non-local effects on ion-electron energy transfer

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Art Carlson
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non-local effects on ion-electron energy transfer

Post by Art Carlson »

Because (1) I have an irresistible inclination to do other people's homework for them, and (2) I have less pleasant tasks that need to be done and am procrastinating, I have been thinking about Rick Nebel's suggestion that non-Maxwellian, non-local effects on ion-electron energy transfer could invalidate Rider's calculations indicating that bremsstrahlung will prevent p-B11 fusion from ever producing net energy, no matter how effective the confinement is. Rick's suggestion, or at least the only part that was concrete enough that I could even start thinking about it, was that the flow of energy from the ions to the electrons in the core of the polywell could be at least partially counteracted by a flow of energy from the electrons to the ions in the outer regions where the electric potential is more positive and therefore the ions less energetic but the electrons more so.

This idea has always bothered me. It reminds me of an Escher drawing where water is traveling in a closed loop, but always flowing downhill. If it really worked that way, then it should be possible to construct a perpetual motion machine by tapping some of the flow of water/heat. Another way to look at it is that collisions produce entropy, and more collisions must produce more entropy, so something in the system has to degrade over time, or else we are removing entropy somewhere.

Although, or perhaps because, I am a plasma physicist, in order to understand a problem I like to translate it into a simple mechanical system. In this case, I would start with a cylinder filled with gas. I can compress it, and it heats adiabatically. When I let it expand again, it returns to its earlier, cooler temperature. Now I add a second cylinder that I drive in the opposite phase. When cylinder A is hot, cylinder B is cold, and vice versa. Now I connect them by a bridge that can conduct heat. Now I have an analogy to the ions and electrons in a polywell. Heat flows from A to B and then from B to A with no net effect. That we must be missing something important becomes apparent if I replace my bridges by heat engines. The net flow of heat is still zero, but now I am extracting work!

What I left out (MSimon probably say it right away) is that I am compressing the gas, cooling it a little, and then allowing it to expand again. Therefore I am doing net work on my pistons. Now that we have a suspicion that we are doing work somewhere that we have not accounted for, we can take another look at the plasma system. Take the ions. They are energetic in the core, but then lose energy by climbing up a potential hill to the edge region. As long as they don't interact with the electrons, they get all this energy back when the roll down the hill again. Rolling up and down the hill is the equivalent of my pistons, suggesting that I am doing work with my electric potentials.

I think it goes like this. The ions roll down the hill to the core. They collide with the electrons and slow down. Since flux is conserved, their density increases. Equivalently, they spend more time in the core if they make a collision than they would otherwise. Thus collisions increase the ion density - and decrease the electron density - in the core. Collisions increase the charge density in the core and decrease it in the outer regions, so a current is flowing inward, from positive potential to negative potential. Either I am driving this somehow from the outside, or my potential well is filling up over time. Either way, there is a term that has not been accounted for in Rick's simple picture.

Calculating this model quantitatively would be a lot of work. Rick was saying, hey, look, here's a term that makes things better than expected. If that were the only additional term, one might conclude that Rider's assumptions were overly pessimistic. I am saying, but here's another term that would tend to make them worse again. Based on gut feeling developed by working in the field, I am pretty sure that the second term will at least compensate the first, and will probably exceed it. While waiting for a proponent to come up with a model detailed enough to be tested, and while waiting for the detailed calculation to be done, I am at least happier to see where the positive and negative terms in the equation will be.

D Tibbets
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Post by D Tibbets »

I think I follow most of your arguments, at least partially. The energy exchange between two fluids sounds suspisiously like a Sterling engine.
I don't think this implies perpetual motion unless you assume 100 percent efficiency and absolutly no losses like heating of the walls. If you could have excellect insulation and nearly frictionless valves you could have a engine that runs down very slowly but not a perpetual motion machine. I think you might be implying that you have to at least come close to matching these conditions for net energy when other energy input and losses are added in.

I guess your energy exchange discriptions might apply, but your model is too simple(?). You have to concider that there is a small excess of electrons present overall and the ions might form at least a small central virtual anode. I don't know how, or if, this would modify things.
If the ions are transferring energy to the electrons in the outer shell, would this be a mechanism for mitigating some of the ion upscatering? Would it also be a mechanism for reducing the population of lower energy electrons that I presume would be accumulating in this area as the electrons fight to thermalize? Would this effect ion annealing claimes?

[EDIT] Opps, rereading AC's post I realize I got the signs backwards on the ion- electron energy exchange in the core versus the edge. Here is a hasty defence of the significance of energy exchange between the ions and electrons through collisions. Certainly the direction of an electron can be changed significantly when it encounters an ion, but I was under the impression that there was not much momentum exchange between two particles with such large mass differentials. I was under the impression that the ion motions were dominated by the gross electrostatic field (space charge?) and that individual electron - ion collisions contributed an insignifficant (or at leas a minor) effect. This was one assumption that I was using in my mind to counter the agrument of ambipolar flows in the cusps.
Standing my wrong argument that ions increased the electron energy on the edge on it's head (A. Carlson said the opposite):
I have wondered how downscattered electrons are preferentially removed along with upscattered electrons in order to prolong the surviving electron thermalization time. If an already downscattered electron on the edge losses energy to ions, it would possibly diffuse across the magnetic fields more rapidly till it would either hit the magrid, or if it orbited along a field line and reached beyond the midline (radius)of a magrid it would recirculate at the reset magrid potential. This possible(?) fate of the low energy electron would help the nonthermalized chariteristics of the electron cloud without much energy loss.

Another handwaving argument- If the electrons lose significant energy to the ions near the edge and gain energy in the core, over multiple collisions the electrons would tend to be hotter and leave the core quicker, and the ions cooler. Because the ions are slower and bouncing around more (zig- zagging instead of more straight lines relative to ions bouncing around only fron ion-ion collisions) they would not transist the core or bounce off the virtual anode as quickly. This would have two possible consequences. The ions of any given energy would remain slightly longer in the core before escaping this region and also have slightly lower speeds on average. The net effect might be that while some core energy is transfered to departing electrons (lower potential well) the effective increased density of the ions in the core compensates so the competing processes cancel out from an energy balance perspective, ie- the enegry exchange in this region is close to a perpetual motion machine. At least untill radiated energy losses are considered (like brenstrahlung). I'm guessing that overall, this might change significantly weather this core ion- electron energy exchange is considered or ignored.



I'm not sure weather you are only trying to present your plasma physics principles in a mechanical model that might be more understandable to pions like me, or if you are also presenting negative arguments in a different format to round out your own understanding, but do the above confounding points tend to change the +/- balance?

Dan Tibbets
Last edited by D Tibbets on Sun Nov 01, 2009 8:11 pm, edited 3 times in total.
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TallDave
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Post by TallDave »

If it really worked that way, then it should be possible to construct a perpetual motion machine by tapping some of the flow of water/heat.
...
Either I am driving this somehow from the outside
In theory it costs you about 10MW to maintain. Not free, but maybe small enough that your little tiny star produces more.

D Tibbets
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Post by D Tibbets »

After a couple of edits, I think my above post makes more sence, I hope.

Dan Tibbets
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Art Carlson
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Post by Art Carlson »

TallDave wrote:
If it really worked that way, then it should be possible to construct a perpetual motion machine by tapping some of the flow of water/heat.
...
Either I am driving this somehow from the outside
In theory it costs you about 10MW to maintain. Not free, but maybe small enough that your little tiny star produces more.
Which theory is that? The baseline number (assuming Maxwellian distributions) for P_fusion/P_Bremsstrahlung is 0.57. If you are contemplating non-Maxwellian distributions, I'm sorry I don't have Rider's exact numbers handy, but he does say, "this minimum recirculating power is substantially larger than the fusion power". So the only published calculation answers your question whether the maintainance power could be "small enough" with a definite "no".

Edit: I just looked up the appropriate section of Rider's thesis. For p-B11, to keep P_brem/P_fus < 0.5, you need P_recirc/P_fus > 42. Not free, indeed.

choff
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Post by choff »

I was rereading the interview with Tom Ligon on "The Polywell Blob" and I came upon this:

Some of the technical details I used to think I understood, but my discussions with Dr. Nebel and others over the last year or so convince me that the understanding of their operation has changed considerably since I left, and continues to do so. Wiffleballs remain, I'm told, unproven as yet, although something with similar net effect does seem to occur. The potential well seems to be a very steep-sided, flat-bottomed "potential bucket," something I remember Dr. Bussard sketching a decade ago. We used to talk about Debye lengths in these machines a lot, but that concept seems to be falling from grace as deeper understanding emerges. There is
stuff going on at a small scale that seems to be allowing these machines to work at far higher densities than I would have guessed, and I'm no longer sure I should talk much about it as I'd probably be dead wrong. Some of my thinking about phenomena I observed in PXL-1, and the likely contribution of cold electrons in creating a wiffle-ball-like effect may be showing up in simulations.)

So, is it possible the electrons are moving very slowly at high potential throughout the inside the magrid, instead of just at the center, and if so, how would that affect the operation?
CHoff

evaitl
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Post by evaitl »

It seems like most of the professionals take Rider's thesis as pretty much bullet proof. Although, there are rumors to the contrary, like this Tom Ligon quote:

http://www.fusor.net/board/view.php?bn= ... 1181348968
I was witness, in fact, in 1995-96, to Dr. Bussard thinking Rider had actually found a fatal flaw in the idea. He dissappeared in the office or a couple of days of furious analysis and calculation, and emerged about the most jubilant I'd ever seen him. He'd discovered that not only was Rider wrong, but the machine itself had held the built-in cure all along, and would work better than the original model had predicted. I believe that was the edge thermalization process that "anneals" out any tendency the device has to Maxwellianize.
This quote may be why most people think Dr. Bussard's answer to Dr. Rider's thesis had to do with energy transfers back and forth between electrons and ions. Perhaps there was something else?

I wonder if we can approach the p-B11 problem sideways. By that, I mean accept Rider's thesis, but find some circumstances where it doesn't apply.

The tri-alpha folks seem to think that colliding beams get us out of the plasmas in thermodynamic equilibrium, therefore get us out of the bremmstrahlung problem.

Lerner seems to think the high magnetic fields in the DPF plasmoids will solve his bremmstrahlung problem.

Could the real answer for the polywell be something simple like the ions are at highest kinetic energy at or near the center and they all tend to correct towards a central foci? The point is that a small central active region may be more like colliding beam reactor except that most of the energy of misses or near-collisions is reclaimed as the ions climb back out of the potential well and come back for another pass. The point is that this breaks the anisotropy which is one of the requirements of much of Dr. Rider's analysis.

I know, this is addressed on pp29 of Dr. Rider's thesis:
http://dspace.mit.edu/handle/1721.1/11412
Spatial variations of temperature and energy may be neglected in the regions of significant sigma d^3 x[n(x)]^2.
and is further explored in section 3.4. This certainly isn't my field, but this looks like a portion of the thesis that could use a bit of scrutiny.

For instance, see pp116:
Specifically interbeam collisions will cause a slowing down of each beam, transverse velocity diffusion of each beam, and logitudinal velocity diffusion of each beam.
A cool thing about the spherical polywell is that this isn't really true. If two ions have a near miss, they will just take off in different directions. Who cares about logitudinal velocity diffusion at the center of a sphere? The ions will have roughly the same kinetic energy to begin with (because they are the same depth in the potential well) so there shouldn't be a slowing down of one beam by another.

Sorry folks, I'm starting to ramble....

chrismb
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Post by chrismb »

The issue is, and the issue for Art's analysis also, that these Colulomb collisions are not going to happen either at the edge or at the centre, they're gonna happen at any old radius (with diminuishing probability wrt r^2) so are going to scatter non-radially. And that's if it works well...

alexjrgreen
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Re: non-local effects on ion-electron energy transfer

Post by alexjrgreen »

Art Carlson wrote:Because (1) I have an irresistible inclination to do other people's homework for them, and (2) I have less pleasant tasks that need to be done and am procrastinating, I have been thinking about Rick Nebel's suggestion that non-Maxwellian, non-local effects on ion-electron energy transfer could invalidate Rider's calculations indicating that bremsstrahlung will prevent p-B11 fusion from ever producing net energy, no matter how effective the confinement is.
Art - first, second and third: thank you!
choff wrote:Some of my thinking about phenomena I observed in PXL-1, and the likely contribution of cold electrons in creating a wiffle-ball-like effect may be showing up in simulations.)

So, is it possible the electrons are moving very slowly at high potential throughout the inside the magrid, instead of just at the center, and if so, how would that affect the operation?
I'm going to argue that there aren't any electrons in the middle at all. Not only because they desperately want to get away from each other, but also because they really, really, really want to get to the magrid if only the magnetic field would let them.

The ions pass through a thin quasi spherical sheet of electrons like alpha particles through gold foil.
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choff
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Post by choff »

I was thinking if the well is shaped like a flat bottomed bucket, the polywell might work like a 3D pinball game with the steep slopes acting like bumpers and the ions millions of pinballs. So you get lots of Brems and electron losses, but it can hold a lot of ions and make a lot of fusion.

Art might be absolutely correct in his analysis of what we understand to be the operating theory behind the machine, unless the theory is all wrong. Nebel and Co. may have moved on to a new understanding of Polywell operation, which is why they don't bother to comment.

I've often wondered if electrostatic forces play a dominant role in well formation. Rather than just the diamagnetic push back, the central electrons repel the electrons trapped on the magnetic field lines, which being inductively entangled collectively pull the magnetic lines outward, causing the cusps to pinch off.
CHoff

Giorgio
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Post by Giorgio »

choff wrote:I've often wondered if electrostatic forces play a dominant role in well formation. Rather than just the diamagnetic push back, the central electrons repel the electrons trapped on the magnetic field lines, which being inductively entangled collectively pull the magnetic lines outward, causing the cusps to pinch off.
FWIW, lately I have been considering if the Polywell might work on the same principles as Lerner Focus Fusion where the recirculating lines prepare the plasma to be "pinched" in well before another passage takes place.

Any thought on this?


Giorgio.

Art Carlson
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Post by Art Carlson »

Art Carlson wrote:The baseline number (assuming Maxwellian distributions) for P_fusion/P_Bremsstrahlung is 0.57. ... For p-B11, to keep P_brem/P_fus < 0.5, you need P_recirc/P_fus > 42.
Let those number sink in. When I see them, I become faint of heart and go running for D-T, or solar power, or freezing in the dark - anything but trying to make a p-B11 reactor work. Some of you ex-Navy, can-do guys may feel up to the task. What I want to ask is, if you really want a shot at success, would you choose the route that is too hard by half, or the route that is too hard by a factor of 40? Why does Rick Nebel think the way to overcome the bremsstrahlung problem with p-B11 is to fiddle with the distribution function? We don't know how to do this, and it is a hard thing to do. Why not just try to live with the bremsstrahlung like a man? You could reach breakeven (in a perfect world) if you could absorb the bremsstrahlung at high temperature and convert it to electricity at 50% efficiency. Maybe you can make a sort of x-ray photvoltaic cell. At least it's easier to brainstorm ideas for using bremsstrahlung radiation than it is for digging a hole in the center of the electron energy distribution. And you only need a factor of 2 or so, not 40.

TallDave
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Post by TallDave »

I think it's hard to say how much control they have over the distributions without knowing the effects of playing with anode height, etc.

Certainly seems worth a shot in WB-8.1, anyway. At the very least they'll be one of the first to burn p-B11 in this kind of machine.
This quote may be why most people think Dr. Bussard's answer to Dr. Rider's thesis had to do with energy transfers back and forth between electrons and ions. Perhaps there was something else?
Dr. Nebel has said the same thing.

evaitl
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Post by evaitl »

Art Carlson wrote:Some of you ex-Navy, can-do guys may feel up to the task.
:shock: I agree. It easier to tap a Russian undersea phone cable than to get p-B11 working. We were fortunate that until somebody actually sold us out, the Russians thought that tapping their phone cables just wasn't possible.
Art Carlson wrote:What I want to ask is, if you really want a shot at success, would you choose the route that is too hard by half, or the route that is too hard by a factor of 40?
You really know the answer to that. This is just too important to walk away from until we know that it is impossible. Neutrons suck and aneutronic fusion would solve just about every problem we have right now. Dr. Rider's thesis gives us a roadmap of things that won't work, but the BE/A curve tells us that something should work.

(A side note, I invoked your name on another board: http://boards.fool.com/Message.asp?mid=28041463. If I mis-quoted you, please let me know.)

I think the optimists here are gambling on an historical repeat.
Lord Kelvin wrote:“Heavier-than-air flying machines are impossible.”
was said by a world-renowned expert despite living in a world full of birds and butterflies.

We live in a universe full of stars that happily burn B11. We don't need to repeat what stars do in the same exact way any more than a 747 needs to flap its wings.

Art Carlson
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Post by Art Carlson »

evaitl wrote:
Art Carlson wrote:What I want to ask is, if you really want a shot at success, would you choose the route that is too hard by half, or the route that is too hard by a factor of 40?
You really know the answer to that. This is just too important to walk away from. Neutrons suck and aneutronic fusion would solve just about every problem we have right now.
I'm not exactly a fan of neutrons, but the problems they cause have technical solutions These solutions may not satisfy you, but for p-B11 no solutions are in sight, so why obsess about it? If you told me that the future of the human race depended not just on energy, or even fusion energy, but on p-B11 energy (a really silly idea), I still wouldn't waste time with the polywell. I'd give it a shot with ICF:

http://en.wikipedia.org/wiki/Aneutronic ... er_balance
In conventional fusion reactor designs, whether based on magnetic confinement or inertial confinement concepts, the bremsstrahlung can easily escape the plasma and is considered a pure energy loss term. The outlook would be more favorable if the radiation could be reabsorbed by the plasma. Absorption occurs primarily via Thomson scattering on the electrons,[5] which has a total cross section of σT = 6.65×10−29 m². In a 50–50 D–T mixture this corresponds to a range of 6.3 g/cm².[6] This is considerably higher than the Lawson criterion of ρR > 1 g/cm², which is already difficult to attain, but might not be out of the range of future inertial confinement systems.[7]
Or maybe I'd just stick with boron bombs in underground cavities.

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