A brief elaboration required for your problem. The application of it will be useful to get a fair idea so please provide that. Why 13.56Mhz? Any specific reason?
It use in Plasma technology
They use a 10-70 kHz power supply with Voltage range 20KV-30KV
But If use 13.56 Mhz frequency, the output voltage can be at range 1-2 KV
A brief elaboration required for your problem. The application of it will be useful to get a fair idea so please provide that. Why 13.56Mhz? Any specific reason?
1000V Pk into 50 ohms is 10KW RMS.
This is not a beginners project, just the cooling of the power stage will be a interesting and there may even be something to be said for grounded grid external anode tube as the amplifier.
Now it could be that you are running 50 ohms at a lower voltage and transforming up in the matching network at the plasma tube (Fairly typical in laser applications), in which case we need to know either the rf power required or the voltage into the 50 ohm line.
Also, what VSWR tolerance is required? Plasma tube startup usually requires very high tolerance of reflected power for a few milliseconds until the plasma is fully ionised.
Ixys/Directed Energy have some good application notes on 13.56MHz class E generators for these kinds of applications.
2kV @300W is equivalent to < 7 A so step up transformer with low primary ESR loss and low Eddy current loss is needed i.e. air coil, but will have poor coupling factor and radiate dangerous EMI to eyes. COnsider Klystron tube & Microwave transformer (MOT) 1.5kW > 1GHz with resonance arc at several kV inside oven using aluminum foil. Also dangerous. But any High Q transformer will also be low bandwidth so consider SRF in selection of magnetics. This is not a solution but other examples to learn from similar to what Dan suggested.