inside the sun
Great responses, mrzz.
It's my turn to contribute to the answers, as much as my knowledge goes.
1) What is low energy applied nuclear physics?
As you noted, it's abount practical nuke applications. MRI, as you recall is indeed "practical" and can be called "low energy" according to your definition, because to describe radioactive decay of an isotope used in medical imaging here, we don't need relativity theory. But the fact MRI process is "low energy" is rather obvious, a name "applied nuclear physics" would be sufficient. So this example does not illustrate, why a specialised field in question was created to start with.The answer to this latest question is: since we understood the reaction within the sun, we wanted to recreate it in controlled conditions, without a need for high energy input, thus benefiting from thermonuclear energy right here in our hands, and not 150 giga metres away. Without high energy input, it meant that the "artificial sun" would be cold (possibly even at room temperature) rather than as hot as a real sun (million degrees). The idea was called "cold fusion":
https://en.wikipedia.org/wiki/Cold_fusion
As you can read, various apparatuses have been created with various chemical compositions, where the researchers have claimed to obtain Helium from Deuterium fusion (the same reaction as inside the sun) but with only few eV (electronoVolt) per nuclei energy input (some pressurisation I guess). Deuterium is "heavy hydrogen" with an extra neutron in addition to the proton. Water composed of Deuterium is also called "heavy water". Typical "hot" nuke reaction such as Deuterium fusion inside the sun requires several MeV energy input per nuclei. As you can read in the above wiki, the very first claim to obtain Helium from heavy water came in 1989, so almost 30y ago. But the experiment failed to reproduce. Since then, "Cold Fusion" term feel into disgrace, their researchers found harder and harder to obtain grants. Eventually, they decided to rename their specialised field to
low-energy nuclear reactions or
condensed matter nuclear science and herein is the answer how the field in question came about. In general, it deals with nuke reactions where energy input is up to few keV per nuclei. It's quite an obscure area today (only few hundred researchers) and they may not recreate deuterrium fusion at room temperature but who knows, they may find out some other nuke reaction that will bring virtually unbound, and revolutionise the global energy production.
2) What is the difference in scale between nuclear physics & low energy applied nuclear physics, please?
I've already answered it above. Tpical nuke reaction involves order of MeV energy input (the same order as the energy output, output should be more if we want to source our energy from it!), while "cold Fusion" researchers are trying to excite nuke reactions with just few eV (unrealistic IMO), up to say few keV (more realistic)
3) I cannot add anything to your answer. Thank you!