I optimized the design of the RF circuit to have better inductor and use transformer to do impedance matching. The core material can be 43. The fig shows more detail about the plan.
For imepdance matching, the resonant part impedance is 44kohm. To better take into account this value, the Q of the circuit should be first measured.
Since, sqrt(44E3/200) = 15. Therefore, the input transfomer should have turns ratio 1:15.
Reference materials:
To decide the core material you can use: https://toroids.info/
and to know how to make RF transformer, use: https://youtu.be/41q0eVpNN8k?si=fb9kXypXaEAJZAcn
After looking at the availability of the cores in Japan, and switching to iron powder cores. I came up with the modified design (attached).
The impedance matching is relatively well, from previous design. I don't want to go above 1kV for now. I don't want arcs flying.