Building a Sun on earth - pointless!!!

Reflections on fusion history, current events, and predictions for the 'fusion powered future.
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Chris Bradley
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Building a Sun on earth - pointless!!!

Post by Chris Bradley » Sun Mar 01, 2009 7:51 pm

Just to nail the misconception that "if we could recreate a miniature Sun on earth then we'd have a useful power supply";

Total power output of the Sun = 3E26W
Total volume of the Sun = 1E27m3

Total output of an Olympic swimming pool volume (2,500m3) of proton burning plasma, equivalent to normalised Sun plasma, = 800W

If you stick solar panels all over the top of a typical house, you'll get somewhere like 2 to 3kW of electrical power from polycrystalline types, which is around what the house actually uses. But you'd need ~14 Olympic swimming pool's worth of solar plasma to generate the same power! (assuming 30% thermal efficiency to electricity) That's quite a real-estate burden on top of building your house! And that's not counting the containment and power extraction facilities!

Let's consider a power station facility with a 3GW installed capacity; you'd need 1E10m3 of solar plasma which is, for example, a volume 10 metre high by 1 kilometre wide by 1,000 kilometres long.

Let's put it into a cube to minimise the surface area and thus the containment vessel materials. I believe we have about 80GW installed capacity here in UK, that'd be a cube 10 kilometres along each edge (taking into account heat conversion loss 1:3) or a sphere of 12 kilometres diameter.

Hmmm... a 10 kilometre high fusion core? US consumption was 800GW in 2007, so that'd be a fusion core twice as big!

In fact, if America were to dedicate one single State to the production of 800GW of electricity with a Sun-like plasma and let's say it is one of their really big states, conveniently in the middle of the country, like Kansas, then the Solar-plasma core required to power the rest of the US would cover the WHOLE of Kansas to a height of 11 metres.

The next possible, and most efficient way, to make use of solar plasma suitable for human use is to round up 2E30kg of hydrogen, allow it to compress itself under its own gravity and allow it to become incandescent under fusion energy emissions at its centre, then sit 93million miles away behind a dual magnetic shield and 100km thick gaseous shield and make use of radiated electromagnetic energy with photo-voltaic panels. Compared with keeping a little sun on hand, this configuration actually saves on real estate, as shown here, and has the advantage that most of the engineering has already been done courtesy of mother nature.

If mankind is intent on using terrestrial nuclear fusion for their energy production, it has to be a fundamentally different and an enormous improvement (in specific power terms) to what the Sun does.

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Re: Building a Sun on earth - pointless!!!

Post by Dan Tibbets » Sun Mar 01, 2009 10:10 pm

Yes and no... for hydrogen (P) the densities and volumes are as you say (I guess). While not bothering to actually look it up, deuterium and lithium burn much quicker in stars. In the newborn Sun the ~one part in 6000 of deuterium burned thousands of times faster so that it was exausted within a few thousand to a few million years. The limiting factors were probably all that contamination with hydrogen- the deuterons couldn't find each other. So, a star made up of mostly deuterium would burn MUCH faster. I'm not sure what the solar mass deuterium star would look like, probably a blue supergiant, if it could hold itself together at all .

Also, keep in mind that P-P fusion dominates in the Sun. Pick a more massive star that can heat its core to ~ 30,000,000 C and CNO fusion would be going on ~ 1,000 times faster.
http://csep10.phys.utk.edu/astr162/lect ... no-pp.html

So, instead of covering my state with solar core plasma, instead fill Washington DC with hotter stellar core plasma (30,000,000 degrees C, or only ~ 2,500 eV). Let the politicians deal with the pressure.

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Re: Building a Sun on earth - pointless!!!

Post by Chris Bradley » Sun Mar 01, 2009 10:31 pm

I'm not sure if you're right or wrong there, but of course each pp reaction spews a D, so a lot of the fusion is, actually, D. But I thought it's the D+p that takes the priority at the 'lower' stellar temperatures. Run a DD reactor on earth, fine (if you can get it going!!), but I'm not sure that's what stars do.

Is the 1:6000 for deuterium a universal occurrence ratio? I thought it is a reflection of what has been left here on earth as hydrogen has disappeared out of the atmosphere - so it would be lower for the rest of the universe? The only other planet by comparison is Venus where the occurrence of D is around 2% of all hydrogen there.

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Re: Building a Sun on earth - pointless!!!

Post by Dan Tibbets » Mon Mar 02, 2009 3:51 pm

Yes, deuterium is produced as one of the intermediaies of P-P fusion to helium, but the initial P-P reaction is the rate limiting step by far. Deuterium concentration is pretty much a cosmic constant. The neucleosynthesis of hydrogen, deuterium, helium lithium and berylium where all that the big bang produced- there was plenty of energy aviable, but only a very breif amount of time aviable for neucleosynthesis. Why helium 4 was produced in such large quanties ( 20% by weight compared to hydrogen- suplimented to this level by super nova(?)). I suspect that more deuterium was produced in the Big Bang, but most of it was presumably fused into helium befor the neucleosynthesis was turned off. The first generation stars (type 1, or metal poor) could only burn the P-P reaction during the main sequence, as there was no carbon in them. Second generation stars have metals (anything past helium) thanks to recycling of supernova debri. So, in my example I should have said a second generation hot star that would be burning mostly by the CNO reaction.

Dan Tibbets

[EDIT]- I miss labeled the star types- Type I are metal rich (like the Sun), and Type II are metal poor.

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Re: Building a Sun on earth - pointless!!!

Post by Chris Roberts » Mon Mar 02, 2009 9:28 pm

Yeah, I remember hearing a statistic a little while ago that kg for kg, the human body releases more energy than the sun. I was pretty skeptical about that, but if one assumes we use all 2000 Calories of energy per day that is 0.023 Calories per second, which converts to 96 watts. Divide by mass of an average adult, (say, 70 kg) and you get 1.38 Watts / kg. Now, the sun's output is 3E26 Watts, and the mass is 1.99E30 kg, you get a grand 1.5E-4 Watts / kg. So, even assuming there are vast errors in my assumptions, the sun is way behind. (For example, even if we say we use only one tenth of the Calories we consume, we still come out way ahead) Then, compare all this to a lump of burning coal, and it starts to make sense why we use the energy sources we currently are....

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Re: Building a Sun on earth - pointless!!!

Post by Chris Bradley » Mon Mar 02, 2009 10:28 pm

Good point. Yes, forgot to mention the specific power wrt mass. Those Olympic swimming pools filled with "normalised Solar plasma" contain a compressed plasma 50% more dense than water! That's about a thousand billion (1E12*) times as dense as a tokamak or fusor.

Now bear in mind that the reaction rate in a thermonuclear plasma, like the Sun, is proportional to density SQUARED!! So if we ran a vacuum plasma at the pressure of a fusor, rather than the Sun's plasma density, for Kansas to power the USA it'd need to cover the whole area of Kansas to a depth of one billion light years! (I've not picked that figure out of the air, it would really be a depth of 1E22km.)

The idea of recreating a Sun on earth is completely, utterly and hopelessly bogus.

If mankind wants to make use of fusing nucleii, it has to do it a whole lot better than the Sun - much much MUCH better!

*(equal to an old-world scientist's "billion". I wonder if that's why the financial markets got in a muddle - they couldn't figure out the difference between a "real billion" and their "made up" billions?!)

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Re: Building a Sun on earth - pointless!!!

Post by Dan Tibbets » Tue Mar 03, 2009 3:18 am

I did some calculations trying to compare to Chris's numbers. After getting lost several times and starting over, my conclusions is that creating a "Sun" (P-P fusion machine)on the Earth is indeed impractical, and it is misleading to avertise terrestrial fusion as such.
But there are some misleading arguements in Chris's statements too. First, I don't know what the plasma pressure in the center of a Tokamak is, but in a Polywell there has been hints that the density in the center may be as high as a 10th of an atmosphere, not 1 billionth. In an amatuer Fusor I presume the central ion density (convergence) is much higher than the general density of ~ 10 to 20 millionths of an atmosphere. So, this may change the numbers by as much as ~ 10^9 (that is befor squaring the density like I think Chris did).

Secondly, the solar density output he is using is based on P-P (estimated to be ~ 99% of the fusion occuring in the Sun). A star twice as hot as the Sun would result in ~ 10,000 fold greater power thanks to CNO fusion. D-D fusion at ten times the temperature( ~ 30 KeV) would be perhaps 10^15 times faster than CNO fusion in a hot star or 10 ^19 times faster than P-P fusion in the Sun*. D-T fusion would be even faster.

The biggest difference is the fuel used, which will greatly offest the thousand fold (or greater) difference in densities involed.


* Reaction rate comparisons based on my reading where ~ P-P reaction rate/ probability was ~ 10 ^-45, compared to D-D probability of ~ 10 ^-25.


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Chris Bradley
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Re: Building a Sun on earth - pointless!!!

Post by Chris Bradley » Tue Mar 03, 2009 7:23 am

Dan DT wrote:
> But there are some misleading arguements in Chris's statements too. First, I don't know what the plasma pressure in the center of a Tokamak is, but in a Polywell there has been hints that the density in the center may be as high as a 10th of an atmosphere, not 1 billionth.
I was presuming a couple of microns pressure, which I don't think was misleading. Suggesting Polywell *does* operate at 1/10 atmosphere is (especially as, even in design-intent, that is only a tiny core and the whole device is an order of magnitude bigger).

But, hey, what the heck, I've got orders of magnitude to play with here!

So the density of av. Sun plasma is ~1E24 protons per cc and your atm/10 Polywelll will have 3E19 fuel atoms per cc. So we 'only' drop by 1E9 in efficiency. Is that right?


> Secondly,... A star twice as hot as the Sun would result in ~ 10,000 fold greater power thanks to CNO fusion.
OK, so that takes it down to 'only' a 1E5 drop in efficiency; so if we tried to bundle up a CNO fusion plasma at atm/10 here on earth. That'd be the whole of Kansas to a depth of 1,000km. I'm not convinced that actually makes it any more practical, but I'll go along with it if you show me the plans! Besides, this improved practicality of yours aside, once it goes over 100km high it's surely no longer a 'terrestrial plasma?!


> The biggest difference is the fuel used, which will greatly offest the thousand fold (or greater) difference in densities involed.
Fuel...and temperature. Temperature is the biggest kick for these fusion reactions, taking them up to cross-sections that Gravity confinement very very gently bumps down to far below the optimum reaction temperatures. It's a huge, massive improvement over nature. Gravity can't confine at these higher temperatures, else it goes nova.

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Re: Building a Sun on earth - pointless!!!

Post by Dan Tibbets » Tue Mar 03, 2009 3:07 pm

Without looking it up, I think R. Nebel was the one who hinted that they were getting ~ 10^ 22 ions per CC. (actually this would be well above one atm, but I didn't use cc since I'm not sure I remember the units correctly). And, as you said, this is the pressure near the center of the Polywell device. Depending on how well the focus/ convergence is I'm guessing this might be ~1/100th to 1/1000th(?) of the volume of the device.

I'm not sure how high a temperature a massive stellar core can reach. Considering that aType O main sequence supergiant can burn through its aviable supply of hydrogen (~ 5-10 percent of total hydrogen in the star) in 1-10 million years, then the core is probably ~ 35-40 million degrees (CNO fusion rate perhaps 50-100,000 times the Sun's fusion rate), which is enough to support the weight of the star.
Once the hydrogen is consumed, slower reactions than the CNO cycle, take over, so the core needs to heat up/ compress more in order to generate enough fusion/ heat energy to support the star against gravity. Helium burning starts at ~ 100,000,000 degrees, higher for carbon production (end of the line for the Sun), till only iron ash is left. The last stages are possibly at a few billion degrees(?).

Thanks for deriving a new volume for CNO stellar fusion plasma (at 30,000,000 degrees C ?) to power the Earth's needs. Now, what would be the volume needed with cheating and using D-D or D-T (again at ~ 30,000 KeV (~20 X the Solar core temperature), or if you are limited to a Tokamak ~ 10,000 KeV)?

ps: Just to add more complexity and conjecture- The CNO fusion rate I gave was for ~ 30,000,000 degrees C or ~ 2.8 KeV. The reaction rate for CNO fusion increases very rapidly (~ temp increase to the 17th power) So, increasing the energy to 60,000,000 degrees C (~5.5 KeV) would increase the fusion rate by as much as 120,000 fold ( 2 ^17). This is assuming that the reaction rate curve is not flattening too much in this modest energy range for a Fusor. I'm basing my mostly ignorant assumpion on the P-B11 reaction graph, which has masses close to the P-C12 reaction. ie- a platue is not reached till several hundred KeV.

Also, I think that the rate limiting step for CNO fusion is at one of the nitrogen stages, so for Terrestrial fusion with this admittedly poor choice for a fuel (compared to deuterium), we can throw alot of carbon at the reaction and not worry about regenerating the carbon (which is needed in stellar CNO cycles). This would further speed up the reaction a small to moderate amount- or not. With these assumptions, how far behind P-B11 fusion would 'terrestrial CNO fusion' be?


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Re: Building a Sun on earth - pointless!!!

Post by Chris Roberts » Fri Mar 06, 2009 8:36 pm

So, does this mean hydrogen bombs are the most efficient energy producing devices in the universe? Or do supernovae or perhaps another exotic astrophysical process deserve that title?

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