The power required to use the gun would be generated by a large battery back pack. The electricty from the telsa coil could be shot from barrel the barrel being made of a non conductive material with a long metal rod in the middle almost like a lightning rod. Due to the high voltage/amps the tesla coil generates and the conductivity of the water in humans the first hit would be an instant kill then nearby enemies would take a lower fraction of the damage as it jumped from person to person.
Advantages:
First hit is 1 hit kill
Damage jumps from person to person
Disadvantages:
VERY heavy makes you move slow
So much energy required only get 1 shot per round