What is the Fusion Rate of Protons and Boron-11?

[Drakkith]

Hey all, i just had a quick question in regards to fusing Boron-11 and a Proton.
If one were to fire protons at a block of Boron-11, about what percent of the protons would actually achieve fusion? Would varying the speed of the protons effect the fusion rate at all? (Other than stopping any reactions if the energy is too low obviously)
Thanks!

 

[Astronuc]

Hey all, i just had a quick question in regards to fusing Boron-11 and a Proton.
If one were to fire protons at a block of Boron-11, about what percent of the protons would actually achieve fusion? Would varying the speed of the protons effect the fusion rate at all? (Other than stopping any reactions if the energy is too low obviously)
Thanks!

It's not quite so simple. If one uses a proton beam, the cross-section (probability) of reaction depends on the energy/speed. However there is generally a much greater probability of scatter, while at the same time there is a loss of energy due to interaction of the proton with the electrons, which is why plasmas are preferred. However to get a plasma, one has to ionize the B-11, but then one has to contend with the high pressures (or low nuclear density) and losses due to cyclotron and brehmsstrahlung radiation.

The parameter most often used to compare fusion reactions is n₁n₂<σv>, where n₁ and n₂ are the two nuclear species involved, and <σv> is an integral over the relative speeds of the nuclei, and σ is the speed (velocity) dependent microscopic cross-section of the reation.

 

[Bob S]

From Wikipedia:

The fundamental difficulty with nonthermal ions is apparent when one compares the fusion cross section (fusion ~1 barn for p-¹¹B at E_cm = 580 keV, where E_cm is the energy in the center-of-mass frame) to the effective cross section for many small-angle Coulomb scattering events that combine to produce a scattering angle of 90° rms in an incident beam (σ_eff ~60 barns for protons scattering on ¹¹B at E_cm = 580 keV).

See http://www.sciencemag.org/cgi/content/full/281/5375/307a



Bob S

 

[Drakkith]

Thanks Astronuc! Is there anywhere you could point me to so that i could get the numbers to crunch for this? I realize there are massive losses due to the interactions you stated and I'd like to see the actual numbers on it just out of curiosity. Thanks again.
Edit: Thanks to Bob S as well. I think i was typing up this reply when you posted. =)

 

[Drakkith]

In a related note, the following was a very interesting read on "Fusion energy without radioactivity: laser ignition of solid hydrogen–boron (11) fuel".

http://www.phys.unsw.edu.au/STAFF/VISITING_FELLOWS%26PROFESSORS/pdf/BlockEnergyEnvir.pdf