According to an experienced Tesla builder I was speaking to about three weeks ago, you hammer a metal pole into the actual ground and connect a cable to that - using a domestic power-supply ground can cause unexpected, potentially dangerous or destructive, side effects.
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+1, unless you have virtually zero inductance house wiring....
It goes to chassis ground. Here's an example https://www.instructables.com/id/How-to-build-a-Tesla-Coil/ so the metal on your grounded power supply will work.