sacrifice

Preach it!
I believe that since he let go of Gugnir at the end of the first movie, Loki doesn't care if he lives or dies. And he would had preferred a death sentence to life imprisonment. Avenging Frigga's death and saving Thor would have been a good ending in his own eyes. Tom Hiddleston filmed the death scene thinking that Loki was going to die, because this was what the original script intended. I believe that Loki himself thought he was going to die, but his magic made him survive.