Super Saiyan 2 is the succesor to the original Super Saiyan form which makes it Dragon Ball GT debut in the episode "The Source of Rilldo's Power"
Super Saiyan 2 has an extended aura with a higher pulsing frequency than the original form. It also has longer rigid hair that extends upward. Also, the form presents electric sparks of energy, especially when powering up. They also may appear on a charging Super Saiyan, but this has never happened in Dragon Ball GT.
Search for the Black Star Dragon Balls Edit
Battling Rilldo, the Machine Mutant Edit
Goku uses this form once in the Dragon Ball GT series, to guard against an attack by General Rilldo
Battling Baby Edit
This form can also be seen while Goku is charging up to Super Saiyan 3 to fight Baby (with his tail restored).