How to generate a short (µs) high power pulse
Your requirements are conflicting.  You say 1 A at 3 kV for no longer than 10 &micro;s, but then say you need about 30 mJ, which is 1 A at 3 kV for 10 &micro;s.  It seems there is very little wiggle room.

My first reaction is to use a car ignition coil.  They can certainly put out 3 kV for short periods of time, and the total energy is nicely limited by what is stored in the magnetic field before the primary is shut off.  If you really care most about delivered energy, then this will work well.

However, getting a square pulse at a controlled voltage and time will be more difficult.  If you are willing to waste most of the energy, then a 3 kV clamp would work.  You adjust the energy so that the time at the 3 kV clamp limit is the 10 &micro;s you want.  Possibly multiple ignition coils will need to be in parallel.