# Has proton-proton fusion ever been observed in the lab?

1. Aug 4, 2013

### Steve Harris

Sure we all know it happens at the core of the Sun, but the half life for a proton there is a billion years because p + p -> D + e + v is so unlikely

A thermonuke bomb using light H would give no extra energy at all above the fission primary. Even the Sun only gives a few watts for bomb sized volumes and a bomb only has fractions of a millisecond, so you'd get millijoules even at Sun densities. Perhaps a bomb gets hotter than the Sun but not by more than an order of magnitude. You see the problem.

D and T fusion are trivial. Protium fusion is so hard that I wonder if it's ever been experimentally demo'd in any way. I have looked but can find only theory. Anybody got a ref for an experiment? This is one you all assumed and me too. But maybe not.

Last edited: Aug 4, 2013
2. Aug 4, 2013

### Simon Bridge

I'd be surprised if it hadn't been.
p-p fusion dominates the Sun at about 15x107K

That would be a kinetic energy per particle of around (back-of-envelope) kT=15x107K x 8.62x10-5eV/K = 12930eV ... so 13keV? (It's been a while so I may be off...)

The LHC can manage colliding 7TeV beams.
I think we'd have to search for papers from people deliberately seeking to make p-p fusion happen... which would have been a while ago so hard to do.

You wouldn't detect the events by the energy given off, though, but by the reaction products.
Neutrinos from the lab events would be too few to be detected - you'd have to detect the deuterium, possibly the photon. It would be the proportions of end results you watch for... much like when you observe the process in the Sun.

3. Aug 4, 2013

### Steve Harris

The title should be "Has proton-proton FUSION ever been observed in the lab?"

At 15 million K the mean proton KE in the Sun's core is indeed about 15 kev. But raising this substantially wouldn't increase fusion cross section much, because it's not inhibited by Coulombic repulsion, at much over these temps. Rather, the problem is the slowness of beta decay, which must happen for protons to stick-- in contrast to all other fusion processes that are far faster since they don't require the weak force to do anything.

So it doesn't matter how energetic or luminous your beam-- you're probing a process with a channel far narrower than anything else possible from a proton-proton collision, plus one you can't just dump energy into willy nilly, since deuterons are weakly bound, and will fly apart even when made with more than a MeV of extra energy input.

This is the basic reason deuterium (D) is so rare in the universe. Stars kill it far faster than they make it, so all D is from the Big Bang. Also, there is no cosmic ray proton-on-proton formation of D (that's that same energy-dump problem as with the Tevatron). It just doesn't happen as you suggest! Yes, you'd be surprised if p-p fusion hadn't been reported, but perhaps you should have been. I don't think it has. I challenge anybody to find me a report of it. People who naively assume it's been seen in the lab, should re-think.

Last edited: Aug 4, 2013
4. Aug 4, 2013

Staff Emeritus
This looks hard. You might get a few atoms of deuterium every zillion attempts, but there's plenty of deuterium around. How would you know for sure where it came from?

5. Aug 5, 2013

### Staff: Mentor

Coincidence detection of deuterium + positron coming from the known interaction point would be a good indication. I guess this would be sufficient to get rid of the background, otherwise you still have the energy spectra to analyze.

6. Aug 5, 2013

Staff Emeritus
How do you know the deuteron was produced and not in your proton target? Remember, this is a weak process - it has neutrino-like cross-sections, on a background with QCD-sized cross-sections.

7. Aug 5, 2013

### the_wolfman

As a fusion scientist, this caught me by surprise. A quick search produced a fairly recent review of modern physics article on the calculation of solar fusion cross sections.
E. Adelberger et al., Rev. Mod. Phys 83, 195 (2011)

In it, the authors note that "The rate for the initial reaction in the pp chain, p+p = d + e+ + nu, is too small to be measured in the laboratory. Instead, the cross section must be calculated from standard weak interaction theory."

There is a difference between calculating cross sections and observing an reaction, but if the cross section is so small that we can't measure it, then its possible that its never been observed in a lab.

8. Aug 5, 2013

### Staff: Mentor

A proton-deuterium collision does not produce a positron. The collision is below 1 MeV, there is no other possible process to produce a positron with a pure hydrogen target. In addition, the positron has more energy than everything else. Other elements in the hydrogen target could be tricky, but that would need a more detailed analysis.

9. Aug 6, 2013

Staff Emeritus
Remember that this is a weak process. Produced with neutrino-sized cross-sections. That means billions of collisions are needed to produce one real event. At that level, you need to worry about ambient positrons, deuterium in the hydrogen, ambient neutrons that make deuterium, cosmic rays....

10. Aug 6, 2013

### Staff: Mentor

An underground experiment will reduce cosmic rays significantly. Where do ambient positrons come from, apart from beta+ radiation?

I get roughly 1 MeV electrostatic potential for the repulsion. Increasing the energy to ~900 keV (compared to ~10keV in the sun) will increase the cross-section so significantly that I don't want to use the sun to estimate the cross-section.

11. Aug 7, 2013

Staff Emeritus
Yes, you could put it in a mine. Do you want to pout your accelerator in a mine as well?

The fraction of pp collisions that will yield a fusion, assuming you are not on a resonance and assuming there are no coherent effects, will be approximately $\frac{a_w}{a_s} \left( \frac{KE}{2M_W} \right)^4 \approx 10^{-22}$. Now, maybe it's not this small, but it's unquestionably small - it's less than one per billion, and almost certainly less than one per trillion.

If you want to argue that there's an experiment that can do this, I think you should design one. I see a problem with getting the necessary flux, and a problem in getting the background down to the required level. Putting it underground makes it even more expensive. And for what? What would we learn about weak interactions by doing this that we wouldn't know better from other measurements?

12. Aug 7, 2013

### Staff: Mentor

I think that is the main problem.

1 MeV can be done with a small cyclotron. They also provide ~mA currents, getting 1023 protons is not an issue and we can focus on the detection.

.4 MeV-positrons in a field of 3mT will have a radius of 40cm. In a drift chamber you can measure dE/dx and the time of flight as well as the radius. Put them in the "wrong" direction, where the beam comes from. The positron does not care about that small momentum, but protons will fly in the wrong direction. Drift chambers of sufficient size can handle millions of particles per second. The outer tracker of LHCb can handle billions of particles per second - okay, it is a bit oversized.
Those drift chambers get efficiencies close to 1 with respect to that rough approximation here.

How much background do we have? The proton energy is not sufficient to break deuterium apart. We can get proton absorption in other elements in the target, followed by a beta+ decay. That is a serious background, as it cannot be separated from fusion on a event-by-event analysis, we would have to look at a spectrum. It can be reduced significatly if the target is very pure. beta+ decays in the material are an issue, too, but natural beta+ sources are rare. Apart from that, random radioactivity, leading to electrons.

I still think it is possible. It is a lot of work and it will give a single measurement only, however.

13. Aug 8, 2013

### Steve Harris

Ah ha! Thanks, the_wolfman. I'm glad it caught you by surprise. That proves it wasn't a stupid question. The meme that the Sun's primary energy reaction is so hard it's never been verifiably done in the lab, is worth spreading as a cool factoid. It goes along with the known "compost heap" rate of energy generation, even at the Sun's center. It's very hot but the next layer is nearly as hot so almost no heat flows. Far less than your own metabolism. It is more reptilian at least by volume (not by mass).

The problem is getting a cite for such a negative statement for Wikipedia. Yours is close. Maybe enough. I'll try it.

Last edited: Aug 8, 2013