Do we know whether the trolls have serious problems when they don't sleep in sopor slime (i.e. on the meteor)? Is sopor required due to Alternia's blood-bathed psychic climate, or because of something innate in trolls themselves?

Sopor Slime is to help prevent nightmares or to possibly protect them from the powers of chucklevoodoo.  We aren’t entirely sure but there shouldn’t be any real negative consequences. 

~Mod T