CNO fusion using a particle accelerator?

Question

The CNO cycle is a catalytic fusion reaction that produces energy in stars larger than the sun. It converts four protons into a helium-4 nucleus using a cycle of carbon, nitrogen, and oxygen isotopes as catalysts and releases $26.7$ MeV of energy mostly in the form of gamma rays.

Could one make this cycle work in the laboratory by bombarding a cold, high-density target made of these isotopes with protons accelerated in a particle accelerator?

If a carbon nucleus has a radius of about $2.7\times10^{-15}$ m, then one would require protons to be accelerated to about $3.2$ MeV in order to overcome the Coulomb repulsion. I guess this can easily be achieved. If the energy of the gamma rays were captured, perhaps one could produce fusion energy by this method?

Answer 1

In addition to the difficulties explained in enumaris' link above, you have the additional problem of this reaction path having several sequential steps in it, each of which must occur in the correct order and have high enough yield so that at the end of the overall cycle, the overall yield (which is the product of the individual yields of each step) is high enough to make the exercise feasible. It isn't clear exactly how one could stage the process in a particle accelerator or how to set aside and "keep fresh" the intermediary products as feedstock for the next step in the process.