energy - How much faster is the fusion we make on earth compared to the fusion that happens in the sun?

I have come across many websites that states that the proton-proton fusion which is the dominant type of fusion that powers the suns, is extremely slow and that is why the sun is still burning to that day. But also I have read that the sun fuses 620 million tons of Hydrogen every second, so that is considered fast for us on the earth scale.

So my question now is : comparing the time it takes to release the same amount of energy, how much faster the D-T fusion for example is compared to proton-proton fusion ?

Answer

The problem with proton-proton fusion is that there is no bound state of two protons. For the fusion to occur one of the protons has to turn into a neutron by beta plus decay. This is mediated by the weak force so it's a slow process and the probability of it happening while the protons are close enough to form a deuteron is very low. By contrast a deuteron and tritium nucleus readily form $^5$He.

The proton proton fusion cross section isn't known from experiment so only calculated values are known and these are somewhat uncertain. I found this paper that summarises the reaction rates. The p-p fusion is about $10^{26}$ times slower than the D-T fusion.