Can Quantum Tunneling Enable Controlled Thermonuclear Fusion?

[Pooua]

I've heard that Sun is not hot enough to sustain thermonuclear fusion at the level we observe. Instead, the solar output relies on quantum tunneling of protons through their natural repulsive barrier. Might this same effect be useful in obtaining controlled thermonuclear fusion? It seems to me that this would require a large quantity of atomic interactions in a confined space. Might an atom laser be useful in producing a finely tuned beam of atoms that could direct large numbers of atoms into a small enough space for them to fuse?

 

[phyzguy]

I've heard that Sun is not hot enough to sustain thermonuclear fusion at the level we observe.

Nonsense! models of the sun using fusion cross sections measured here on the Earth are in excellent agreement with the measured solar parameters. See, for example:

http://en.wikipedia.org/wiki/Standard_Solar_Model
http://www.ap.stmarys.ca/~guenther/evolution/ssm1998.html

 

[Pooua]

Nonsense! models of the sun using fusion cross sections measured here on the Earth are in excellent agreement with the measured solar parameters. See, for example:

http://en.wikipedia.org/wiki/Standard_Solar_Model
http://www.ap.stmarys.ca/~guenther/evolution/ssm1998.html

Oh, I did not know that quantum tunneling is not commonly accepted as the reason solar fusion works as well as it does. I got my information from this video:



In the comments, the author says:

"People have been asking for the math. So here it is. The Sun's core temp is ~13.6 MK. For hydrogen nuclei the Coulomb barrier is roughly 0.1 MeV. This corresponds to a temperature in excess of 1 GK! Luckily, tunneling and the distribution of speeds among nuclei lower the actual temperature required. So without tunneling even the Sun's core isn't hot enough for fusion. To see most of this worked through, check out this link:

http://burro.cwru.edu/Academics/Astr221/StarPhys/coulomb.html"

for a less mathematical explanation, try:

http://en.wikipedia.org/wiki/Nuclear_fusion#Requirements"

I do not see that your first link, to the Wikipedia article on stellar evolution, addresses the question of solar fusion in sufficient detail to say whether or not quantum tunneling has any affect.

Your second link, to the Standard Solar Model, says that Sun's core is about 16 million kelvin. I've heard before that terrestrial thermonuclear fusion has to reach 100 million kelvin to 150 million kelvin because our projects are so much smaller than Sun, and I was led to believe that Sun simply is an inefficient furnace. The idea that quantum tunneling is required to account for the temperature difference makes more sense to me than simply stating that Sun is an inefficient furnace.

You might also want to refer to: http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/coubar.html"

 

[K^2]

Pooua, yes, pp fusion is dominated by tunneling. The barrier energy and temperatures are quoted correctly. At these energies, you'll only have a handful of protons at sufficient energy to react. (Odds of particle having energy E is exp(-E/kT) ~ exp(-100) ~ 10^-43, and Sol has roughly 5*10^56 protons, so we are talking about 50 trillion protons capable of fusing at anyone time.) But with tunneling, it becomes much more reasonable, since a particle with half of the barrier energy will already have good odds of fusing, and if you run the numbers, there are a LOT of these.

So it's not fair to say that fusion cannot proceed without tunneling at all, but tunneling is how it happens.

There is also a Carbon Cycle, which has lower activation energy, but it's not a dominant cycle in Sun.

 

[phyzguy]

Maybe I misunderstood your initial point. You said that "Sun is not hot enough to sustain thermonuclear fusion at the level we observe". This is clearly false, since the sun is powered by thermonuclear fusion. If your point is that quantum mechanics is required to understand nuclear fusion cross sections, well, I doubt anyone would argue with that!

 

[Vanadium 50]

But the sun is an inefficient furnace. It only burns ~10^-10 of its hydrogen per year. That's far too low to be commercially viable.

 

[Pooua]

Thanks for the confirmation about Sun's reliance on quantum tunneling.

What I really would like to know is, how would one make a practical fusion generator? I know that the U.S., former Soviet Union and several countries have spent billions of dollars and half a century trying to answer that question. I am wondering if there might be some other way to go about it than the ways commonly attempted?

I suppose the key to exploiting quantum tunneling would be to have many reaction and a lot of material. I don't know how much would be necessary, or how difficult it would be to confine that much material long enough to make it useful.

 

[mrspeedybob]

But the sun is an inefficient furnace. It only burns ~10^-10 of its hydrogen per year. That's far too low to be commercially viable.

A furnace that can keep going for 10,000,000,000 years without refueling seems like a pretty efficient furnace to me. What would make it more efficient would be to concentrate all of it's output on the Earth while simultaneously slowing its reaction by a corresponding amount. If this were achievable our 5,000,000,000 year time horizon could be dramatically lengthened.

 

[Astronuc]

A furnace that can keep going for 10,000,000,000 years without refueling seems like a pretty efficient furnace to me. What would make it more efficient would be to concentrate all of it's output on the Earth while simultaneously slowing its reaction by a corresponding amount. If this were achievable our 5,000,000,000 year time horizon could be dramatically lengthened.

Concentrating all of it's [Sun's] output on the Earth would incinerate the surface of the earth, and in fact melt the Earth's surface. The Sun's mass is roughly 333,000 times the mass of the earth. The mean density of the sun is 1408 kg/m³, or 1.4 times that of water at 4°C. The central density is ~1.622 x 10⁵ kg/m³, something we cannot reproduce on earth. The solar core pressure is ~2.477 x 10¹¹ bar, which again is well beyond the capability of terrestrial technology. The Earth's atmospheric pressure at sealevel is ~ 1.01325 bar.

Ref: http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html

The sun will do it's thing regardless of the earth. We only need a small portion of the energy output of the sun. During the summer, the Earth gets plenty of warmth from the sun.

 

[mrspeedybob]

I did throw in that we'd have to simultaniously slow it's reaction. I guess it might be more practicle to build a Dyson sphere.