How long should I run my engine to charge the battery back up after a jump start

The battery should be fully re-charged using an appropriate battery charger. The vehicles alternator is not a battery charger - it’s purpose is to ‘maintain’ the battery charge.. However it will eventually charge the battery but no one can determine the amount of time needed to do so - idle rpms typically doesn’t produce the ideal charging voltage. The alternator can actually be damaged by utilizing these practices!