On a sunny day (Wed, 31 May 2017 15:57:39 -0700) it happened John Larkin wrote in :
Surface size depends on number of turns, current, frequency, do you need some core material?, board surface outside needs some cover (moisture in air high relative humidity) else it is just a big capacitor to air, would not trust it at 18 kV for a microsecond. You would need to cover it with several mm of some isolating stuff, not just 'solder screen'. Yes I have read that paper, not much new we did not know.
Go optical.