Fast switching high voltage relay controlled by an arduino

So I'm making a coil gun and I have a capacitor bank for it. Right now it only goes up to 320 volts but that will almost certainly go up higher later. I have the arduino controlling when the capacitors discharge into a coil. The arduino detects a button press and then turns on a pin which lets current flow though a make shift relay I made. Playing with the timing I found that 4 milliseconds is a good discharge time for my setup.

My "make shift relay" consist of two transistors. One transistor is a big 60A 600v transistor that requires 8 volts on it's gate or more to properly switch (I use a 9 volt battery). It switches in a matter of nanoseconds. The other is a much smaller transistor that can control weather the 9 volt lets current though to the larger transistor's gate; this transistor is controlled by the arduino and switches about 3 times slower than the big one but still in the order of small nanoseconds. So effectively what I have is a relay that switches very quickly (quicker than I can measure or delay on the arduino) and handles some pretty high voltages.

While this is great and all I'd like something more compact. Requiring a battery in my circuit is annoying. Because I need rather fine control of timing I'd like to keep the switching time on the order of nano seconds but also allow even higher voltages than 600. I don't think I will ever go over a 1400 volts (that's a rather padded estimate too!) so the relay doesn't need to handle more than that.

I have found rleays like the following:
If you look at the datasheet though it says it has a switching times of 10 to 5 milliseconds! This is too high for my application.

Is there some kind of relay I could buy that would eliminate this circuit? Preferably the battery as well.

You can eliminate the battery with a simple voltage doubler feeding into a capacitor.

A transistor that's bigger than a relay? I'd say that was a feature on a coil gun, not a problem.

I'm using an arduino due so I'd need more than double to properly operate my larger transistor. Could I just run them in series or do they make other higher voltage step up circuits? Also how can I ensure the switching times are still in the nanoseconds with these circuits?

But ya if I can eliminate the dc battery and the other transistor they I think just having the one transistor would be great!