Like @Theraot suggests, rocks are a good idea. Depending on the kind of rock your retreat is built on, you might have up to 60ppm lithium in those rocks. Out of the millions of tonnes of rock that you could easily have access to (particularly if your retreat is built at least partially underground, or especially if that part is still being built), you might therefor have a few hundred tonnes of lithium available to you. Of that quantity just under 8% is Lithium-6.
Now, you're going to also need a few other things. Particularly, you're going to need a source of protons, and some Helium-3. These are a little harder to get hold of, but don't worry because the reaction you're going to perform produces as much of them as it consumes. You're only going to consume the lithium-6.
The key is to fuse a proton with an atom of lithium-6. This will release a helium 3 (which will need extracting during reprocessing later on), a helium 4 (which is waste, although there are some fun party tricks you can perform with it), and 4 million electron-volts of energy.
At the same time, you will also fuse a helium 3 atom with another lithium-6 atom. This will release a proton (you see where this is going) and 2 more helium 4 atoms, and 16.9 million electron-volts.
So, you've used 2 atoms of lithium-6 and got 20.9 million electron-volts and some waste helium (and some other products that need to be reprocessed to feed back into the reaction again in order to sustain it).
Now, to relate this to useful units. A mole of lithium-6 weighs 6 grams and contains roughly 6x10^23 atoms. This means that 6 grams can run 3x10^23 of our reactions and thus generate a little over 6x10^30 electron volts, which is to say about 267 megawatt hours, or enough power to keep the average person going for 12 years (or just under 3 years if they're American).
This means that the rocks under your citadel ought to be able to keep a population of, say, 50,000 people going for somewhere between 60 and 240 years, depending on how frugal they are with power. Obviously shorter for a larger population and longer for a smaller population.
Other than potential availability (depending on your city's location), there are other advantages to this over fusing deuterium from (heavy) water:
- The relative abundance of lithium-6 versus lithium-7 is far higher than deuterium versus hydrogen. This means that you have to process less of it to get a useful quantity out.
- The process does not release significant numbers of neutrons. Neutrons have a habit of being difficult to capture and turning many materials they may strike into radioactive sources. Neutrons are dangerous and difficult to work with. You don't want neutrons being produced in your reactor if you can possibly help it.
- It's less cliche than deuterium-based fusion.
My question: What would be the best energy source for this type of setup?
People I don't like, obviously. Toss 'em in the matter converter to put them to good use.... waste not, want not, and all that. Point being that "best" is a subject term and depends heavily on what your goals are. $\endgroup$