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The core problem here is that gigawatt is a unit of power, not of energy. A gigawatt is a lot of power, equivalent to that produced by a large electric power plant, but without knowing how much total energy is also required it's somewhat of a useless figure. Since 1.21 gigawatts over, say, a nanosecond isn't much total energy.

If we hypothesize that the time machine doesn't require much total energy and merely has some unusual requirement for a very short high power pulse then potentially lightning could be used as a source of power.

However, it's overstating things to say that generating 1.21 gigawatts is difficult, if all you need is a short pulse then it's not that hard to do with a bank of capacitors or with a tesla coil.

In short, it's a bit of tech babble that doesn't make much sense though is still technically correct.