Maximum size allowed by energy flux constraints

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

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Art Carlson
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Re: Problem

Post by Art Carlson »

bcglorf wrote:Ow, my head hurts. I'm merely a software engineer but unless I know even less about physics than I think I do that's NOT how to calculate the pumping requirements.

My uneducated guess is that what's important is the mass of your alpha's per second.
Chris is right that pumps are rated in terms of liters per second. If you double the gas pressure, you double the number of grams you can pump per second.

Aero
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Post by Aero »

While we're busy checking math, maybe someone would like to help me with my guess as to how long it takes an alpha particle to exit the machine. I think our previous assumption has always been that the alphas exited almost instantaneously, but with Dr. Nebel's post stating that they hang around for about 1000 cycles before exiting the cusp, the previous assumption is obviously not very good.

My guess now is that the alphas take about 1 ms to escape. That is:
1000 cycles through the machine, particle velocity about 10^7 m/sec, and cycle length close to 10 meters. The velocity and cycle length may both be high, but the exit time is non-zero.

Then the other question is, "What difference does it make?" Its only 10^18 more alphas in the core anyway.
Aero

MSimon
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Post by MSimon »

Let us look at it another way.

A pB11 reactor generating 100MWf (same as 100 MWth - gross power) burns about 200 g of B11 a day. That would be (200/11 * 6E23 * 3) He4 atoms per day. Roughly 350 E23 atoms of helium per day. Or 3.5 E25 atoms of He4 a day. That is 4E20 He atoms a second.

The operating pressure of the reactor is 1E-7 torr. That would be 3E12 He4 atoms per liter (if He4 was the only gas being pumped). So the pumping required is about 1E8 liters a second for He4 alone. That is a lot.

OTOH the ITER guys have a plan for that much pumping if not more. I say copy their pumps.
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MSimon
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Post by MSimon »

OTOH the density of the gas in ITER is about 1E17 per liter. So maybe their pumps will not do the trick.

http://www.iop.org/EJ/abstract/0741-3335/48/5A/S46

This may call for a custom design. Which may be one of the reasons for the high cost of a 100 MW prototype.
Engineering is the art of making what you want from what you can get at a profit.

JohnP
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Post by JohnP »

my apologies for doubting chrismb's calculation.

However, that's assuming the alphas are evenly distributed in the chamber. Since we're going to have superconductors and LHe(?) anyway, maybe we could condense them with cold.... or electrostatically. Corral them in a part of the chamber, then suck 'em out. Would that work?

Skipjack
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Post by Skipjack »

I think this is a very high, if not unachieveable number. At least it seems rather insane to me. The turbopumps of the Space Shuttle Main Engines can pump 3917 litres per second. That is already a lot, but still just a 40 millionths of what would be needed?!!

Or lets take the F1 engine of the SaturnV.
Here is the excerpt from Wikipedia:
A gas-generator was used to drive a turbine which in turn drove separate fuel and oxygen pumps, each feeding the thrust chamber assembly. The turbine was driven at 5,500 RPM by the gas generator, producing 55,000 brake horsepower (41 MW). The fuel pump produced 15,471 gallons (58,564 litres) of RP-1 per minute while the oxidizer pump delivered 24,811 gal (93,920 l) of liquid oxygen per minute.

Ok, so you have a 41 MW turbopump that can still not even pump a millionth of what you would need? If that is the case, then we might just as well give up on this alltogether. Because the pump allone would require waaay more than 100 MW.

MSimon
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Post by MSimon »

Skipjack wrote:I think this is a very high, if not unachieveable number. At least it seems rather insane to me. The turbopumps of the Space Shuttle Main Engines can pump 3917 litres per second. That is already a lot, but still just a 40 millionths of what would be needed?!!

Or lets take the F1 engine of the SaturnV.
Here is the excerpt from Wikipedia:
A gas-generator was used to drive a turbine which in turn drove separate fuel and oxygen pumps, each feeding the thrust chamber assembly. The turbine was driven at 5,500 RPM by the gas generator, producing 55,000 brake horsepower (41 MW). The fuel pump produced 15,471 gallons (58,564 litres) of RP-1 per minute while the oxidizer pump delivered 24,811 gal (93,920 l) of liquid oxygen per minute.

Ok, so you have a 41 MW turbopump that can still not even pump a millionth of what you would need? If that is the case, then we might just as well give up on this alltogether. Because the pump allone would require waaay more than 100 MW.
Uh. The densities of the materials pumped are vastly different. I believe pumping power is delta pressure times mass flow. The mass flow might be as much as 10 Kg a day (including all species).
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Skipjack
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Post by Skipjack »

Yes, but in return the pressure is much lower (the fuel tanks of the saturnV had a positive pressure). Also the fuel was acting as a coolant. Not sure about the vacuum pumps there...
Anyway, if I am totally off, here, then maybe these turbopumps can at least act as a model to give you smarter guys an idea.

MSimon
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Post by MSimon »

Aero wrote:While we're busy checking math, maybe someone would like to help me with my guess as to how long it takes an alpha particle to exit the machine. I think our previous assumption has always been that the alphas exited almost instantaneously, but with Dr. Nebel's post stating that they hang around for about 1000 cycles before exiting the cusp, the previous assumption is obviously not very good.

My guess now is that the alphas take about 1 ms to escape. That is:
1000 cycles through the machine, particle velocity about 10^7 m/sec, and cycle length close to 10 meters. The velocity and cycle length may both be high, but the exit time is non-zero.

Then the other question is, "What difference does it make?" Its only 10^18 more alphas in the core anyway.
I'm not sure that the 1000 passes is strictly true for He4. It will depend on the energy distribution. Above a certain energy He4 ions will escape directly with one pass.
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MSimon
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Post by MSimon »

Skipjack wrote:Yes, but in return the pressure is much lower (the fuel tanks of the saturnV had a positive pressure). Also the fuel was acting as a coolant. Not sure about the vacuum pumps there...
Anyway, if I am totally off, here, then maybe these turbopumps can at least act as a model to give you smarter guys an idea.
10 Kg a day. 15 psi delta p. It is not a lot of watts. There will probably be more energy in losses (by a factor of many thousands) vs actual pumping power.
Engineering is the art of making what you want from what you can get at a profit.

KitemanSA
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Post by KitemanSA »

I know alphas don't penetrate much but certainly they will penetrate a bit. Couldn't we place a very thin membrane between the thermal wall and the chamber that the alphas would penetrate and then get neutralized and trapped behind? The pressure would rise a lot and pumping would be so much easier.
Worse comes to worst, if we go thermal conversion, line the chamber with diamond foil and trade it out occasionally. MeV alphas penetrate diamond fairly deeply. Not sure how much could be stored that way berfore needing to trade it out. "Problem for the student". :)

D Tibbets
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Post by D Tibbets »

M. Simon's numbers of ~ 10^20 alphas per second and pressures are close to the back of the skull calculations I was doing. 10^-9 would be nice but I recall ~ 10^-7 being closer to the outer chamber pressures obtained with curent machines once they were fired up and befor they shut down due to continous pressure buildup from the gas puffers which led to arcing.
I'm somewhat confused (again) by M. Simons comparison. A gas pressure of 10^17 molecules/ions per liter would be ~2.24 x10^18 molecules per 22.4 liters (molar volume at one atmosphere) which would be equal to a pressure of ~ 2.24x10^18 molecules / 6.02 x 10^23 molecules per atmosphere or ~ 4 x 10^ -6 atmosphere. This is ~ ten to twenty times the pressure of the Polywell . But, this density of molecules is distributed over a much larger volume in a Tokamak. In otherwords, if the volume of the Polywell vacuum vessel was increased ~ 20 fold to match the volume of the power producing Tokamak (reasonable size comparison?) the pumping volumes would be comparable. So, if nothing else worked, increasing the vacuum vessel size appropiatly should bring it into the ballpark of the Tokamac vacuum pumping estimates, if my assumptions and convoluted reasoning are correct. This is only concering the volume that has to be cleared, not the effects of different densities. Or, another way to look at it is that the vacuum pumps have to work harder to extract a more rareified gas, but they have to do it in a corespondingly smaller volume. Is there a break even somewhere?

Also, if the alphas are flying out mostly through the cusps, an electrical grid could not only harvest energy from them , but (at a small power cost?) direct most of them straight into a pumping port, perhaps with cone shaped baffles to prevent backflow- something like a diffusion pump. This, I speculate, could greatly increase pumping efficiency.

Concerning the lifetime of the alpha particles befor they escape, some speculation. The electrons were quoted as traveling at ~ 1 billion cm per second at ~ 10,000 electron volts. At several million electron volts the alpha particles would be traveling much faster, how much I don't know. Assume 10-20 times as fast. I'd choose a higher number, but then I'd have to argue with Einstien. If an electron traverses a 3 meter diameter magrid in ~ 0.3 microseconds, then the alpha lifetime would be 0.3 microseconds per transit X 1000 transits = 0.3 milliseconds. If the speed is 10 to 20 times as fast the lifetime would be in the neighborhood of ~ 0.03 milliseconds in a 3 meter diameter machine.

[EDIT] Ignor the above paragraph as I ignored the mass difference between the ions and electrons when I assigned the potential induced velocity.

In terms of the effect of the alphas on the electrostatic fields, I suspect there is an effect, but because the fuel ions are presumably several orders of magnitude more prevelent and survive several orders of magnitud longer, the effect would be miniscule.

Now, my head hurts...

Dan Tibbets
Last edited by D Tibbets on Wed Jul 01, 2009 8:45 pm, edited 1 time in total.
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chrismb
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Post by chrismb »

MSimon wrote: The operating pressure of the reactor is 1E-7 torr.
Well, let's see about that;

So the cross-section of a hydrogen atom is around 5E-20m^2. Density of 1E-7 torr is 3E-15/m^3. Mean free path from that is around 7,000m. Say 7,000 passes for a ~1m order-of-mag reactor.

(What do you reckon the density of those much larger neutral boron molecules is that will be floating around?? And don't forget all those sputtered metallic contaminants!)

Now you can see from viewtopic.php?p=13258&#13258 that you need around 200,000 reciprocations before getting a fusion reaction out of it.

So - I would suggest a background pressure of 1E-7 torr is way way too high to avoid thermalisation.

Even at my 1E-9 torr suggestion, you're only 'on average' a mean-free-path length's worth of reciprocations to an 'average' fusion event probability, which means that 50% of the particles will still thermalise, even at 1E-9 torr, but we're in the ball-park around there and can then look, and hope, to be on the '>6 sigma' end of the particle population that might not thermalise.

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Post by chrismb »

MSimon wrote:OTOH the density of the gas in ITER is about 1E17 per liter. So maybe their pumps will not do the trick. This may call for a custom design.
You're dead right there, I think. Fundamentally, tokamaks work on the principle of a theralised plasma, whereas IEC cannot function in this way. So thermal plasma fusion has the advantage of density - and it is a huge advantage!

The other point made, cooling the plasma local to extraction, is also true of tokamaks - the interaction of the plasma with the divertors does exactly that [cools the plasma down, increasing density, before extraction] and there isn't a simple relationship between the extraction pressures and the plasma/chamber/edge and core pressures.

By a random and essentially unknown piece of good fortune, the helium ash in JET has been found to build up, differentially, around the divertors, so giving hope that the helium, whcih would otherwise contaminate the plasma, can be selectively extracted. So, I'm guessing there's a lot of ITER folks with their fingers crossed [for many reasons, but at least] in hope that He ash extraction is also possible at ITER's divertors.

(When I say 'cool divertors', these babies are sucking up 20MW/m^2 which is the upper limit of materials, so it is not clear to me that such large tokamaks are viable anyway, in material terms.)

rnebel
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Post by rnebel »

If you are interested in pumps, the specifications for ITER can be found at:
http://www.iter.org/a/index_nav_4.htm
. If I am reading this correctly, the pumping power is about 60,000 liters/second. This is ~ 30 times more than the WB-7. It doesn't take a lot of power. Our system takes ~ 500 watts of power. ITER probably requires 10-20 kW.

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