Could Fusion Reactions Occur Randomly in the Atmosphere or Planetary Cores?

[BWV]

Sorry for the clickbaity title, real science question-

The part below of the Wikipedia article on Nuclear Fusion seems to imply that some miniscule number of fusion reactions might occur randomly at normal temperatures (of course no ability to turn this into an energy source)

increases from virtually zero at room temperatures up to meaningful magnitudes at temperatures of 10–100 keV. At these temperatures, well above typical ionization energies (13.6 eV in the hydrogen case), the fusion reactants exist in a plasma state.

So just due to statistical mechanics, somewhere in the atmosphere two hydrogen ions are colliding and fusing as I write this? or could (even more improbably) individual atoms collide and fuse beside H+?

 

[Astronuc]

In the sun, an estimate of the fusion rate per proton is ≈5×10⁻¹⁸s⁻¹, which is very small. It's even less on earth. Another estimate, again in the sun, the probability of fusion per collision is ∼2×10⁻³¹, and less on the earth.
https://www.astro.princeton.edu/~gk/A403/fusion.pdf

Now we do get solar protons and much less so, deutrons, as well as GCR nuclei, and they have very high energies. Besides scattering, which protons are more likely to do with each other, we get spallation reactions, which fission nuclei (both terrestrial and GCR), or more likely produce anti-protons, from which we annihilation reactions and spallation reactions.
http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/cosmic.html
https://home.cern/news/news/experiments/cosmic-collisions-lhcb-experiment
https://www.nationalgeographic.com/...atter-belt-earth-trapped-pamela-space-science

The Bevatron at the University of California, Berkeley was constructed in 1954 for the specific purposeof producing antiprotons and confirming the existence of these antiparticles as predicted by Dirac. In 1955 Emilio Segrè and Owen Chamberlain confirmed the existence of the antiproton in experiments conducted on this device.In the late 1970s antiprotons,p, were also observed as a very small primary component of cosmic rays incident on the Earth. As antiprotons annihilate with protons in the Earth’s atmosphere, these observations were made at high altitude in balloons or satellites (including the Space Station). These primary antiprotons incosmic rays are believed to be created in outer space by the interaction of protons with atomic nuclei, A, by the process . . .

https://iopscience.iop.org/chapter/978-1-64327-362-4/bk978-1-64327-362-4ch1.pdf

It's not cold fusion however, since the energies of the incoming particles are in the MeV, GeV and >>GeV range.

 

[TeethWhitener]

Probably not. You have to crank through the numbers a little (caveat: I am not a nuclear physicist). The bottom of the wiki page on nuclear fusion gives empirical formulas for $\langle\sigma v\rangle$ for DD and DT fusion at temperatures below 25 keV. Putting in T = 25 keV for the DT reaction gives a value of $\langle\sigma v\rangle \approx 2.18\times 10^{-15}$. Doing the same calculation for room temperature (T = 25 meV) gives $\langle\sigma v\rangle \approx 1.04 \times 10^{-40}$. Now, I have no idea how well this empirical formula works at such tiny temperatures, but I bet it's not off by more than 10 orders of magnitude, in which case we can expect the DT reaction to run at least $10^{15}$ times slower at room temperature than at 25 keV, all other considerations equal. So it's very unlikely that any fusion is going on at room temperature at any given time.

 

[BWV]

It's not cold fusion however, since the energies of the incoming particles are in the MeV, GeV and >>GeV range.

Thanks - cold in the sense that temp is an average of the energies of the particles in a given area and this average can be low -‘cold’ - but contain a few individual particles at high enough energy to randomly hit each other and enter the reaction?

 

[mfb]

You find many particles with 10 times the average, and you find some with 20-100 times the average, but you don't expect to find even a single particle with 300 times the average (which is still below 10 eV at room temperature), even if you take all of Earth and wait for the lifetime of Earth.

Muon-catalyzed fusion of some stray hydrogen molecule should happen once in a while.

 

[TeethWhitener]

Thanks - cold in the sense that temp is an average of the energies of the particles in a given area and this average can be low -‘cold’ - but contain a few individual particles at high enough energy to randomly hit each other and enter the reaction?

You can do @mfb ’s calculation yourself (it’s not a bad little exercise). Just take a Maxwell-Boltzmann distribution at room temperature and integrate above whatever energy cutoff you deem appropriate to get the fraction of hydrogens with the necessary energy to fuse. I haven’t done it, but mfb’s answer doesn’t sound unreasonable.

 

[BWV]

Ok, so even if the Bolzman dist implies a close to zero cutoff under normal conditions - if we go to the upper atmosphere where the temperature is 'cold' (much hotter than the ground though) there are cosmic rays providing high energy alpha particles in excess of what the distribution would predict?

 

[Vanadium 50]

if we go to the upper atmosphere

Why on Earth (pun intended) would you want to to do this? The density is low.

Look, fusion in the4 sun is slow. Even with core temperatures in the millions of kelvins and densities 15x that of lead, it takes tens of billions of years for the average nucleus to fuse. Going to something a thousand times cooler and millions of times less dense is not a winning proposition.

 

[BWV]

Why on Earth (pun intended) would you want to to do this? The density is low.

Look, fusion in the4 sun is slow. Even with core temperatures in the millions of kelvins and densities 15x that of lead, it takes tens of billions of years for the average nucleus to fuse. Going to something a thousand times cooler and millions of times less dense is not a winning proposition.

So spallation (fusion) of cosmic ray particles (per Astronuc above) happens quite a bit and responsible most of the light elements (Li, Be ,B) in the Universe

Also the assumption for Bolzman is a closed system, so high energy particles coming from outside that system would be an outlier, correct?

 

[mfb]

Also the assumption for Bolzman is a closed system, so high energy particles coming from outside that system would be an outlier, correct?

Sure, but that's not cold. It's just a natural version of accelerator-based fusion, which is routinely done e.g. as neutron source.

 

[BWV]

Sure, but that's not cold. It's just a natural version of accelerator-based fusion, which is routinely done e.g. as neutron source.

Right, so to summarize

A) fusion of particles in cosmic rays is common enough that it accounts for most of the light elements in the universe and occurs in regions like the upper atmosphere where the over all temperature is cold (individual collisions are improbable, but time and quantity make up for it). These particles travel with enough energy to fuse if they collide

B) there is likely no fusion going on in my living room as at the distribution of particle energies assigns essentially a zero probability to any having enough energy to collide and fuse

 

[Vanadium 50]

fusion of particles in cosmic rays is common enough that it accounts for most of the light elements in the universe

Where do you get this?

 

[BWV]

Where do you get this?

OK looks like I misread 'responsible for the abundance' as 'responsible for most', but

https://en.wikipedia.org/wiki/Cosmic_ray_spallation

Cosmic ray spallation is thought to be responsible for the abundance in the universe of some light elements—lithium, beryllium, and boron—as well as the isotope helium-3. This process (cosmogenic nucleosynthesis) was discovered somewhat by accident during the 1970s: models of Big Bang nucleosynthesis suggested that the amount of deuterium was too large to be consistent with the expansion rate of the universe and there was therefore great interest in processes that could generate deuterium after the Big Bang nucleosynthesis. Cosmic ray spallation was investigated as a possible process to generate deuterium. As it turned out, spallation could not generate much deuterium, but the new studies of spallation showed that this process could generate lithium, beryllium and boron; indeed, isotopes of these elements are over-represented in cosmic ray nuclei, as compared with solar atmospheres (whereas hydrogen and helium are present in about primordial ratios in cosmic rays).

 

[Vanadium 50]

Where does this say fusion? Spallation is not fusion. If anything, it's the opposite.

Your clickbaity cold fusion is neither "cold" nor "fusion". Other than that, it's fine.

 

[BWV]

Where does this say fusion? Spallation is not fusion. If anything, it's the opposite.

Your clickbaity cold fusion is neither "cold" nor "fusion". Other than that, it's fine.

Confused then - if the nucleosynthesis from spallation (colliding alpha particles) creating He3, Li, Be and B is not fusion, then what is it?

 

[mfb]

It's closer to fission than fusion, but there is a large range of possible processes and many of them are neither. They are nuclear reactions, that's covering all of these interactions. In fusion you combine two nuclei to one larger nucleus.

 

[BWV]

It's closer to fission than fusion, but there is a large range of possible processes and many of them are neither. They are nuclear reactions, that's covering all of these interactions. In fusion you combine two nuclei to one larger nucleus.

OK, so most (all?) cosmic ray spallation creation of H3, B, Be and Li is from alpha particles hitting and breaking up heavier molecules

 

[Astronuc]

OK, so most (all?) cosmic ray spallation creation of H3, B, Be and Li is from alpha particles hitting and breaking up heavier molecules

Galactic Cosmic Rays (GCR) are the slowly varying, highly energetic background source of energetic particles that constantly bombard Earth. GCR originate outside the solar system and are likely formed by explosive events such as supernova. These highly energetic particles consist of essentially every element ranging from hydrogen, accounting for approximately 89% of the GCR spectrum, to uranium, which is found in trace amounts only. These nuclei are fully ionized, meaning all electrons have been stripped from these atoms. Because of this, these particles interact with and are influenced by magnetic fields. The strong magnetic fields of the Sun modulate the GCR flux and spectrum at Earth.
https://www.swpc.noaa.gov/phenomena/galactic-cosmic-rays

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2019SW002428

https://phys.org/tags/cosmic+rays/

Cosmic rays are energetic particles originating from outer space that impinge on Earth's atmosphere. Almost 90% of all the incoming cosmic ray particles are protons, almost 10% are helium nuclei (alpha particles), and slightly under 1% are heavier elements and electrons (beta minus particles) . . .Cosmic rays can have energies of over 10²⁰ eV, far higher than the 10¹² to 10¹³ eV that man-made particle accelerators can produce. (See Ultra-high-energy cosmic rays for a description of the detection of a single particle with an energy of about 50 J, the same as a well-hit tennis ball at 42 m/s [about 94 mph].)

Edit/update - From 2016 - MEASUREMENTS OF COSMIC-RAY HYDROGEN AND HELIUM ISOTOPES WITH THE PAMELA EXPERIMENT
https://iopscience.iop.org/article/10.3847/0004-637X/818/1/68

 

[BWV]

Perhaps a mod can change the clickbait title to something like:

Does fusion occur naturally outside of the cores of stars?

that was the real question anyway

 

[BWV]

Another candidate would be in the cores of planets, in varying degrees depending on mass

This is old (1998), so not sure what current thinking might be
https://iopscience.iop.org/article/10.1086/305797/fulltext/36734.text.html

we compare the conditions for electron degeneracy pressure and temperature for the cores with an Fe–D compound of Earth, Jupiter, and Saturn to the core with deuterium gases of the coldest brown dwarf, WISE 1828+2650, in respect to three-body deuteron nuclear fusion, based on electron capture and internal conversion processes. Our results suggest that deuteron nuclear fusion is possible in the cores of Earth, Jupiter, and Saturn as well the coldest brown dwarf.