Do we and other countries have the right to intervine in Libya's civil war?

What we are doing IS right considering we are helping stop that madman Gandolfalphi (sure lets say u spell it like that), but do the rebels really want our help? What happens if the rebels win? Then lets say we need to leave troops there to keep the peace. Now we have to send troops there for 10 years??? Maybe im freaking out a little but is this the right thing?????