Central electron temperature and p-B11 power balance

[TallDave]

the size of the device was explicitly limited to the debye length (densities 10^18, radius 1cm),

This is something I've seen come up before and I'm not clear on. Can you calculate a Debye length for a dynamic non-LTE environment? Some seemed to think this is unrealistic last time it came up, and I never saw a clear answer.

[TallDave]

Ah, here we go:

I do have 1-D Particle-in-Cell (PIC) simulations which have global electrostatic fields in the quasi-neutral limit. The same is true of the Vlasov-Poisson equilibria generated by Bussard’s people in the early to mid 90s. All of these cases produce electrostatic fields over distances long compared to the Debye length. The way these are produced is by flooding the system with hot electrons and starving it for ions. This forms systems with potential wells comparable to the electron injection energy, and the electron inertia spreads the potentials over the entire radius.

[Art Carlson]

Furthermore, all the relevant processes depend on the square of the density, so the Q we calculate will not depend on the absolute value of density or any variations in density over space. (Some peolple seem to be having trouble absorbing this point).

Yes, but some of them depend on ion density, others on electron density.

Of course, the relative densities of the three species must be optimized, within the constraint of quasineutrality. (Another point that isn't sinking in very fast.)

Also, how would this be affected by POPS improvements?

I am - at least in principle - looking for the distribution functions for the 3 species that maximize Q. I am not at this time concerned with the question of whether the functions can be made uniform in space or constant in time. There is a maximum value that Q can take on at one place and time. The average Q for a non-uniform distribution or one evolving in time (whether periodic like POPS or secular) will certainly be less than this maximum.

[Art Carlson]

Ah, here we go:

I do have 1-D Particle-in-Cell (PIC) simulations which have global electrostatic fields in the quasi-neutral limit. The same is true of the Vlasov-Poisson equilibria generated by Bussard’s people in the early to mid 90s. All of these cases produce electrostatic fields over distances long compared to the Debye length. The way these are produced is by flooding the system with hot electrons and starving it for ions. This forms systems with potential wells comparable to the electron injection energy, and the electron inertia spreads the potentials over the entire radius.

There can certainly be electric fields in or around a quasi-neutral plasma. That's why it's *quasi* neutral rather than *strictly* neutral. The point here is that Chacon got his best results for systems that violated quasi-neutrality. Nebel and anybody else in his right mind envisions running the polywell in a quasi-neutral regime in order to get useful power densities, so Chacon's results must be applied with caution.

[Art Carlson]

(2) Rider's parametrized distributions are close to optimum.

Rick mentioned at one point that square wells (such as Rider used) give very different results (i.e., much worse) than "more realistic" parabolic wells such as in the Chacon paper.

I'm talking about electron velocity distributions, not spatial distributions of the electric potential. That's a different Rider paper.

But since you bring it up, the plots I've seen of the potential profile in simulated polywells looked pretty square. I believe this is a necessary consequence of the high beta operating regime (and, as I never get tired of saying, quasineutrality).

[rnebel]

As near as I can tell, the arguments being made here are the same as those made by Rider many years ago. The problem is that you can’t study the polywell physics in isolation, you have to study the system as a whole. This is the mistake that Rider made and it appears to be the mistake that is being made here. You can’t just look at the coupling between the ions and the electrons, you have to look at where the electrons go.
The electron temperature in a polywell is set by the potential well and it is largely unaffected by the ion-electron collisions. The reason is that electrons which are upscattered by ions are removed from the system. These upscatterd electrons will rattle around in the polywell until they exit through a cusp. Since they have been upscattered, they will have more energy than the applied potential between the coils and the wall. Consequently, they will leave the system and go to the wall. As they proceed to the wall, they will lose almost all of their energy through direct energy conversion (this is what happens when a particle runs up a potential hill). Consequently, the electrons located inside the polywell don’t heat.
Of course, you don’t get something for nothing. If electrons are being lost to the chamber walls, they have to be replaced by the e-guns. Although the TOTAL current in the system doesn’t increase, the electron flowthrough goes up. The reason the total current doesn’t increase is because the electrons go to the wall, not to the high voltage coil cases.

[Art Carlson]

Thanks for the reply, Rick. I understand that the loss of up-scattered electrons acts to keep the electrons cold. If you do it right, you also only have to pay for the energy differential, not the whole energy of the electrons being recycled.

But I'm afraid I don't see the relevance to my argument. We have protons whipping through the system, or at least some parts of the system, with energies relevant for fusion. In these same regions, there are (you tell us) cold electrons. So two things are happening to my protons: occasionally one fuses with a boron ion and gives me a bunch of energy, and continuously they rub against the electrons and loss kinetic energy. If the power being lost by the protons to the electrons (regardless of what the electrons then do with this energy, whether they lose it by up-scattering out of the well or whether they lose it by radiating bremsstrahlung), if the power being lost by the protons to the electrons is greater than the power the protons are generating through fusion, I have a problem.

[rnebel]

Actually, you can get the energy differential back as well (though in practice it won't be 100%, I'm sure). What you do is keep the electron guns at a little higher potential than the wall which is at ground. In vacuum tubes they do this by having a small resistor between the e-guns and ground. You could probably look at more elaborate schemes of direct energy conversion to get the thermal spread, as well.

[Jboily]

Thanks for the reply, Rick. I understand that the loss of up-scattered electrons acts to keep the electrons cold. If you do it right, you also only have to pay for the energy differential, not the whole energy of the electrons being recycled.

But I'm afraid I don't see the relevance to my argument. We have protons whipping through the system, or at least some parts of the system, with energies relevant for fusion. In these same regions, there are (you tell us) cold electrons. So two things are happening to my protons: occasionally one fuses with a boron ion and gives me a bunch of energy, and continuously they rub against the electrons and loss kinetic energy. If the power being lost by the protons to the electrons (regardless of what the electrons then do with this energy, whether they lose it by up-scattering out of the well or whether they lose it by radiating bremsstrahlung), if the power being lost by the protons to the electrons is greater than the power the protons are generating through fusion, I have a problem.

Here is the calculation of the Ions-Electron power balance I was talking about earlier.
http://www.sciencemag.org/cgi/content/f ... /5375/307a
Sorry it took me so long to find it, the web link was on my old computer. I have not finished to transfer all my info yet.

It is for a colliding beam feasibility, but I believe this should apply equally to the polywell system.

They are talking about a system generating about 45 watts in fusion power, with a 44 watts of bremsstrahlung radiation., and they calculating 2000 watts electron heating. This would mean Q very low Q in this system, using their parameters. The heated electrons can be removed from the system, and reinserted trough the electron gun.

Applying these calculations to the BFR would mean we need an electron energy direct conversion with an efficiency better then 98%. Being optimistic in nature, I would think a few more tricks can be used here, allowing less stringent power recirculation.

Applying these calculations to the BFR would mean we need an electron energy direct conversion with an efficiency better then 98%. Being optimistic in nature, I would think a few more tricks can be used here, allowing less stringent power recirculation.

The electron heat is obviously a very important factor. It however do not have to be a complete loss. The heated electrons can be kept recirculating in the machine. Maybe we need only to remove the electrons at the tail end of the high energy distribution, removing the one that are very hot. This would help with the direct conversion efficiency, and allow more time to the hot electron to redistribute their energies to the colder electrons.

I hope this help

[Jboily]

Art,
I just realized my link is the same study as the one you provided at the start of this tread. I guess we are reading int differently

[Stefan]

Is it really a good thing to get rid of the upscattered ions?
Afterall the mechanism we use to give energy to the system (and thus the ions) is injection of hot electrons.

Wouldn't an increase in electron energy cause a deeper potential well, thereby giving energy back to the ions (assuming most of them are outside of the center at any given time)?

I guess there would be some balance with the ions having a smaller average energy than the electrons, the question than becomes whether this is much smaller and what the ion energy distribution would look like.

[hanelyp]

A point is made about ions loosing energy to electrons in the center of the polywell. But what about electrons loosing energy to ions around the edges? Since the ions and electrons are circulating between those regions, I'd expect those effects to cancel to some degree.

[Jboily]

A point is made about ions loosing energy to electrons in the center of the polywell. But what about electrons loosing energy to ions around the edges? Since the ions and electrons are circulating between those regions, I'd expect those effects to cancel to some degree.

For what I gather, I think the main problem is that there is not enough energy transfer from the electrons back to the ions. The electrons would get hot, and loose their energy trough bremsstrahlung and synchrotron radiation. It is better to recuperate this energy somehow, and re-transfer it to the ions.
I don't think we heat the ions with the electrons, we simply are using then to maintain a potential well to trap the ions. The ions are “heated” by simply falling down the potential well.
It is not necessary to remove the up scattered Ions, they just comes out on their own. The more we can trap in the wb, the better. It is the electrons we need to remove.

[Stefan]

I don't think we heat the ions with the electrons, we simply are using then to maintain a potential well to trap the ions. The ions are “heated” by simply falling down the potential well.

By falling down the ions take energy from the electrons.
Either they lower the well depth, thus taking potential energy from the electrons inside it, or they cause more hot electrons to be injected so the well can be maintained.

[Jboily]

I don't think we heat the ions with the electrons, we simply are using then to maintain a potential well to trap the ions. The ions are “heated” by simply falling down the potential well.

By falling down the ions take energy from the electrons.
Either they lower the well depth, thus taking potential energy from the electrons inside it, or they cause more hot electrons to be injected so the well can be maintained.

In continuous operation, you will get roughly the same Ions going down the well, then there are going back up. What we are talking about is that there is a population of electrons that is getting hot, some having more eV then others. We need to remove this energy somehow, and give it back to the ions, most of it would otherwise be lost from the system. This recycling need to be very efficient, in the order of 99.99% according to Art. Injecting Proton at a higher eV and keeping the Boron colder will help, but we still need to solve the electron energy recycling.