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Do we know of a means by which artificial nuclear fusion could be used to mimic stellar carbon-12 production?
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Not a physicist, merely a science enthusiast with a high school science education.
My understanding is that we're having a hard enough time smashing hydrogen together into helium (and actually getting back more energy than we put into the process) that making specific isotopes of heavier elements with the current state of technology is between 'extraordinarily unlikely' and 'impossible'. We would have to manage to get past Helium and then on to Lithium, Beryllium, and Boron to get to Carbon -- I imagine the amount of energy required to produce even just a few C12 atoms would be off the charts.