it turns out, give very different results.

I'm referring to a different paper by Rider, where he considers the recirculaing power fraction associating with maintaining a non-maxwellian distribution. It is a local calculation and has nothing to do with the shape of the potential.

(But since you bring it up, why do you say that parabolic wells are more realistic? You can't maintain a radial electric field in a plasma without violating quasineutrality somewhere.)

[TallDave]

Sure, but electron losses from a driven non-ambipolar Polywell should be substantially different from the ion/electron losses from a neutral magnetically confined plasma in LTE (I know you're skeptical Polywell really works that way, but even granting a significant difference concedes the point imo), fusion reactions for the Lawson's criterion value of 1.5 x 10^20s/m^2 are calculated over the Maxwellian average of the temperature of a plasma in LTE, and in a Polywell you don't really care about heat loss anyway. Temperature is generally the easy part in electrostatics.


Anyways, here's Rick on electron thermalization:

For present generation machines the electron confinement time is less than the electron collision time so thermalization isn't an issue. For reactors, the electron collision time and the confinement time become comparable. Electron distributions are expected to be isotropic, but not thermal. Thermalization is a global process because electron orbits cover the entire interior. If electrons lose their energy (kinetic + potential), they will accumulate near the coil cases until they leave the system.

So we're preferentially sucking out the lowest-energy electrons.

But since you bring it up, why do you say that parabolic wells are more realistic?

IIRC, that's what was actually observed in the Japanese fluouroscopy experiments. But I'm really just quoting there; "realistic" is the actual wording from the Chacon/Miley/Barnes/Knoll abstract.

You can't maintain a radial electric field in a plasma without violating quasineutrality somewhere.

We already know a Polywell violates quasineutrality at the edge, since it's not ambipolar.

I'm referring to a different paper by Rider, where he considers the recirculaing power fraction associating with maintaining a non-maxwellian distribution.

Yes, that was the subject of a lot of discussion pre-WB-7. I wouldn't say the concerns have been fully addressed, but there's some reason to hope that there's an edge annealing or beam-bunching effect that tends to even out ion velocities at low kinetic energy, leading to a fairly monoenergetic distribution. Rick has a better description of how that might work here somewhere, as I recall. Maybe I'll try to dig it out.

A polywell is 100% driven, so you have to convert the energy coming out the plasma into a form that you can put it back into the plasma.

Sure, if you're trying to calculate where outputs equal inputs (of course, there's nothing that says a Polywell necessarily has to generate its own power supply). But that's a lot more important for a device that achieves ignition. For a Polywell, you might as well go whole hog and ask the question for 10 times as much energy out as in, since that's about what you need for a working reactor.

[Betruger]

Our case is special: we have no data to go by.

Look up "Beam Power Tube".

I'm afraid I'm not qualified to present further arguments here.. Maybe Dr Carlson could say what he thinks of your suggested alternative.

[Art Carlson]

Maybe Dr Carlson could say what he thinks of your suggested alternative.

It's irrelevant.

[Roger]

So I presume, having been suitably chastened and having gone to wikipedia or elsewhere, you have determined that "Maxwellian" ~ "thermal", which Polywell is NOT.

So they say. Do we have any experimental evidence for that? How about robust theoretical arguments? I think both are pretty thin.

Dr Bussards paper on measured brem loses circa IIRC 1989? 1/32nd IIRC.

Dr Carlson, is it easy to measure Brem radiation?

[alexjrgreen]

Maybe Dr Carlson could say what he thinks of your suggested alternative.

It's irrelevant.

Which is where you part company with Dr Bussard...

[Art Carlson]

So I presume, having been suitably chastened and having gone to wikipedia or elsewhere, you have determined that "Maxwellian" ~ "thermal", which Polywell is NOT.

So they say. Do we have any experimental evidence for that? How about robust theoretical arguments? I think both are pretty thin.

Dr Bussards paper on measured brem loses circa IIRC 1989? 1/32nd IIRC.

Dr Carlson, is it easy to measure Brem radiation?

For electron energies of several keV, the bremsstrahlung spectrum extends well into the UV. Since the spectrum is broad and peaked at longer wavelengths (see here), you have a good deal of flexibility about where you measure,. If you don't like vacuum ultraviolet you can move down to quartz UV or even visible light, so getting data is pretty easy.

Your troubles start in trying to distinguish bremsstrahlung from line radiation. Basically you have to know your plasma conditions and impurities well so you can choose a region without too many lines. It would be a good idea to measure at a few different wavelengths to allow you to check the consistency of the data.

The intensity is proportional to n_e^2*Z_eff. On ASDEX Upgrade (a tokamak), bremsstrahlung is used to determine Z_eff since density is well known from other diagnostics, especially interferometry. The exception is when a glitch (happens all the time) makes the interferometer lose count of the fringes. Then the bremsstrahlung measurement is used to as a rough and short-time indicator of the density to get the interferometer back on track.

I don't know where you want to go with this. If you want to use bremsstrahlung as a diagnostic of the electron energy distribution, to my knowledge that has never been done before, and I would approach the idea very skeptically.

[Art Carlson]

Alex, would you like to make a constructive contribution here, or are you just talk? You have accused me of being prejudiced, playing politics, making judgments without investigating the claims, and favoring the status quo - all in this thread. You bring up POPS and beam power tubes, implying I haven't done my homework, without telling us in what way you think the theory or experiment in those areas refutes my calculation. As for calculations, at least I have one. I am waiting for you to write your first equation. The fact is, on the question of whether the electron distribution in a polywell is maxwellian, we have no experimental data whatsoever and not much in the way of theory. I'm making an effort to come to grips with the physics. Maybe I'm wrong, but it's a starting point. If you can suggest a better alernative, please do. Otherwise pipe down.

[alexjrgreen]

You have accused me of being prejudiced, playing politics, making judgments without investigating the claims, and favoring the status quo - all in this thread.

The cap doesn't fit. Of all the experienced Tokamak researchers, you're the one taking the trouble to properly debate this.

You bring up POPS and beam power tubes, implying I haven't done my homework

If the data don't match the theory, then either the calculations are wrong or some of the assumptions are...

Dr Bussard considered the Polywell to be a slightly gassy vacuum tube and Rick took up the Polywell baton after researching POPS. Coincidence?