Electron recirculation

Discuss how polywell fusion works; share theoretical questions and answers.

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TallDave
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Post by TallDave »

The inverse square law doesn't apply? I would think an electron's attraction would depend on its distance from the charged surfaces, in addition to the relative charges. But maybe that's just my ignorance.

93143
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Post by 93143 »

Of course the inverse square law applies. I didn't say the field was going to be uniform; I said it was going to be uniformly inwards. It will be much stronger near the magrid.

But without any charged structure in between the magrid and the wall, there's nothing to cause the field to reverse. That is, if by sending alphas from the magrid to the wall you can decelerate them, then electrons in that region will accelerate towards the wall. This would require a negatively charged magrid.

With a positive magrid, it doesn't matter what the charge on the collector plates is. Gauss' Law, remember? Alphas only see the positive magrid, and they accelerate slightly as they head out to smash at more than full speed into the wall. This results in a thermal system.

TallDave
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Post by TallDave »

Alphas only see the positive magrid, and they accelerate slightly as they head out to smash at more than full speed into the wall. This results in a thermal system.
OK, so you need the reversed field region to decelerate the alphas. That makes sense.
Hopefully putting them in the magrid shadow will be enough. If not, the intercept problem at that distance will not be nearly as bad, and cooling will be much simpler. On top of that, there are no superconducting magnets to worry about. It may still be hard, but if we can make the magrid work we can make the trap grid work.


Hrm. Hard usually equates to expensive. Hopefully this is still significantly cheaper and more efficient than steam turbine generators.

drmike
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Post by drmike »

The center of the reactor will have more ions than electrons, so it's positive, but just outside that center there will be more electrons than ions. Net field there is outwards for ions, in for electrons. As you get close to the MaGrid, the potential rises. It keeps rising until you get to the 2 MeV (or 1.8 or whatever) deceleration grid. Net field is inwards for ions and outwards for electrons there.

This flipping of the virtual cathode is called a "double well" structure and is described by experiments done by K. Yoshikawa et al 2001 Nucl. Fusion 41 717-720.

So long as the double well forms, we get fusion and direct conversion too.

Just a few engineering details to deal with, that's all!
:wink:

93143
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Post by 93143 »

drmike wrote:The center of the reactor will have more ions than electrons, so it's positive, but just outside that center there will be more electrons than ions. Net field there is outwards for ions, in for electrons. As you get close to the MaGrid, the potential rises. It keeps rising until you get to the 2 MeV (or 1.8 or whatever) deceleration grid. Net field is inwards for ions and outwards for electrons there.
Outside the magrid the potential falls off again. That's how recirculation works. It's also how the virtual cathode forms in the first place (electron acceleration). The potential only starts rising again after you pass the trap grid on the way to the wall.

If you're running without a trap grid, no potential difference in the system is going to be more than a few percent, at most, of the necessary alpha stopping voltage. Direct conversion is completely separate from magrid operation.

I'm at home, so I can't access that paper. (I think I've read it before - it's certainly been referenced often enough that I should have...) If I'm not mistaken, they simply describe the virtual anode caused by ion focus in the larger virtual cathode. All this does is slow down and deflect the ions slightly at the focus and allow electrons that otherwise wouldn't have made it to transit the core. We're talking about a bump a few kV high here in maybe a 20-30kV potential well.

TallDave
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Post by TallDave »

Right you are 93143, it's a 200V bump in a 7.5kV well.

I'm still not certain it impacts recirculation at all reasonable distances, but afaik there's no way around decelerating the alphas.

dch24
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Post by dch24 »

93143 wrote:Why is the direct conversion collector separate from the outer wall? Practical considerations?
I think yes: running the vacuum pumps and feed-through ports at ground is easier than at a high positive voltage. In other words, after the first BFRs are built for power plants, newer designs might be able to put the collector and the outer wall together and save space.
93143 wrote:Also, why is there current going through the direct conversion grid? The collector, not the decelerator, is what provides the electrons to neutralize the fusion products.
The deceleration happens in the space between the cage and the collector, so that the alphas eventually just kiss the collector.
93143 wrote:Where did he say that? I recall the "1e6 electron transits before loss" thing, but the reduction in energy out from even 1 electron lost per fusion would be the electron energy times the fusion rate, which is nowhere near the fusion power.
I think drmike answered this... ?

93143
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Post by 93143 »

dch24 wrote:I think yes: running the vacuum pumps and feed-through ports at ground is easier than at a high positive voltage. In other words, after the first BFRs are built for power plants, newer designs might be able to put the collector and the outer wall together and save space.
Okay, but the collector/inner wall should be at ground anyway, so that it will accumulate enough positive charge to exactly balance the negative charge on the deceleration grid. I suppose it could turn out to be easier power-supply-wise to split the voltages between the trap grid and the collector and ground the shell, but then you've got a megavolt gap between the collector and the shell that doesn't do anything...
The deceleration happens in the space between the cage and the collector, so that the alphas eventually just kiss the collector.
Yes, so the collector is where electrons are pulled out of the metal, requiring replacement (ie: current). Therefore that's where the power lines should be attached.
93143 wrote:Where did he say that?
I think drmike answered this... ?
I'm pretty sure he didn't...

MSimon
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Post by MSimon »

93143 wrote:
dch24 wrote:I think yes: running the vacuum pumps and feed-through ports at ground is easier than at a high positive voltage. In other words, after the first BFRs are built for power plants, newer designs might be able to put the collector and the outer wall together and save space.
Okay, but the collector/inner wall should be at ground anyway, so that it will accumulate enough positive charge to exactly balance the negative charge on the deceleration grid. I suppose it could turn out to be easier power-supply-wise to split the voltages between the trap grid and the collector and ground the shell, but then you've got a megavolt gap between the collector and the shell that doesn't do anything...
The deceleration happens in the space between the cage and the collector, so that the alphas eventually just kiss the collector.
Yes, so the collector is where electrons are pulled out of the metal, requiring replacement (ie: current). Therefore that's where the power lines should be attached.
93143 wrote:Where did he say that?
I think drmike answered this... ?
I'm pretty sure he didn't...
Some answers:

1. Designing a BFR with a 2 MV outer shell should not be too hard. You just need a big building to get the clearance. However that raises the cost of the shielding. We will have to see what the design trade offs are.

2. We are designing a vacuum tube. Multiple "grids" can be used to get the potential gradients you want in any given place.

3. Absolute maximum according to Paschen curves I have read is 50KV/cm on a continuous basis. That is 40 cm for 2 MV. Add in a 2X safety factor and you are at 80 cm. Large but probably OK. Shrinking that with experience.

4. The collector plates will be collectors of spent particles. They will be collecting heat and delivering neutralizing electrons (a few Amps at most). The energy will be delivered by the 2 MV (approximately) "electrostatic" collector grids. One of the problems that will have to be dealt with is the energy spread of the particles both within the bands (about 100 KV wide - estimated) and between bands (1.25 and 1.9 MV) for pB11. Easiest way to start is just have the collector grids at 1.25 MV and just let the extra energy from the 3.8 MeV (is that right?) alphas get turned into heat. That amounts to about 10% of the total energy. We can fix that - if it is fixable - in the 2nd generation. Add in the alpha losses to the grid and drive power and you are probably some where in the 50% to 70% range for electrical output/fusion energy. Not bad. That means worst case cooling rqmts are a little less (2/3rds) than a typical fission plant. Also cooling will not affect efficiency, so the heat can be rejected at a relatively high temperature. Greatly reducing the cost of the cooling towers (if needed).
Engineering is the art of making what you want from what you can get at a profit.

93143
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Post by 93143 »

MSimon wrote:2. We are designing a vacuum tube. Multiple "grids" can be used to get the potential gradients you want in any given place.
Thanks. That's what I've been trying to get across here. The potential gradient we want outside the magrid is one that recirculates electrons and (incidentally) repels ions. The magrid doesn't need to be what decelerates the alphas.
4. The collector plates will be collectors of spent particles. They will be collecting heat and delivering neutralizing electrons (a few Amps at most). The energy will be delivered by the 2 MV (approximately) "electrostatic" collector grids.
But those grids really are electrostatic. Ideally, there's no current flow to or from them. The current flow is between the magrid and the collector plates, across a potential difference almost identical to that between the trap grid and the collector plates. The fact that the trap grid is what sets up the space charge effect resulting in this potential difference should be irrelevant to the power system.

charliem
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Post by charliem »

MSimon wrote:4. The collector plates will be collectors of spent particles. They will be collecting heat and delivering neutralizing electrons (a few Amps at most). The energy will be delivered by the 2 MV (approximately) "electrostatic" collector grids.
There's no need that collector "plates" are solid, they can be grids, and they can double as decelerators and collectors at the same time.

That arrangement would have some advantages over a solid one, less heat, easy compensation of the expected energy spread, easy separation of the collector system in two, one for 2.46+-0.1 MeV and another for 3.76+-0.1 MeV ions.

In that case there were no pure "electrostatic" grids, in the sense that each one would give current, although at different voltages.

93143
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Post by 93143 »

charliem wrote:There's no need that collector "plates" are solid, they can be grids, and they can double as decelerators and collectors at the same time.
I hope you're not suggesting that an alpha can be decelerated by a grid it's still inside of. I've lost count of the times I've tried to explain why you can't do that.

If you mean that the particle passes the grid, slows down, doubles back and hits the grid on the far side, that's every bit as bad, because it will hit the grid with the same energy it had when it passed it (the full fusion energy) and you've got a thermal system again. Assuming you can actually hit the grid in the first place, and not have alphas just falling back through the core most of the time.
That arrangement would have some advantages over a solid one, less heat, easy compensation of the expected energy spread, easy separation of the collector system in two, one for 2.46+-0.1 MeV and another for 3.76+-0.1 MeV ions.
The outer collector should be a solid wall. That way there's no way to miss it. Multiple grids could be used to bleed off lower-energy alphas, but the inner one will receive the full flux of high-speed particles (hopefully it's in the magrid shadow so it doesn't heat up too much) and won't collect any, and the next one is going to have trouble actually picking up low-band alphas before the field from the first grid hauls them back into the reactor.

We really don't want a high flux of thermalizing alphas making repeated transits through the core just because they can't get to the wall and aren't lucky enough to hit the intermediate collector grid. Some funky solid collector geometry, combined perhaps with magnetic fields to separate the alpha energy bands, might do the trick. It's tough when emission is isotropic, although we do have shadows from the magrid to work with...

EDIT: I got an idea.

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Post by MSimon »

The 2 MeV electrostatic grids will be delivering the energy. Assuming 100 MWe output that would be in the neighborhood of 50 Amps.

The power out/in of any grid would depend on its voltage and the current flow.

Remember: induced (electrostatically) currents are just as good as real currents (from a battery). Which is why I put electrostatic in quotes. They are electrostatic in terms of fields. They will have real currents of significant magnitude flowing through them.
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charliem
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Post by charliem »

93143 wrote:I hope you're not suggesting that an alpha can be decelerated by a grid it's still inside of. I've lost count of the times I've tried to explain why you can't do that.
I think I understand the meaning of your statement but find it a bit confusing. Of course that an [isolated] charge inside a spherical chamber, its walls charged to any level we want, wont be influenced by it, because inside that sphere the E-field is null and our isolated charge cant be accelerated in any direction by a non existing field, but in a polywell machine there will be lots of things inside any of the grids.

I'm refering to a disposition of concentrical spherical grids at different potentials. In that case there's going to be an E-field in between, and any [moving or not] charge/ion that gets in the middle will feel the corresponding force.

This is how I see it (with some numbers to try make it a bit more clear). I'll take the magrid (MG) as the potential reference (0 Volt) and postulate a 25 kV/cm gradient. Going outwards from it we'll find the next structures (all spherical):

# 4 cm out is grid G1, the uncoupling grid (-100 kV), the one that shields the magrid from any external E-field and repels the electrons that get out through the cups to help force them back inside.

# 51, 53 and 55 cm beyond G1 three more grids G2-G3-G4, to decelerate and collect 2.46+-0.1 MeV ions (at +1.18, +1.23 and +1.28 kV respectively).

# 44, 46 and 48 cm beyond G4 another three, G5-G6-G7, to decelerate and collect 3.76+-0.1 MeV ions (+1.83, +1.88 and +1.93 kV).

# 4 cm from G7 the external wall, at +100 kV over G7 (+2.03 kV) to help repel any remaining ion with an initial energy over 3.86 MeV (or just use this wall to do the work of G7 and simplificate things a bit).

So the total radium of this contraption would be:

1.4(the magrid)+0.04(to G1)+0.48(to G2)+0.04(G3-G4)+0.48(G5)+0.04(G6-G7)+0.04(external wall) = 2.52 meters.

(if we plan on a higher potencial gradient that size could be reduced).

I know that getting 6 different currents at 6 different voltages complicates electronics. The benefit is that the grids and external wall dont need to be that hardened.

P.D. About transparengy of the grids the higher the better. If G1 is not completely inside the magrid shadow and, say, it is only 98% transparent, then it's going to intercept some 1.6 MW (if the magrid itself intercepts a 20%). G2-G3-G4, with a combined trasparency of 96% would intercept about 0.35 MW worth of the originally 3.76 MeV ions (by then 1.3 MeV) and near 100% of the 2.46 MeV (now between 0 and 200 keV).

P.D. 2: Of course you can use any number of grids per energy level that you want, 3, 2, 1, or 33, as long as they're highly transparent.

93143
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Post by 93143 »

charliem wrote: I'm refering to a disposition of concentrical spherical grids at different potentials. In that case there's going to be an E-field in between, and any [moving or not] charge/ion that gets in the middle will feel the corresponding force.
Okay, GOOD. Thank you...
P.D. About transparengy of the grids the higher the better.
For power loss, yes. What makes you think that just because an ion reaches its apogee (so to speak) at the radius of a particular grid, that it will get picked up and neutralized by that grid?

Sorry about my short temper... I have a meeting on Friday where I'm probably going to have to tell them I don't know why, after two months, the sound speed comes out wrong in my implementation of a real-fluid transcritical equation of state. It's not like I haven't been through the calculus exhaustively once already...

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