Other methods of carbonation?

So there are only 3 methods of carbonation that I have heard of.

1. Natural carbonation- bottling before the cider is done fermenting and let the yeast eat up the sugars then heat pasturize.

2. Priming- letting the cider ferment to your desired level if sweetness. Then adding priming sugar so the cider doesn't lose any sweetness while it carbonates. Then heat pasteurizing to stop the yeast.

3. Force carbonation- Stopping fermentation with heat or additives, putting the cider in a keg, or other air tight container that can withstand pressure, and then pressurize the vessel with 25psi of CO2 and waiting for the CO2 to dissolve.

I want to know if these are the only methods of carbonation that can be used. Or if there are other methods that are fairly easily used.

Well, I'll have to say that number 2 is a misnomer. You can't let it ferment to your desired level sweetness. What do you do then? Ask the yeast to pretty-please stop fermenting?

The yeast will keep going until there is no sugar left or they get poisoned by the alcohol.

If you prime and bottle when it gets to your desired level of sweetness, the yeast will keep going from there and end up overcarbed and/or make bottle bombs.

One thing you can do that's not on your list is to let it ferment out completely, back sweeten with something unfermentable and then prime and bottle.

As far as I know, fermentation (1 & 2) and Pressurized force carbonation (3) are the only ways to carbonate. It is possible to introduce CO2 through agitation without pressure, but it's a very very weak carbonation.

Pasteurization isn't really a part of carbonation, it's used to stop carbonation and fermentation to control residual sweetness in carbonated cider.

on review, I suppose it might be possible to carbonate with some kind of effervescent chemical or even frozen CO2, but those are way out in left field and impractical.

1 and 2 are basically the same, just two schools of thought on whether to add sugar or not. I guess it depends on how dry you let it get before bottling. You could also let it totally dry out, then prime and bottle. Then, you wouldn't need to paseurize.

Other than that, kegging is the only other way. You can also naturally carbonate in the keg if so desired, but the results are really no different than force carbing.

For #3 you can stop the yeast with cold crashing. Also a few people are experimenting with filtering, which should work in theory

If you want a sweet bottle conditioned cider, you can also use nitrogen reduction. This is what many of the traditional cider houses do. Its tricky though, you need a consistent source of low nitrogen juice, the right yeast, and willingness to burst some bottles. I've done a few batches this way, using 3333 yeast and bottling right after cold crashing. That yeast retains just enough puff after the crash to carb the bottles and no more. I havent burst any bottles doing this, knock on wood.

I would not recommend using nitrogen reduction unless you already have some experience and success with cold crashing. For someone just getting into this, I'd recommend either #1 or #3, depending on how much quantity you are going for