[qlulqhlw] Simple nuclear fusion reactions

With only 1 fuel:

1 + 1 -> 2

In the next generation, the following side reactions can happen:

1 + 2 -> 3
2 + 2 -> 4

(The numbers represent substances; it is just a coincidence that the above reactions are arithmetically correct.)

With 2 fuels:

1 + 2 -> 3 (desired reaction)

The following side reactions can also occur in the first generation:

1 + 1 -> 4
2 + 2 -> 5

For the next generation, we enumerate all possible reactions among 1 through 5, excluding those already mentioned:

1 + 3 -> 6
1 + 4 -> 7
1 + 5 -> 8
2 + 3 -> 9
2 + 4 -> 10
2 + 5 -> 11
3 + 3 -> 12
3 + 4 -> 13
3 + 5 -> 14
4 + 4 -> 15
4 + 5 -> 16

The number of possible reactions and products combinatorially explodes (pun intended), even after 2 generations.  (What is a formula that counts the possibilities after N generations?)

In reality, many reactions will be highly improbable.  It might be possible to remove a product quickly enough so that it does react in the next generation.

Additional complexity: One reaction could probabilistically produce two different products.  A reaction could have more than one product.  (This is very common: e.g., D + T => He4 + n.)  Two reactions could produce the same product (law of small numbers).  A product could radioactively decay (quickly) into one or more other products.  Reactions could go more than two generations.

If any of the reactions produce neutrons, they will irradiate the surrounding structure, producing radioactive waste.  Fusion is probably never clean.