I'm of the personal opinion that the Minbari use one of the theoretical fusion systems we know of today... They simply are able to miniaturize it to an immense degree, enabling them to fit more reactors into a given area than most other races. As an example (and ONLY an example), an Earth Alliance fusion reactor large enough to produce 30 terawatts might take up half a cubic kilometer of volume while a Minbari reactor capable of the same thing might only take up a few dozen cubic meters.
Another thing to consider, Minbari and other advanced races don't necessarily need to be capable of producing massively greater amounts of power than "infant and toddler" Younger Races, they can easily get by with merely being able to use it more EFFICIENTLY. From modern understanding of physics, there's a ceiling to the amount of power one can get from a fusion reaction. But I've never heard of a theoretical limit other than 100% efficiency, that's supposedly flat impossible, to the level of efficiency one can achieve in the use of that power. And there's even a few devious ways around the 100% efficiency limit.
For instance, if you need X amount of power to achieve Y result while using Z method where X would require one to get 100% efficiency from one's power generation method, then you've got a problem. But it isn't insurmountable. It's possible that with proper research and experimentation a new method of achieving Y result can be found that does not require X to be 100% efficiency from your power generator. Example: Pulling 20 tons of weight with only your body to do it. If the 20 tons is simply a 20 ton block on the ground, even 100% efficiency from your body's muscles wouldn't be enough to do the job. But put that 20 tons on wheels, and if you're a powerlifter, you now have a good chance of pulling the 20 tons without needing 100% efficiency or better from your body. Don't believe me? Watch some of the "strong man" competitions sometime. Pulling 18 wheelers is a favorite event!
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