The basic idea of a carbon tax is to increase the cost of emitting carbon, so green processes are relativly cheaper. So companies polltuing the enviroment go bancrupt, whereas companies using green technologies do not. This is already working very well with coal in the EU. that is currently dieing a very quick death. The issue is that it obviously increases cost. However the money is not lost and can be used for all sorts of usefull things governments do anyway.

What the EU has is not a carbon tax thou, but a tariff system. The EU has an internal emissions market, which works fairly well by now. The issue is that it only works in the EU, so companies can just move the production outside the EU and use dirtier processes and not have to buy credits. So the idea here is to have a carbon tariff in which companies selling products into the EU have to pay what they would have paid in the EU for the necessary carbon credits minus the cost of carbon credits or taxes in the countries of origin. So countries outside the EU have a massive insentive to introduce carbon pricing of some sort as well, so their comapnies pay the money to them and not to the EU, which is a massive market. Hence the idea is that this snowballs and acts as an insetive to go for green technologies outside the EU, which is the second biggest importer in the world after the US.