Watts is a measure of power, not energy.

Watt is a joule per second, J/s

so if you reduce the time to Nano-Seconds, 10^-9, then you get Giga-Watts, 10^9, but your Joules, or energy, stays exactly the same.

If you want Tera-Watts, 10^12, then you need Pico-Seconds, 10^-12

All assuming you are using 1 Joule of energy, if you use 1000 Joules of energy, you can get Tera-Watts in Nano-Seconds.

So this is no mathematical surprise or mystery.

However the usefulness if impulses is another story, here's why:

You start with Position, x, measured in meters [m]

You take the derivative of Position, x, with respect to time, meaning the rate at which x changes with time,

This is Velocity, V, measured in meters/second [m/s]

Now you take the derivative of Velocity, with respect to time, meaning the rate at which V changes with time,

This is Acceleration, a, measured in meters/second^2 [m/s^2]

Then, the magic part, you take the derivative of acceleration, with respect to time, meaning the rate at which a changes with time,

This is called the "Jerk", measured in meters/second^3 [m/s^3], and a lot of interesting stuff can happen when you have action going on in the Jerk function. This is commonly looked at while designing cam-shafts for engines, because they open and close valves, with large changes in position, in tiny portions of time, as you can imagine if your engine is going 6000 rpm, that's 100 Hz for the crankshaft, which means one valve is opening AND closing 50 times a second, which means it has, say, 5 milliseconds to open, 5 milliseconds to close, and 10 milliseconds to stay closed before it opens again. So you are applying real forces, in extremely small amounts of time, and things will destroy themselves if you ask for too much to fast. The valve accelerates open, and accelerates closed, this 'rate of change of acceleration' is the impulse, or the jerk. It's the same thing we are dealing with when we use pulsed Direct Current, because the rise time (and fall time) of that current is milliseconds, or nanoseconds, and the impulse, or Jerk, or 4th derivative, is huge (or has huge effects).

What are these huge effects? consider quickly, Newtons law, that every action has an equal and opposite reaction, right, except there are some assumptions here, and the assumptions are that it is a "Point Mass" (which can never exist) and that it is a "rigid body" (which can never exist), and what is really going on, is that forces are transferred through and object at the speed of sound in the material, which you can think of as microscopic pressure waves moving through the object from atom to atom, or molecule to molecule.

SO, if you hit it, and remove your force FASTER that the speed of sound in that material, you will NOT get an equal and opposite reaction force, and hence, magic.

Just like Tesla said, Direct Current Impulses are the key to free energy.