It should be less about generating revenue and more about preventing a loophole. The loophole is that it's possible for one party to make a profit at the expense of everyone else. That means there's an incentive / reward for destructive behavior.
IMHO, though, the tax should be just enough to neutralize that incentive. Anything more and you are selectively penalizing one industry, which I don't think is fair. Airlines didn't invent the concept of burning fuel to power machinery; society did, chose it as the basis for all industrial technology, and used it for everything. Air travel is just one thing on that list.
Also, the airlines were not the only ones who benefited. More or less, we all did. If ticket prices always included the carbon cost, then your business would have had to pay a higher price to fly you to that business meeting. And you would have had to pay a higher price to go on that vacation or visit those relatives.
We all had a party and trashed the place. We should all clean it up together.
So far that reason, to the extent that we can fix things with government action (funding research, etc.), I think the costs should be taken that out of the general fund. That not only everyone pays for what everyone benefited from, it also means it can be progressive and have other attributes of good tax policy.