Wow, that is a heavy winding on the output of the welding transformer. From what little I can see, and I could be wrong, the SCR fires the mains across the welding transformer primary which is connected to the electrodes by the high current secondary, which is effectively short circuited at the weld point. The only thing limiting current is leakage inductance and series resistance of the windings and electrodes. If correct, the device is dangerous and not readily modifiable, but I am making a number of assumptions based off a photo and could well be wrong.