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[TallDave]

I was envisioning the electrons being routed away from the collectors to the wall (as Rick had talked about), but I'd forgotten the gradient to the wall goes the other way now. Doesn't really make sense now that I think about it some more.

[D Tibbets]

You'd have to have a way to pick up upscattered electrons before they got past the trap grid, or whatever structure it is that maintains a negative potential relative to both the magrid (tens of kV) and the wall (MV). Electron direct conversion using the magrid potential well is all well and good, but if an electron gets out into the high-voltage alpha converter it's going to slam into the ash collectors at very high energy, somewhere in the range of a MeV.

Detailed design of the system may smear out the sharp distinction I've drawn, but the upshot is that you can't use the same gradient to decelerate alphas and electrons at the same time. You have to do one first, then the other. And it strikes me that the potential for catastrophic energy drain is much lower if you do the light, relatively low-energy electrons first.

I think you are assuming that the decelleration grid= acceleration grid, depending on the charge on the particle.

That's a law of physics.

I'm guessing that this is true only in part as the 'venition blind' arrangenet of electrostatic (and magnetic?) plates allows selective removal of particles based on some range of energy. Thus the escaping electrons would not be accellerated past the entire series of plates but be captured early on. This would represent an energy loss, but it would be less (much less?) than allowing the electron to pass the entire series of plates (blinds).

There has to be a negative potential gradient for the electrons to run up, or recirculation won't work at all.

Just make sure the first collectors are close enough to the bottom of that gradient that the decelerated electrons don't gain back a significant amount of energy before hitting them. I guess, anyway...

Yes, accelleration= decelleration over all. But when you have particles with different inertias, you can selectively remove/ collect them at various sub stages- that is sort of how a mass spectromiter works. I think that is what you are saying in your last sentance.

Dan Tibbets

[D Tibbets]

Just make sure the first collectors are close enough to the bottom of that gradient that the decelerated electrons don't gain back a significant amount of energy before hitting them. I guess, anyway...

How about shielding strong enough to deflect electrons, but weak enough it doesn't alter the path of alphas very much?

Do you want to collect the upscattered electrons or not?

If you stick the electron emitters deep enough in the magrid potential well, very few electrons will ever make it out far enough to enter the alpha collector system. That might actually be the best way to go, since asymmetrically bleeding off the high-energy tail reduces the average energy of the distribution, which could be bad. I don't know if magrid losses are any more even-handed, but they probably aren't any worse.

But if an electron does make it out to the collectors, why would you want to prevent it from hitting the first plate? If it misses the first one, it will be going that much faster when it hits the second one. Shield the second one, and it's going even faster when it hits the third one. Shield all the collectors and you have MeV-range electrons slamming into the outer wall. Never mind the fact that the only way to "shield" these things is magnetically, since they sort of have to be positively charged to do their job, and magnetic shielding powerful enough to deflect a MeV-range electron is definitely going to screw with nearly-stationary alphas coming in for a landing.

I'll take the assumption that TallDave ment- 'magnetic fields to deflect electrons into the first collector, while the ions continue on.'


Dan Tibbets

[D Tibbets]

I've got a dumb question, and it's possibly off topic as well, just tell me if so and I'll ask somewhere else.

I've been curious what is supposed to happen if you could create a perfectly spherical magnet field and used it for containing a cloud of electrons. I know, it's impossible, but I'm curious what the expected Maxwellian distribution of the electrons is supposed to be if they are contained in that manner long enough. Is my intuition correct in believing that the center should have lower electron density and/or velocity distributions than the rest of the volume, even over a long time frame? It seems to me from Rider's paper that the 'correct' answer is that the velocity and density throughout the sphere should become uniform over time. I know plasma physics isn't supposed to fit my intuition, but it seems really odd to me that a sphere of electrons wouldn't keep a non-uniform distribution of velocity/density simply by virtue of the electric field created by the electrons themselves.

I believe that the electrons energy is equal throughout the wiffleball, even when first injected. But, the total energy = KE +PE. Thier kinetic energy is maximal merar the wiffleball border, and their potential anergy is maximal at the point closest to the center that they can reach. These extreams are highest when the electron is first injected (or recirculated). With repeated bounces off the not quite spherical wiffleball, and electron- electron collisions dominating near the center the electrons highly elliptical orbits will gradually (or quickly, depending on realitive time scale) become more circular, till the eventially are traped on a magnetic field line at the evolving wiffleball border, if they haven't escaped through a cusp hole befor then. At this stage the collisions of the electrons traped on field lines dominate and along with black body radiation, and other mechanisms (?) gradually the velocities drop till they can kiss the walls of the magnets. The population of electrons would be nearly evenly distributed at this final stage, but I'm guessing even now the electrons would not have an equal kinetic energy distribution. The reason the more centrally located electrons have more kinetic energy at this stage is because of thier position. If the had lower speeds they would be sinking further twoards the magnets. I'm not sure how the potential energy distribution would be in this situation.

In any case thsee are pictures under static conditions. Better to concider the dynamic picture. In otherwords, how the electron distribution is changing over time, and limited by the expected lifetime of the electrons in the system. How quickly this changes from the initial radial picture with an elliptical potential well to a thermalized picture with a square potential well, etc. is one of the bones of contention, or, at least that is my impression. This also effects the arguments about bremsstrulung radiation - see my next post.


Dan Tibbets.

[D Tibbets]

I think assuming 100 % recirculation as assumed by Rider is a good thing is completely ignoring the point. The removal of the tiny fraction of the highest energy electrons is the supposed benificial effect. Obvously, with 100% recirculation this would not be possible and at least partially invalidates the comparison.

Ultimately, his argument is about transferring energy from one group of electrons to another. Maybe you can do that with some fancy laser or RF system on a population of electrons with no losses. If you want to physically remove some of the elextrons from the machine and reinject then at a different energy, that accomplishes the same thing. The calculation applies either way.

It is not a question of transferring energy from one group of electrons to another without any losses, but doing so with acceptable losses. Or more percisely, removing a high energy electron while recovering a substantial portion of it's energy.
In the context of bremsstrulung radiation. I assume there are two mechanisms in the Polywell whereby this effect is minimized.
First- through the slow in the center electrons where most of the ion- electron collisions occur (cold electron temp. compared to a hot ion temp.). This is dependant on the non (or minimally) thermalized distribution of the electrons over their lifetime.
The second- the ongoing thermalizing process will creat a tail of high energy electrons that would have higher velocities as they pass near the denser ion populations near the center (here I am assuming enough ion convergence to offset the larger volume outside the 'core' and slower individual ions which would spend more of their time in the perifery) in addition the greater speed of the upscattered electrons in the perifery that produce more bremsstrulung radiation whenever they pass near the less dense ions in this region.
These upscattered electrons are traveling faster, so if the wiffleball retains an electron for an average of 10,000 passes*, the upscattered high energy electrons would have a shorter lifetime, thus preferentially leave the system faster. Once outside the magrid, if it's KE is greater than the magrid potential it will leave (after surrendering back the energy equivalent to the magrid potential) eg- if the magrid is 10,000 positive volts, and the upscattered escaping electron is 15,000 eV, this undesired electron is removed from the system at the cost of 5,000 eV, one third of the cost without the magrid charge. Convoluted downstream energy converters that could harvest energy from both these electrons, along with the ions, would decrease ths energy drain even more.
If your using D-D fuel, without direct conversion, some of the energy would still be recovered from the escaped electrons, and the bremsstrulung radiation through a thermal cycle.

I wonder what percentage of losses this would represent compared with the othe electron transport losses?

* I have heard wiffleball trapping factors of ~ 1000 (for alphas) to, 10,000 passes (for electrons). Does it make sense that these numbers are different? Both of these are purely due to the wiffleball modified magnetic confinement. The recirculation multiplies the effective electron confinement ~ 10X or more. Fuel ion confinement is apparently well beyond this due to the electrostatic confinement, though I'm uncertain of the degree.

Dan Tibbets

[Art Carlson]

The Chacon paper gives energy gain for a highly simplified system, providing a stringent upper limit.

Doing the full bounce-averaged Fokker-Planck simulation is a lot more complex a look than Rider ever took at ion distributions. While it doesn't address brem, it does address Rider's other objection about ion upscattering. Sorry, I'm having trouble keeping track of which of Rider's points you're talking about.

It sounds like Chacon did a detailed calculation only for the ions, whereas Rider is interested mainly in the electron distribution and IIRC assumed thermal ions. I think there are good arguments why the details of the ion distribution won't affect the ion-electron energy transfer much, mainly that the ions are practically standing still with respect to the electrons anyway. Note also that Chacon concludes

steady-state distributions in which the Maxwellian ion population is dominant correspond to lowest ion recirculation powers (and hence highest fusion energy gains).

His abstract also says he has addressed electron losses "heuristically" and concluded that "large Q-values are still possible", but it is not clear whether he considered convective or radiative energy loss, or both.

*** Hold the phone. I suspect he is calculating the gain for D-T. If that is true than we can use his calculation as a strong argument against p-B11 in "Penning fusion systems", and probably in polywell systems as well. I guess I (and anyone using Chacon as an argument) really should read the full paper. I thought I had done that, but I can't find it in my files, so maybe I was drawing my conclusions from the abstract alone. Can somebody send me a copy? An electronic copy is easier to quote, but I should also be able to pick up a paper copy at the IPP on Tuesday. ***

I haven't worried much about Rider's many other arguments. Since I had no particular interest in IEC systems, the question that interested me most was whether p-B11 was possible in any configuration. I have always (or at least almost always) been referring to his bremsstrahlung calculations.

I guess I'm still not sure why you don't accept Rick's explanation that where the electrons go matters. Reading Rider's section on ion-electron energy transfer, it seems intuitively obvious that Rick's explanation breaks Rider's asumptions. Or are you just asking for something better than handwaving?

Mostly the latter. I am willing to entertain Rick's hypothesis, accepting it is another matter. His proposal does break Rider's assumption, but he hasn't shown, or even particularly motivated, why it should bring an improvement.

[Betruger]

"A bounce-averaged ion Fokker–Planck code for Penning fusion devices"?

[Art Carlson]

"A bounce-averaged ion Fokker–Planck code for Penning fusion devices"?

I think I'm talking about "Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker–Planck model", Phys. Plasmas 7, 4547 (2000), but correct me if another paper is more helpful.

[Betruger]

I'll send you that one too.

[usernameguy]

There's coverage now of the successful pinch in the Economist (and the print version, too):

http://www.economist.com/sciencetechnol ... d=14698355

(BTW I thought the temperature for aneutronic fusion was *hotter*, not cooler, as the article suggests.)

[TallDave]

Art,

OK, fair enough.

I am also skeptical Polywell or any fusion system can deliver p-B11 anytime soon; frankly, D-D with decent power density would be more than enough for me.

Aneutronic is the holy grail, but also perhaps a Hail Mary, as brem looks like a difficult nut to crack.

[Art Carlson]

I'll send you that one too.

Thanks. My observations:
"Energy gain calculations in Penning fusion systems using a bounce-averaged Fokker–Planck model"
PHYSICS OF PLASMAS, VOLUME 7, NUMBER 11, NOVEMBER 2000
L. Chaco´n, G. H. Miley, D. C. Barnes, D. A. Knoll

1. They reference "T. H. Rider, Phys. Plasmas 2, 1853 ~1995!." for the statement "electron power losses [in a polywell] through the magnetic field cusps have been estimated to be deleterious". I didn't think Rider had analysed the rate of electron losses through cusps. Is this a new one from the prolific Rider?
2. Why is "the beam-like ion distribution function" a "crucial issue"? With sufficiently good confinement, why couldn't an IEC system operate with Maxwellian ions? In this context he cites a paper by Nevins and another by Barnes giving an upper limit on Q in an IEC device using D-T (!) of 0.5 resp. 1.3. If that is even remotely correct, then we can immediately dismiss all other fuel cycles. -- Maybe that is the point of this paper, that it is an unnecessarily pessimistic assumption to assume (?) that an IEC device must have a highly non-Maxwellian ion distribution.
3. The cloud of electrons in a classical Penning trap cannot confine ions because the component of the electric field parallel to B points away from the plane of symmetry. In the experimental device described in this paper, the electrons seem to be confined not by the Penning configuration, but more by a magnetic mirror with electrostatic end-plugging.
4. As suggested above, "This work assumes a 50% D-T fuel mixture". Thus the Q=100, for what it's worth, applies to D-T. Since the Lawson criterion is 500 times more stringent for p-B11 than for D-T, my first guess at the corresponding maximum Q for that reaction would be 0.2, but that would need to be looked at more carefully.
5. The paper does explicitly talk about bremsstrahlung, but I found it hard to distill a simple statement about its magnitude. I think the best I can do is repeat the statement from the abstract: "The effect of electron losses on the Q-value has been addressed ..., indicating that large Q-values are still possible ...." If we are talking about Q=100 in a D-T system, then that suggests bremsstrahlung power about 1% of fusion power, which is the figure I have in mind from tokamaks. If the fusion power density with p-B11 is 500 times smaller, that suggests that bremsstrahlung would limit Q to about 0.2. At least none of this contradicts the numbers calculated by Rider, which therefore leaves his calculation as the state of the art for the maximum Q achievable in p-B11 systems.

[chrismb]

[2]Why is "the beam-like ion distribution function" a "crucial issue"? With sufficiently good confinement, why couldn't an IEC system operate with Maxwellian ions?

Because then you'd be describing a thermalising scenario. IEC relies on the fast fuel ions having enough energy to fuse because they do not regain their energies, unlike a thermalised system where "your investment [of energy] may go down as well as up". IEC is like buying a car, once you've put the energy in you hope that the energy 'keeps' its value as long as possible whilst it does the job required of it but in reality it is only going in one direction, whereas thermal plasma is like investing in a portfolio of funds (which, perhaps I should suggest as an analogue, goes chaotic every now-and-again!).

[4]As suggested above, "This work assumes a 50% D-T fuel mixture". Thus the Q=100, for what it's worth, applies to D-T. Since the Lawson criterion is 500 times more stringent for p-B11 than for D-T...

Again, I would suggest a clear distinction needs to be drawn between IEC and thermalised systems. The reason beam/IEC methods are condemned by the hot-magnetic-bucket brigade is because the cross-section for scattering is much higher than the cross-section for fusion. The direct equivalence between the likely conditions for different fuels is therefore not held between IEC and thermalised mechanisms because whereas for thermalised systems the scattering cross-sections are effectively irrelevant (they just re-feed the reaction mass and scattering never results in 'losses', notwithstanding the brems discussion) in an IEC system the rate of loss through scattering is all-dominant. Some scattering, particularly charge-swapping which will dominate losses in IEC under low drive potentials, goes down by several orders of mag at higher energies (such as at p11B conditions). So conditions that work for thermalised systems may not work for IEC, and vice versa.

(All that being said I still think Polywell is more likely to be a bad thermal system than a good IEC system.)

[Betruger]

Doc you can find the Rider ref. in 1. here, and I can send you a copy of that too, if you need it.
And also "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium"; I don't rememeber if this one was discussed already.

[MSimon]

Doc you can find the Rider ref. in 1. here, and I can send you a copy of that too, if you need it.
And also "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium"; I don't rememeber if this one was discussed already.

Quite some time ago. A year. Maybe two.