Build up the charge in giant technobabble supercapacitors wired up to both the generators and engine with room temperature superconductors.

Storing 200TJ of Electricity for rapid discharge

Batteries store energy, and so do capacitors.

https://en.wikipedia.org/wiki/Capacitor#Energy_stored_in_a_capacitor

Conventional capacitors provide less than 360 joules per kilogram of specific energy, whereas a conventional alkaline battery has a density of 590 kJ/kg. There is an intermediate solution: Supercapacitors, which can accept and deliver charge much faster than batteries, and tolerate many more charge and discharge cycles than rechargeable batteries.

Thus, you need a set of supercapacitors to store the charge, and then discharge it when needed.

I can't figure out how a burst circuit would work as it seems like a 200TJ charge going around in a loop would burn awfully hot and destroy the circuit rapidly and also the rapid drop in Energy then reheated would damage it too.

Without using the term, you're describing a short circuit, and they're always bad. You never want that.

But you still need the supercapacitors to discharge rapidly without burning up the wires. Thus, you need superconductors.

https://en.wikipedia.org/wiki/Superconductivity

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials, called superconductors, when cooled below a characteristic critical temperature.

Thus, no heating nor destruction of your infrastructure.

But since maintaining temperatires below 30K is... difficult, you'll need high-temperature superconductors.

https://en.wikipedia.org/wiki/High-temperature_superconductivity

Whereas "ordinary" or metallic superconductors usually have transition temperatures (temperatures below which they are superconductive) below 30 K (−243.2 °C), and must be cooled using liquid helium in order to achieve superconductivity, HTS have been observed with transition temperatures as high as 138 K (−135 °C), and can be cooled to superconductivity using liquid nitrogen.

While 138K is still damned cold, it's doable. Presumably, though, since you have fusion reactors and star ships, you'll have also developed true high-temp superconductors.

Everything is in place now:

1. Fusion reactor is connected to
2. high-temp superconductors (big, fancy wires) which input electricity to
3. a huge array of supercapacitors. When that 200TJ are needed,
4. electricity flows through high-temp superconductors on the "output" side of the supercapacitors,
5. straight into your sci-fi starship drive.

Simple, really.