I have used a small car ignition coil, driven by a full H-Bridge at a resonant frequency of around 20kHz (at approximately 60Vpp) to produce a mini plasma speaker. The output voltage is well over 30kV before breakdown of the spark gap occurs. Pushing it to higher voltages causes breakdown of the plastic casing, a phenomena it survived for well over a half an hour before I noticed the small purple streamers pouring out the bottom and onto my bench.
TV flyback transformers can also be operated as resonant rise systems to produce high voltages.
So non air core systems are definately around but I have no knowledge of a system that operates in the hundreds of kilovolts range that is not air-cored.
David